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IEEE Journal of Selected Topics in Quantum Electronics

Integrated-optical realizations of quantum key distribution over maximally unbiased bases

Moshe Nazarathy, Igor Tselniker, Y. Regev, Meir Orenstein, Matias Katz

Published Jul 1, 2006• 5 citations
Publisher

Abstract

Quantum key distribution (QKD) protocols based on higher order maximally unbiased bases (MUBs), potentially displaying improved range-security performance, are optically realized for higher (>2) dimensions and/or for multiple (>2) transmission and detection bases, inspired by analogies with the differential phase shift keying and pulse position modulation (PPM) formats of classical optical communication. In particular, we introduce optical realizations for: 1) a six-state protocol in qubit space, employing an extra phase modulated interferometer in the transmitter, detecting the photon in the PPM basis of three consecutive time slots and 2) a 16-state MUB protocol in four dimensions, based on differential phase encoding over four adjacent time slots. The transmitter (Alice) and receiver (Bob) for this system are realized using generalized Mach-Zehnder interferometers with four delay arms, and three phase modulators, further requiring a quantum Hadamard-4 gate, realized using four cross-connected directional couplers, to be implemented as an integrated-optical circuit. The conception and analysis of these optical realizations of abstract higher order QKD MUB-based protocols is inspired by a novel insight into the structure of the MUB set constructed by modulating a generator matrix (typically a Hadamard matrix) with a set of phasemasks. The operating characteristics of these generalized protocols are derived in terms of three simple figures of merit, the Eve detect (or Disturbance) rate, the Eve information rate, and the key creation rate.

