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Apparatus and methods for quantum key distribution — Massachusetts Institute Of Technology (US10158481B2)

ABSTRACT

Abstract

Systems, apparatus, and methods using an integrated photonic chip capable of operating at rates higher than a Gigahertz for quantum key distribution are disclosed. The system includes two identical transmitter chips and one receiver chip. The transmitter chips encode photonic qubits by modulating phase-randomized attenuated laser light within two early or late time-bins. Each transmitter chip can produce a single-photon pulse either in one of the two time-bins or as a superposition of the two time-bins with or without any phase difference. The pulse modulation is achieved using ring resonators, and the phase difference between the two time-bins is obtained using thermo-optic phase shifters and/or time delay elements. The receiver chip employs either homodyne detection or heterodyne detection to perform Bell measurements.

Description

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a bypass continuation application of International Application No. PCT/US2016/034639, filed May 27, 2016, and entitled “Apparatus and Methods for Quantum Key Distribution,” which claims the priority benefit of U.S. Application No. 62/167,515, filed May 28, 2015, and entitled “MEASUREMENT-DEVICE-INDEPENDENT QUANTUM KEY DISTRIBUTION BASED ON PHOTONIC INTEGRATED CIRCUITS.” Each of these applications is hereby incorporated herein by reference in its entirety.

BACKGROUND

Measurement-device-independent quantum key distribution (MDI-QKD) is a method of distributing secret keys that can be immune to detector side channel attacks. The scheme includes at least two sending chips (usually referred to as Alice and Bob), which encode signals in single photons through either time-bin encoding or polarization encoding, as well as a receiver chip (usually referred to as Charlie), which measures the signals in the maximally-entangled Bell basis.

To implement the MDI-QKD protocol, Alice and Bob randomly and independently prepare photon signals in one of the four BB84 states: |0

, |1

in the Z-basis, or |+

, |−

in the X-basis. These photons are then sent via the quantum channel to Charlie who is instructed to perform a Bell state measurement. The four Bell states are summarized in Table 1. Alice and Bob can also apply the decoy state protocol to their photon signals to estimate the gain (i.e., the probability that Alice and Bob's signals yield a successful Bell measurement) and the quantum bit error rate (QBER, the rate of false successful Bell measurements due to single photon contributions).

Charlie announces whether or not his Bell state measurements are successful along with the Bell state obtained. Alice and Bob retain only the data that correspond to successful Bell state measurements and discard the rest. For the data they retained, Alice and Bob each reveal their basis choices over the public channel and retain only those instances where they chose the same basis. Bob then flips parts of his data to directly correlate his measurements with those of Alice. Finally, Alice and Bob apply error correction and privacy amplification to establish identical secret keys.

TABLE 1

The four Bell states and possible bit flips

to directly correlate Alice and Bob's bits

Bell state reported by Charlie

|ψ − > =

|ψ + > =

|φ − > =

|φ + > =

Basis chosen by

(|01> −

(|01> +

(|00> −

(|00> +

Alice and Bob

|10>)/{square root over (2)}

|10>)/{square root over (2)}

|11>)/{square root over (2)}

|11>)/{square root over (2)}

Z basis

Flip

Flip

—

—

X basis

Flip

—

Flip

—

The rate of secret key generation (in bits per second, per Bell state), in the limit of large number of signals exchanged for each Bell state |k>ε{|φ + >, |φ − >, |ψ + >, |ψ − >} is

R

 k 〉

≥

r ⁢

{

Q ⁢

1 , 1

z ,

 k 〉

⁡

[

1 -

H

2

⁡

(

e

⁢

1 , 1

x ,

 k 〉

)

]

-

Q ⁢

vsa , vsb

z ,

 k 〉

⁢

fe ⁡

(

E ⁢

vsa , vsb

z ,

 k 〉

)

⁢

(

H

2

⁢

vsa , vsb

z ,

 k 〉

)

}

( 1 )

where r is the repetition rate in Hz

Q ⁢

1 , 1

z ,

 k 〉

⁢

⁢ and ⁢

⁢

1 , 1

x ,

 k 〉

are the gain and QBER due to single photon signals;

Q ⁢

vsa , vsb

z ,

❘ k

〉

⁢

⁢ and ⁢

⁢

e ⁢

1 , 1

x ,

❘ k

〉

are the gain and QBER for signals emitted by Alice and Bob with mean photon number V sa and V sb , respectively; fe≥1 is the error correction inefficiency; H 2 (x)=−x log 2 x−(1−x)log 2 (1−x) is the binary entropy function. The equation for the secret key generation rate assumes that Alice and Bob use the Z-basis for key generation and only use the X-basis for security checks. The quantities

Q ⁢

vsa , vsb

z ,

❘ k

〉

⁢

⁢ and ⁢

⁢ E ⁢

vsa , vsb

z ,

❘ k

〉

can be measured directly as the MDI-QKD system is run, while the quantities

Q ⁢

1 , 1

z ,

❘ k

〉

⁢

⁢ and ⁢

⁢

e ⁢

1 , 1

x ,

❘ k

〉

can be measured using the decoy-state protocol.

