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Quantum key distribution using bright polarized coherent states

L. F. M. Borelli, A. Vidiella-Barranco

Published Mar 9, 2004• 1 citation
OpenAlex

Abstract

We propose a novel protocol for quantum key distribution based on the quantum polarization properties of coherent states. The key elements are encoded either in the component amplitude difference or in the phase difference of Gaussian-modulated strong coherent fields. The quantum counterpart (Stokes operators) of the classical parameters which represent the preponderance of x-linear polarization over y-linear polarization and phase difference information of the electrical field components are used as the non commuting operators essential for the security of our protocol. 1

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We propose a novel protocol for quantum key distribution based on the quantum polarization properties of coherent states. The key elements are encoded either in the component amplitude difference or in the phase difference of Gaussian-modulated strong coherent fields. The quantum counterpart (Stokes operators) of the classical parameters which represent the preponderance of x-linear polarization over y-linear polarization and phase difference information of the electrical field components are used as the non commuting operators essential for the security of our protocol. 1
We discuss a continuous variables method of quantum key distribution employing strongly polarized coherent states of light. The key encoding is performed using the variables known as Stokes parameters, rather than the field quadratures. Their quantum counterpart, the Stokes operators Ŝi ( i =1,2,3), constitute a set of non-commuting operators, being the precision of simultaneous measurements of a pair of them limited by an uncertainty-like relation. Alice transmits a conveniently modulated two-mode coherent state, and Bob randomly measures one of the Stokes parameters of the incoming beam. After performing reconciliation and privacy amplification procedures, it is possible to distill a secret common key. We also consider a non-ideal situation, in which coherent states with thermal noise, instead of pure coherent states, are used for encoding.
We present a protocol for quantum key distribution using discrete modulation of coherent states of light. Information is encoded in the variable phase of coherent states which can be chosen from a regular discrete set ranging from binary to continuous modulation similar to phase-shift keying in classical communication. Information is decoded by simultaneous homodyne measurement of both quadratures and requires no active choice of basis. The protocol utilizes either direct or reverse reconciliation both with and without postselection. We analyze the security of the protocol and show how to enhance it by the optimal choice of all variable parameters of the quantum signal.
In secure communication, quantum key distribution (QKD) based on coherent states is well known for its simple implementation, but it suffers from loss-dependent attacks, and generally underestimates the final secure key rate. To address this problem, the authors present a six-coherent-state phase-encoding QKD protocol based on non-phase-randomized coherent states, with which secret key rates and transmission distance can be significantly improved. The security of the protocol is determined using a recently developed security-proof technique based on semidefinite programming. These results point to this protocol as a promising candidate for high-speed, provably secure QKD.
We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol in the case where the key information is encoded in the relative phase of a coherent-state reference pulse and a weak coherent-state signal pulse, as in some practical implementations of the protocol. In contrast to previous work, our proof applies even if the eavesdropper knows the phase of the reference pulse, provided that this phase is not modulated by the source, and even if the reference pulse is bright. The proof also applies to the case where the key is encoded in the photon polarization of a weak coherent-state pulse with a known phase, but only if the phases of the four BB84 signal states are judiciously chosen. The achievable key generation rate scales quadratically with the transmission in the channel, just as for BB84 with phase-randomized weak coherent-state signals (when decoy states are not used). For the case where the phase of the reference pulse is strongly modulated by the source, we exhibit an explicit attack that allows the eavesdropper to learn every key bit in a parameter regime where a protocol using phase-randomized signals is provably secure.