DOI
10.1109/jstqe.2006.876175

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Quantum key distribution (QKD) protocols based on higher order maximally unbiased bases (MUBs), potentially displaying improved range-security performance, are optically realized for higher (>2) dimensions and/or for multiple (>2) transmission and detection bases, inspired by analogies with the differential phase shift keying and pulse position modulation (PPM) formats of classical optical communication. In particular, we introduce optical realizations for: 1) a six-state protocol in qubit space, employing an extra phase modulated interferometer in the transmitter, detecting the photon in the PPM basis of three consecutive time slots and 2) a 16-state MUB protocol in four dimensions, based on differential phase encoding over four adjacent time slots. The transmitter (Alice) and receiver (Bob) for this system are realized using generalized Mach-Zehnder interferometers with four delay arms, and three phase modulators, further requiring a quantum Hadamard-4 gate, realized using four cross-connected directional couplers, to be implemented as an integrated-optical circuit. The conception and analysis of these optical realizations of abstract higher order QKD MUB-based protocols is inspired by a novel insight into the structure of the MUB set constructed by modulating a generator matrix (typically a Hadamard matrix) with a set of phasemasks. The operating characteristics of these generalized protocols are derived in terms of three simple figures of merit, the Eve detect (or Disturbance) rate, the Eve information rate, and the key creation rate.
We design mutually unbiased bases (MUBs) in 4, 8, and 16 dimensions, which are compatible with quadrature phase-shift keying (QPSK) optical transmission, based on novel insights into the structure of the MUB set, viewed as the modulation of a Hadamard matrix with a set of phase masks. The new protocol is based on the generation of a pair of MUBs as tensor products of the lowest dimension (2-D) MUBs, followed by novel unbiasing transformations, which operate on pairs of MUBs and make them mutually unbiased among the pairs. We discovered that the unbiasing transformations consist of controlled-phase quantum gates acting on multiple qubits. We further conceive an abstract BB84-like higher order quantum key distribution MUB-based protocol, based on multiple entangled photons.
This paper presents novel quantum key distribution (QKD) schemes that use differential phases of sequential pulses as an information carrier. Alice sends a photon in a linear superposition state of three temporal slots, in which each amplitude is phase-modulated by {0,π}. Bob measures the phase difference of an asymmetric interferometer, and tells Alice time-instance at which the photon was counted. From this time information and her modulation data, Alice knows which detector counted the photon in Bob s site. Then, the two parties create a secret key. The scheme is suitable for fiber transmission systems and offers key creation efficiency higher than conventional phase-encoding QKD. The above scheme utilizes fully non-orthogonal four states. Differential phase shift QKD utilizing two non-orthogonal states is also presented. Alice sends a coherent pulse train with less than one photon per pulse, which is phase modulated by {0,π} for each pulse, and Bob measures the pulse train by a one-bit delay circuit. The system has a simple configuration such that Alice has no interferometer and sends no intense reference pulse, unlike to conventional QKD scheme using two non-orthogonal states, and also has an advantage of high key creation efficiency.
Quantum Key Distribution (QKD) provides a secure way of generating shared cryptographic keys between a sender (Alice) and a receiver (Bob). The original BB84 protocol uses a two-dimensional polarization basis, limiting the information content of a single photon to 1 bit. Using the transverse position of single photons as one basis and the Fourier space as a second basis, one can construct a pair of mutually unbiased higher-dimensional bases. This improves not only the security of the protocol, but also the key generation rate. We present experimental results with a Spatial-Light-Modulator-based encoding scheme employing two nearly orthogonal alphabets with on the order of 103symbols each and an information content of about 10 bit.
Quantum key distribution (QKD) is a technology that allows two users to communicate with theoretically perfect security using standard optical fibres. This is possible by transmitting the key on single photons, meaning a measurement by an eavesdropper disturbs the system in a way observable to the legitimate parties. The technology has advanced since the first protocol proposed in 1984, to the stage where there are now many protocols that can be experimentally implemented. These protocols have allowed secure keys to be generated over distances greater than 400 km and with secure key rates over 10 Mbit/s. In a metropolitan QKD network, it would be desirable for as many users to be connected as possible. Unfortunately, each protocol comes with different requirements on the transmitter and receiver. Even within a single protocol, different clock rates can require individualised transmitter and receiver hardware. This prohibits users from communicating with all receivers, unless they have complex transmitters with hardware for many protocols. This thesis develops a transmitter for practical QKD that is able to adapt to a number of different protocols with no changes to the hardware. The transmitter works using optical injection locking, where a pulse preparation laser adopts the phase of a phase preparation laser. Controlling the phase and intensity of the pulses in this way removes the side channel ordinarily present with direct modulation, in that the phase, intensity and frequency simultaneously change in response to an applied current. The cavity-enhanced electro-optic effect allows for the first demonstration of sub-volt half-wave phase modulation at high clock rates. The transmitter successfully demonstrates phase encoding, intensity encoding and on-demand phase randomisation. This allows for the experimental realisation and direct comparison of different QKD protocols, including one that has never before been implemented due to experimental complexity. A stable intensity modulator is also developed, based on a Sagnac interferometer. This removes a side channel in QKD systems and integrates well with the directly-modulated quantum transmitter. This development also means that the transmitter can implement all current two-party QKD protocols based on weak coherent pulses. The transmitter has the potential to become the standard transmitter for future quantum communication networks due to its stability, versatility and power efficiency. The design could also be demonstrated on a photonic chip, making it compact enough to fit in small transmitter units.
New methods are proposed for extending the range of fiber-optic one-way quantum key distribution (QKD), inspired by classical optical communication formats. A new time-domain technique based on pulse position modulation (PPM) is combined with differential phase-shift keying to optically implement a six-state protocol. Finally, some recently proposed PPM schemes are critically reviewed and applied to synthesize a new QKD asymmetric optical realization, applicable to local or metropolitan area networks.
A novel type of quantum key distribution (QKD) protocol, called DPS (differential-phase-shift) QKD, was proposed several years ago. A sender transmits a highly-attenuated coherent pulse train with {0, π} phase, and a receiver receives it with a one-bit delay Mach-Zehnder interferometer followed by photon detectors. A secret key is created from photon detection events, whose security is based on the fact that an eavesdropper cannot perfectly measure the phase information of a highly-attenuated coherent pulse train. This protocol has some features of simple setup, potential for a high key creation rate, and robustness against photon-number-splitting attack. This paper overviews DPS-QKD. The operation mechanism is described, and then some experimental efforts are introduced, featuring use of a glass waveguide Mach-Zehnder interferometer and advanced single-photon detectors. The highest key rate and the longest distance have been achieved with the DPS-QKD protocol. Some modified schemes are also presented, including that utilizing quantum entanglement, that using decoy pulses, and that using macroscopic coherent light.