A more detailed description of the protocol with two decoy states is as follows. The protocol can be performed with more than two decoy states, but in practice it can be desirable to have as few decoy states as possible. The first four steps of the protocol—state preparation, state distribution, Bell state measurement, and sifting—are repeated N times until the successful sifting conditions are met.

Step 1: State preparation. Alice and Bob randomly and independently choose an intensity for their photon signals: V a ∈{V sa , V da,1 , V da,2 } for Alice and V b ∈{V sb , V db,1 , V db,2 } for Bob. V sa (V sb ) corresponds to the intensity of the signal state for Alice (Bob) and V da,i , (V db,i ) for 1,2 corresponds to the intensity of the decoy states for Alice (Bob). The two decoy states typically have weaker intensities than the signal state. Alice and Bob then randomly and independently choose a basis B i ∈{Z,X}, and a bit r i ∈{0,1} with probability of P vi,ri /2 for i=a (Alice) or b (Bob). They then prepare a quantum signal of intensity v i encoding qubit |r i > in basis B i for both i=a or b.

Step 2: State distribution. Alice and Bob send their prepared quantum signals to Charlie via the quantum channel.

Step 3: Bell state measurement. If Charlie is not an adversary to Alice and Bob, he then measures the quantum signals received in the maximally-entangled Bell basis. Charlie then announces whether or not his measurement is successful, including the Bell state obtained.

Step 4: Sifting. If Charlie announces a successful Bell measurement, Alice and Bob then announce their intensity and basis choices. For each Bell state |k>∈{|φ + >, |φ − >, |ψ + >, |ψ − >}, Alice and Bob bin their data in

Z ⁢

va , vb

❘ k

〉

⁢

⁢ and ⁢

</mspac

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a bypass continuation application of International Application No. PCT/US2016/034639, filed May 27, 2016, and entitled “Apparatus and Methods for Quantum Key Distribution,” which claims the priority benefit of U.S. Application No. 62/167,515, filed May 28, 2015, and entitled “MEASUREMENT-DEVICE-INDEPENDENT QUANTUM KEY DISTRIBUTION BASED ON PHOTONIC INTEGRATED CIRCUITS.” Each of these applications is hereby incorporated herein by reference in its entirety.

BACKGROUND

Measurement-device-independent quantum key distribution (MDI-QKD) is a method of distributing secret keys that can be immune to detector side channel attacks. The scheme includes at least two sending chips (usually referred to as Alice and Bob), which encode signals in single photons through either time-bin encoding or polarization encoding, as well as a receiver chip (usually referred to as Charlie), which measures the signals in the maximally-entangled Bell basis.

To implement the MDI-QKD protocol, Alice and Bob randomly and independently prepare photon signals in one of the four BB84 states: |0

, |1

in the Z-basis, or |+

, |−

in the X-basis. These photons are then sent via the quantum channel to Charlie who is instructed to perform a Bell state measurement. The four Bell states are summarized in Table 1. Alice and Bob can also apply the decoy state protocol to their photon signals to estimate the gain (i.e., the probability that Alice and Bob&#39;s signals yield a successful Bell measurement) and the quantum bit error rate (QBER, the rate of false successful Bell measurements due to single photon contributions).

Charlie announces whether or not his Bell state measurements are successful along with the Bell state obtained. Alice and Bob retain only the data that correspond to successful Bell state measurements and discard the rest. For the data they retained, Alice and Bob each reveal their basis choices over the public channel and retain only those instances where they chose the same basis. Bob then flips parts of his data to directly correlate his measurements with those of Alice. Finally, Alice and Bob apply error correction and privacy amplification to establish identical secret keys.

TABLE 1

The four Bell states and possible bit flips

to directly correlate Alice and Bob&#39;s bits

Bell state reported by Charlie

|ψ − &gt; =

|ψ + &gt; =

|φ − &gt; =

|φ + &gt; =

Basis chosen by

(|01&gt; −

(|01&gt; +

(|00&gt; −

(|00&gt; +

Alice and Bob

|10&gt;)/{square root over (2)}

|10&gt;)/{square root over (2)}

|11&gt;)/{square root over (2)}

|11&gt;)/{square root over (2)}

Z basis

Flip

Flip

—

—

X basis

Flip

—

Flip

—

The rate of secret key generation (in bits per second, per Bell state), in the limit of large number of signals exchanged for each Bell state |k&gt;ε{|φ + &gt;, |φ − &gt;, |ψ + &gt;, |ψ − &gt;} is

R

 k 〉

≥

r ⁢

{

Q ⁢

1 , 1

z ,

 k 〉

⁡

[

1 -

H

2

⁡

(

e

⁢

1 , 1

x ,

 k 〉

)

]

-

Q ⁢

vsa , vsb

z ,

 k 〉

⁢

fe ⁡

(

E ⁢

vsa , vsb

z ,

 k 〉

)

⁢

(

H

2

⁢

vsa , vsb

z ,

 k 〉

)

}

( 1 )

where r is the repetition rate in Hz

Q ⁢

1 , 1

z ,

 k 〉

⁢

⁢ and ⁢

⁢

1 , 1

x ,

 k 〉

are the gain and QBER due to single photon signals;

Q ⁢

vsa , vsb

z ,

❘ k

〉

⁢

⁢ and ⁢

⁢

e ⁢

1 , 1

x ,

❘ k

〉

are the gain and QBER for signals emitted by Alice and Bob with mean photon number V sa and V sb , respectively; fe≥1 is the error correction inefficiency; H 2 (x)=−x log 2 x−(1−x)log 2 (1−x) is the binary entropy function. The equation for the secret key generation rate assumes that Alice and Bob use the Z-basis for key generation and only use the X-basis for security checks. The quantities

Q ⁢

vsa , vsb

z ,

❘ k

〉

⁢

⁢ and ⁢

⁢ E ⁢

vsa , vsb

z ,

❘ k

〉

can be measured directly as the MDI-QKD system is run, while the quantities

Q ⁢

1 , 1

z ,

❘ k

〉

⁢

⁢ and ⁢

⁢

e ⁢

1 , 1

x ,

❘ k

〉

can be measured using the decoy-state protocol.

A more detailed description of the protocol with two decoy states is as follows. The protocol can be performed with more than two decoy states, but in practice it can be desirable to have as few decoy states as possible. The first four steps of the protocol—state preparation, state distribution, Bell state measurement, and sifting—are repeated N times until the successful sifting conditions are met.

Step 1: State preparation. Alice and Bob randomly and independently choose an intensity for their photon signals: V a ∈{V sa , V da,1 , V da,2 } for Alice and V b ∈{V sb , V db,1 , V db,2 } for Bob. V sa (V sb ) corresponds to the intensity of the signal state for Alice (Bob) and V da,i , (V db,i ) for 1,2 corresponds to the intensity of the decoy states for Alice (Bob). The two decoy states typically have weaker intensities than the signal state. Alice and Bob then randomly and independently choose a basis B i ∈{Z,X}, and a bit r i ∈{0,1} with probability of P vi,ri /2 for i=a (Alice) or b (Bob). They then prepare a quantum signal of intensity v i encoding qubit |r i &gt; in basis B i for both i=a or b.

Step 2: State distribution. Alice and Bob send their prepared quantum signals to Charlie via the quantum channel.

Step 3: Bell state measurement. If Charlie is not an adversary to Alice and Bob, he then measures the quantum signals received in the maximally-entangled Bell basis. Charlie then announces whether or not his measurement is successful, including the Bell state obtained.

Step 4: Sifting. If Charlie announces a successful Bell measurement, Alice and Bob then announce their intensity and basis choices. For each Bell state |k&gt;∈{|φ + &gt;, |φ − &gt;, |ψ + &gt;, |ψ − &gt;}, Alice and Bob bin their data in

Z ⁢

va , vb

❘ k

〉

⁢

⁢ and ⁢

⁢ X ⁢

va , vb

❘ k

〉

according to their intensity and basis choices. The first four steps of the protocol are repeated until

Z ⁢

va , vb

❘ k

〉

❘

≥

N ⁢

va , vb

❘ k

〉

⁢

⁢ and

⁢

❘

X ⁢

va , vb

❘ k

〉

❘

≥

M ⁢

va , vb

❘ k

〉

,

where

N ⁢

va , vb

❘ k

〉

⁢

⁢ and ⁢

⁢ M ⁢

va , vb

❘ k

〉

are chosen such that large enough statistical samples for the post-processing steps are available. Bob then corrects his data by flipping parts of his bits according to Table 1 so that his data are directly correlated with Alice&#39;s data.

Step 5: Post-processing. Post-processing is performed independently for each Bell state |k&gt;∈{|φ + &gt;, |φ − &gt;, |ψ + &gt;, |ψ − &gt;}. This step can include several sub-steps, including:

Step 5a: Parameter estimation. Alice and Bob choose a random subset of

Z ⁢

vsa , vsb

❘ k

〉

and store the respective bit strings Z |k&gt; and Z |k&gt; ′, respectively. They then use the remaining bits R |k&gt; of

Z ⁢

vsa , vsb

❘ k

〉

to compute the QBERs

E ⁢

vsa , vsb

❘ k

〉

=

1



R ❘ k

〉



⁢

Σ l

⁢

r l

⊕

r l ′

,

where r l ′ are Bob&#39;s bits. If

E ⁢

vsa , vsb

❘ k

〉

is higher than the QBER tolerance, Alice and Bob then abort any subsequent steps for this particular |k&gt;. The whole protocol only aborts if

E ⁢

vsa , vsb

❘ k

〉

is higher than the allowed QBER tolerance for all four choices of |k&gt;. If

E ⁢

vsa , vsb

❘ k

〉

is within the allowed QBER tolerance, then Alice and Bob use

Z ⁢

vsa , vsb

❘ k

〉

⁢

⁢ and ⁢

⁢ X ⁢

vsa , vsb

❘ k

〉

to estimate the values of

Q ⁢

1 , 1

z ,

❘ k

〉

,

e ⁢

1 , 1

x ,

❘ k

〉

⁢

⁢ and ⁢

⁢ Q ⁢

vsa , vsb

z ,

❘ k

〉

for this particular |k&gt;).

Step 5b: Error correction. If this particular |k&gt; passes the parameter estimation step, Bob obtains an estimate {circumflex over (Z)} |k&gt; of Z |k&gt; using an information reconciliation scheme, which requires Alice to leak some information of Z |k&gt; . Alice then computes a hash of Z |k&gt; using a random universal hash function, which is sent to Bob along with the value of the hash. Bob then computes the hash of {circumflex over (Z)} |k&gt; and aborts the protocol for this particular |k&gt; if the hash of {circumflex over (Z)} |k&gt; disagrees with the hash of Z |k&gt; .

Step 5c: Privacy amplification. If this particular |k&gt; passes the error correction step, Alice and Bob apply another random universal 2 hash function to Z |k&gt; and {circumflex over (Z)} |k&gt; to obtain the (shared) secret key, respectively.

Currently, the above MDI-QKD protocol is implemented with bulk optical components. One drawback of bulk optical systems is that they usually use manual assembly of many parts (e.g., mirrors, phase modulators, lenses, etc.). It can also be challenging to make bulk optical systems mechanically stable to guard against component misalignment due to vibration and temperature variations.

SUMMARY

Embodiments of the present invention include apparatus, systems, and methods for quantum key distribution. In one example, an apparatus for distributing a quantum key includes an input waveguide, a first ring resonator, a second ring resonator, and an output waveguide. The first ring resonator is evanescently coupled to the input waveguide to receive a first pulse of light via the input waveguide. The second ring resonator is evanescently coupled to the input waveguide to receive a second pulse of light via the input waveguide. The output waveguide is evanescently coupled to the first ring resonator and the second ring resonator to receive the first pulse of light from the first ring resonator and the second pulse of light from the second ring resonator. The apparatus also includes at least one modulator, operably coupled to at least one of the first ring resonator, the second ring resonator, and the output waveguide, to delay at least one of the first pulse of light or the second pulse of light so as to generate a photonic qubit in an X-basis or a Z-basis

In another example, a method of distributing a quantum key is disclosed. The method uses a transmitter including an input waveguide, a first ring resonator evanescently coupled to the input waveguide, a second ring resonator evanescently coupled to the input waveguide, and an output waveguide evanescently coupled to the first ring resonator and the second ring resonator. The method includes selecting one of an X-basis and a Z-basis for distributing the quantum key. In response to selection of the Z-basis, at least one of the following two steps is performed: delaying a first pulse of light propagating in the first ring resonator to create the quantum key in a |0

state in the Z-basis; or delaying the first pulse of light propagating in the first ring resonator to create the quantum key in a |1

state in the Z-basis. In response to selection of the X-basis, at least one of the following two steps is performed: delaying the first pulse of light propagating in the first ring resonator with respect to a second pulse of light propagating in the second ring resonator to constructively interfere the first pulse of light with the second pulse of light so as to create the quantum key in an |+

state in the Z-basis, or delaying the first pulse of light propagating in the first ring resonator with respect to the second pulse of light propagating in the second ring resonator to destructively interfere the first pulse of light with the second pulse of light so as to create the quantum key in an |−

state in the Z-basis.

In yet another example, an apparatus for measurement-device-independent quantum key distribution includes an input waveguide to guide an input pulse of light and an output waveguide to deliver quantum keys. The output waveguide includes a receiving section, evanescently coupled to the input waveguide, to receive the input pulse of light, a propagation section to guide the input pulse of light received by the input section, and a loop section having at least one segment evanescently coupled to the propagation section so as to couple at least a portion of the input pulse of light back to the propagation section. The apparatus also includes a first ring resonator evanescently coupled to the propagation section of the output waveguide and a first modulator, operably coupled to the first ring resonator, to delay a first pulse of light propagating in the first ring resonator. The apparatus further includes a second ring resonator evanescently coupled to the propagation section of the output waveguide and a second modulator operably coupled to the second ring resonator and having a first modulation mode and a second modulation mode. In the first modulation mode, the second modulator delays a second pulse of light propagating in the second ring resonator so as to cause the first pulse of light to constructively interfere with the second pulse of light. In the second modulation mode, the second modulator delays the second pulse of light so as to cause the first pulse of light to destructively interfere with the second pulse of light.

It should be appreciated that all combinations of the foregoing concepts and additional concepts discussed in greater detail below (provided such concepts are not mutually inconsistent) are contemplated as being part of the inventive subject matter disclosed herein. In particular, all combinations of claimed subject matter appearing at the end of this disclosure are contemplated as being part of the inventive subject matter disclosed herein. It should also be appreciated that terminology explicitly employed herein that also may appear in any disclosure incorporated by reference should be accorded a meaning most consistent with the particular concepts disclosed herein.

BRIEF DESCRIPTION OF THE DRAWINGS

The skilled artisan will understand that the drawings primarily are for illustrative purposes and are not intended to limit the scope of the inventive subject matter described herein. The drawings are not necessarily to scale; in some instances, various aspects of the inventive subject matter disclosed herein may be shown exaggerated or enlarged in the drawings to facilitate an understanding of different features. In the drawings, like reference characters generally refer to like features (e.g., functionally similar and/or structurally similar elements).

FIG. 1A shows a schematic of a photonic integrated transmitter including ring resonators for quantum key distribution.

FIG. 1B illustrates the generation of qubits using the transmitter shown in FIG. 1A .

FIG. 2 shows a schematic of a photonic integrated receiver that can be used with the transmitter shown in FIG. 1A .

FIG. 3 shows a schematic of a photonic integrated transmitter including ring resonators and a phase shifter to generate qubits for quantum key distribution.

FIG. 4 shows a schematic of a completed layout of the transmitter shown in FIG. 1A and FIG. 3 .

FIG. 5 shows a schematic of a hair-clip double-pass configuration of ring resonators that can be used for quantum key distribution.

FIG. 6 shows a schematic of a QKD transmitter including unbalanced interferometers.

FIG. 7 shows a schematic of a QKD transmitter

FIG. 8 shows a schematic of a completed layout of the transmitter shown in FIG. 7 .

FIG. 9 illustrates a method of generating and distributing quantum keys.

FIG. 10 shows a transmitter that can be used in continuous variable QKD.

FIG. 11 shows a receiver that can be used in continuous variable QKD.

FIGS. 12A and 12B show schematics of homodynes and heterodyne detections systems, respectively, that can be used in the receiver shown in FIG. 11 .

FIG. 13A shows a schematic of a system for cavity-integrated QKD.

FIG. 13B shows transmission of a ring cavity that can be used in the system shown in FIG. 13A .

FIG. 13C shows photocurrent responses of detectors that can be used in the system shown in FIG. 13A .

FIG. 14 shows a schematic of a cavity-integrated QKD transmitter for wavelength-division-multiplexing (WDM) operation.

FIG. 15 shows experimental results of a cavity-integrated QKD system.

DETAILED DESCRIPTION

Overview

To address the drawbacks of bulk optical systems in implementing QKD protocols, systems, apparatus, and methods described herein employ a compact approach using an integrated photonic chip that is capable of operating at rates higher than a Gigahertz. The compact MDI-QKD system is based on photonic integrated circuits (PICs). The system includes three different chips: two identical transmitter chips and one receiver chip. Each of the two parties (Alice and Bob) who are interested in generating shared secret keys operates a single transmitter chip. An untrusted party (Charlie) operates the receiver chip that measures the photonic quantum information signals (quantum bits, or qubits) generated by the two transmitter chips.

In the time-bin encoding scheme, the transmitter chips encode photonic qubits by modulating phase-randomized attenuated laser light within two early or late time-bins. Each transmitter chip can produce a single-photon pulse either in one of the two time-bins or as a superposition of the two time-bins with or without any phase difference. The pulse modulation is achieved using ring resonators, and the phase difference between the two time-bins is obtained using thermo-optic phase shifters and/or time delay elements.

In the polarization encoding scheme, the transmitter chips encode information in the polarization of the phase-randomized attenuated laser light. The chips generate light pulses polarized horizontally, vertically, along +45°, or along −45°. Similar to the time-bin encoding scheme, pulse modulation is provided by ring resonators. Polarization control is obtained by using on-chip polarizing beam splitters or by using polarization rotators based on Berry&#39;s phase.

The transmitter chips described herein can generate arbitrary single photonic qubit state. Therefore, these transmitter chips can also be used in other quantum cryptography protocols that involve preparing and sending photonic qubit states, e.g. the BB84 protocol, the coherent-one-way protocol, etc.

When the two photonic qubits arrive at the untrusted party, the receiver chip measures the two qubits in the maximally entangled Bell basis. For the time-bin encoding, The Bell basis measurement is performed by mixing the two qubits using a 50:50 beam splitter and then detecting the output signals using two single photon detectors. For polarization encoding, the Bell measurement is achieved by mixing the two qubits using a 50:50 beam splitter followed by a polarizing beam splitter in each of the output ports and then detecting the output signals using four single photon detectors. Suitable on-chip single photon detectors include superconducting nanowire single-photon detectors.

The use of PIC in QKD systems offers several important advantages over the traditional bulk optic implementations. First, chip-level integration of all optical components allows miniaturization and economical production of QKD systems. Second, chip-level integration can also augment traditional CMOS microprocessors and other microchips with unconditionally secure communication capabilities.

Transmitters with Ring Resonators for Quantum Key Distribution

FIG. 1A shows a schematic of a transmitter 100 including ring resonators to modulate pulses of light for quantum key distribution. The apparatus 100 includes two ring resonators: a first ring resonator 120 a and a second ring resonator 120 b (collectively referred to as ring resonators 120 ). The first ring resonator 120 a is evanescently coupled to a first input waveguide 110 a . A first detector 130 a is coupled to the end of the first input waveguide 110 a to monitor the intensity of the input light propagating in the first input waveguide 110 a . Similarly, the second ring resonator 110 b is evanescently coupled to a second input waveguide 110 b , which is further coupled to a second detector 130 b at the end. A common output waveguide 140 is evanescently coupled to the two ring resonators 120 to guide light coupled out from the ring resonators 120 . The output light then can be used for possible quantum keys.

Each ring resonator 120 a/b also includes a corresponding modulator 125 a/b , which can perform several functions. In one example, the modulators

125 a and 125 b (collectively referred to as modulators 125 ) can apply a time delay to light pulses propagating in the ring resonators 120 . To this end, the modulators 125 can change the optical path length of the ring resonators 120 by changing the refractive index of the ring resonators 120 via the thermal-optical effect, electro-optical effect, or any other method known in the art. In another example, the modulators 125 can control the timing of light pulses that are delivered by the ring resonators 120 . To this end, the ring resonators 120 can trap light (i.e., without transmitting the light to the output waveguide 140 ) without modulation. Upon modulation, the ring resonators 120 can change their resonance conditions and transmit light to the output waveguide 140 . In this case, by controlling the timing of the modulation, the timing of the outputs from the ring resonators 120 can also be adjusted.

FIG. 1B illustrates the operation of the apparatus 100 to generate qubits for quantum key distributions. The apparatus 100 can generate four types of qubits: |0&gt; and |1&gt; states in Z-basis and |+&gt; and |−&gt; states in X-basis. As shown in FIG. 1B , photonic qubit states in time-bin encoding “e” and “l” correspond to early and late time bins, respectively. Solid lines correspond to a single photon pulse in the time bin. Dashed lines correspond to a single photon superposition between the two time bins. The phase difference between pulses in the two time bins is indicated by Δφ.

To prepare states in the Z-basis, a pulse can be modulated in the early time bin or in the late time bin (states |0&gt; or |1&gt;, respectively) using one of the ring resonators 120 . In other words, within a specified time slot divided into two bins (i.e., an early bin and a late bin), modulating the ring resonator

120 a or 120 b to couple out one photon to the output waveguide 140 during the early bin (e.g., within the first half of the time slot) yields a qubit in the 10&gt; state. On the other hand, modulating the ring resonator

120 a or 120 b to couple out one photon to the output waveguide 140 during the late bin yields a qubit in |1&gt; state.

To prepare states in the X-basis, both ring resonators

120 a and 120 b can be used. To prepare the |+&gt; state, a pulse can be created in the early time bin using one resonator

120 a or 120 b and another pulse in the late time bin using the same resonator

120 a or 120 b . The difference between the two time bins can be integer multiples of the light oscillation period in the selected ring resonator

120 a or 120 b . To prepare the |−&gt; state, a pulse can be created in the early time-bin using one resonator (e.g., 120 a ) and another pulse in the late time-bin using the other resonator (e.g., 120 b ) such that the two pulses from the two ring resonators 120 a/b destructively interfere with each other.

Alternatively, |+&gt; and |−&gt; qubits in the X-basis can be created using two ring resonators 120 . To create a qubit in |+&gt; state, the two pulses from the two ring resonators 120 can constructively interfere with each other. To create a qubit in |−&gt; state, the two pulses from the two ring resonators 120 can destructively interfere with each other.

To facilitate the operation of the apparatus 100 , a calibration step can be performed before qubit generation for quantum key distribution. The calibration can be carried out by tuning the laser wavelength such that the outputs from the ring resonators

120 a and 120 b destructively interfere with each other. One user, e.g. Alice, can then broadcast the wavelength she uses to Bob.

The apparatus 100 shown in FIG. 1A uses two ring resonators 120 for illustrative purposes. In practice, the apparatus 100 can include more than two ring resonators so as to further increase the flexibility of quantum key distribution. For example, the apparatus 100 can include four ring resonators for each transmitter used by Alice and Bob. Each time Alice and Bob create a qubit, they can choose to use two of the ring resonators. Alice or Bob can then broadcast which two ring resonators are to be used. This can ensure that both Alice and Bob maintain indistinguishability between Alice&#39;s signals and Bob&#39;s signals.

The entire apparatus 100 can be fabricated in a single chip so as to decrease the size and improve the miniaturization and compactness. Various thin-film based platforms can be employed to fabricate the apparatus 100 . In one example, the apparatus 100 can be fabricated on a silicon-on-insulation (SOI) platform. In another example, the apparatus 100 can be fabricated on a lithium niobate platform (also referred to as lithium niobate-on-insulator platform). In yet another example, the apparatus 100 can be fabricated on an aluminum nitride (AlN) platform. In yet another example, the apparatus 100 can be fabricated on a silicon nitride.

The input waveguides 110 a and 110 b in the apparatus 100 receive input light to generate potential quantum keys. In one example, the two input waveguides

110 a and 110 b can be coupled to a common light source that delivers the input light. In another example, the two input waveguides

110 a and 110 b can receive input light from separate light sources.

In operation, the <figure-callout id="110a" label="input waveguides" file

CLAIMS

Claims ( 20 )

The invention claimed is:

1. An apparatus for distributing a quantum key, the apparatus comprising:

an input waveguide;

a first ring resonator, evanescently coupled to the input waveguide, to receive a first pulse of light via the input waveguide;

a second ring resonator, evanescently coupled to the input waveguide, to receive a second pulse of light via the input waveguide;

an output waveguide, evanescently coupled to the first ring resonator and the second ring resonator, to receive the first pulse of light from the first ring resonator and the second pulse of light from the second ring resonator; and

at least one modulator, operably coupled to at least one of the first ring resonator, the second ring resonator, and the output waveguide, to delay at least one of the first pulse of light or the second pulse of light so as to generate a photonic qubit in an X-basis or a Z-basis,

wherein the first ring resonator is configured to emit a third pulse of light and the at least one modulator is configured to delay the third pulse of light with respect to the first pulse of light so as to form a |+

state in the X-basis.

2. The apparatus of claim 1 , wherein the at least one modulator is configured to delay third pulse of light with respect to the first pulse of light by a period equal to an integer multiple of an oscillation period of a carrier of the first pulse of light.

3. The apparatus of claim 1 , wherein the at least one modulator is configured to delay the first pulse of light with respect to the second pulse of light so as to form the photonic qubit in a |−

state in the X-basis.

4. The apparatus of claim 1 , wherein the at least one modulator is configured to delay the first pulse of light with respect to the second pulse of light by a period selected to create a π phase difference between the first pulse of light and the second pulse of light.

5. The apparatus of claim 1 , wherein the at least one modulator is configured to delay the first pulse so as to form the photonic qubit in a state in the Z-basis.

6. The apparatus of claim 1 , wherein the at least one modulator comprises a phase shifter, operably coupled to the output waveguide, to vary a phase difference between the first pulse of light and the second pulse of light.

7. The apparatus of claim 1 , wherein the output waveguide comprises:

a receiving section;

a propagation section to guide the first light received by the receiving section; and

a loop section having at least one segment evanescently coupled to the propagation section so as to couple at least a portion of the first pulse of light back to the propagation section,

wherein at least one of the first ring resonator and the second ring resonator is evanescently coupled to the propagation section of the input waveguide.

8. The apparatus of claim 1 , further comprising:

a detector, optically coupled to the input waveguide, to monitor an intensity of the first pulse of light.

9. The apparatus of claim 1 , further comprising:

a phase randomized light source, in optical communication with the input waveguide, to provide the first pulse of light and the second pulse of light.

10. The apparatus of claim 1 , further comprising:

an attenuator, operably coupled to the output waveguide, to attenuate an intensity of at least one of the first pulse of light and the second pulse of light so as to create a decoy state.

11. The apparatus of claim 1 , further comprising:

a phase shifter, operably coupled to the output waveguide between the first ring resonator module and the second resonator module, to apply a phase shift to the second pulse of light.

12. An apparatus for distributing a quantum key, the apparatus comprising:

an input waveguide;

a first ring resonator, evanescently coupled to the input waveguide, to receive a first pulse of light via the input waveguide;

a second ring resonator, evanescently coupled to the input waveguide, to receive a second pulse of light via the input waveguide;

an output waveguide, evanescently coupled to the first ring resonator and the second ring resonator, to receive the first pulse of light from the first ring resonator and the second pulse of light from the second ring resonator;

at least one modulator, operably coupled to at least one of the first ring resonator, the second ring resonator, and the output waveguide, to delay at least one of the first pulse of light or the second pulse of light so as to generate a photonic qubit in an X-basis or a Z-basis; and

a photonic integrated receiver to detect the photonic qubit, wherein the photonic integrated receiver comprises:

a substrate;

a coupler fabricated in the substrate and comprising:

a first input waveguide to receive qubits provided by a first party;

a second input waveguide to receive qubits provided by a second party;

a first output waveguide; and

a second output waveguide;

a first detector coupled to the first output waveguide; and

a second detector coupled to the second output waveguide.

13. A method of distributing a quantum key using a transmitter comprising an input waveguide, a first ring resonator evanescently coupled to the input waveguide, a second ring resonator evanescently coupled to the input waveguide, and an output waveguide evanescently coupled to the first ring resonator and the second ring resonator, the method comprising:

selecting one of an X-basis and a Z-basis for distributing the quantum key;

in response to selection of the Z-basis, performing at least one of:

delaying a first pulse of light propagating in the first ring resonator to create the quantum key in a |0

state in the Z-basis; and

delaying the first pulse of light propagating in the first ring resonator to create the quantum key in a |1

state in the Z-basis; and

in response to selection of the X-basis, performing at least one of:

delaying the first pulse of light propagating in the first ring resonator with respect to a second pulse of light propagating in at least one of the first ring resonator or the second ring resonator to constructively interfere the first pulse of light with the second pulse of light so as to create the quantum key in an |+

state in the Z-basis; and

delaying the first pulse of light propagating in the first ring resonator with respect to the second pulse of light propagating in at least one of the first ring resonator or the second ring resonator to destructively interfere the first pulse of light with the second pulse of light so as to create the quantum key in an |−

state in the Z-basis.

14. The method of claim 13 , wherein selecting one of the Z-basis and the X-basis comprises randomly selecting one of the Z-basis and the X-basis.

15. The method of claim 13 , wherein modulating the first ring resonator comprises at least one of thermally modulating or electro-optically modulating the first ring resonator.

16. The method of claim 13 , further comprising:

propagating the first pulse of light in a propagation section of the output waveguide;

propagating the first pulse of light through at least one of the first ring resonator and the second ring resonator evanescently coupled to the propagation section of the output waveguide; and

coupling at least a portion of the first pulse of light back to the propagation section of the output waveguide.

17. The method of claim 13 , wherein delaying the first pulse of light propagating in the first ring resonator comprises delaying a phase randomized attenuated laser pulse propagating in the first ring resonator.

18. The method of claim 13 , further comprising:

attenuating the quantum key to create a decoy state.

19. The method of claim 13 , wherein delaying the first pulse of light propagating in the first ring resonator with respect to a second pulse of light propagating in the second ring resonator comprises applying a π-phase shift to the second pulse of light with respect to the first pulse of light.

20. An apparatus for measurement-device-independent quantum key distribution, the apparatus comprising:

an input waveguide to guide an input pulse of light;

an output waveguide comprising:

a receiving section, evanescently coupled to the input waveguide, to receive the input pulse of light;

a propagation section to guide the input pulse of light received by the input section; and

a loop section having at least one segment evanescently coupled to the propagation section so as to couple at least a portion of the input pulse of light back to the propagation section; and

a first ring resonator evanescently coupled to the propagation section of the output waveguide;

a first modulator, operably coupled to the first ring resonator, to delay a first pulse of light propagating in the first ring resonator;

a second ring resonator evanescently coupled to the propagation section of the output waveguide; and

a second modulator operably coupled to the second ring resonator and having a first modulation mode and a second modulation mode,

wherein, in the first modulation mode, the second modulator delays a second pulse of light propagating in the second ring resonator so as to cause the first pulse of light to constructively interfere with the second pulse of light and, in the second modulation mode, the second modulator delays the second pulse of light so as to cause the first pulse of light to destructively interfere with the second pulse of light.

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