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arXiv:1609.07064

Quantum key distribution by phase flipping of coherent states of light

Barbosa, G. A., van de Graaf, J., Paulo Mateus, Nikola Paunković

Published Sep 22, 2016• 0 citations
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Abstract

In this paper we present quantum key distribution protocol that, instead of single qubits, uses mesoscopic coherent states of light $|α\rangle$ to encode bit values of a randomly generated key. Given the reference value $α\in\mathbb C$, and a string of phase rotations each randomly taken from a set of $2M$ equidistant phases, Alice prepares a quantum state given by a product of coherent states of light, such that a complex phase of each pulse is rotated by the corresponding phase rotation. The encoding of $i$-th bit of the key $r=r_1 \dots r_\ell$ is done by further performing phase rotation $r_i π$ (with $r_i = 0,1$) on the $i$-th coherent state pulse. In order to protect the protocol against the man-in-the-middle attack, we introduce a verification procedure, and analyse the protocol's security using the Holevo bound. We also analyse the possibility of beam splitting-like and of collective attacks, showing the impossibility of the former and, in the case of our protocol, the inadequacy of the latter. While we cannot prove full perfect security against the most general attacks allowed by the laws of quantum mechanics, our protocol achieves faster quantum key distribution, over larger distances and with lower costs, than the single-photon counterparts, maintaining at least practical security against the current and the near future technologies.

DOI
10.48550/arxiv.1609.07064

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In this paper we present quantum key distribution protocol that, instead of single qubits, uses mesoscopic coherent states of light ∣α⟩|α\rangle∣α⟩ to encode bit values of a randomly generated key. Given the reference value α∈Cα\in\mathbb Cα∈C, and a string of phase rotations each randomly taken from a set of 2M2M2M equidistant phases, Alice prepares a quantum state given by a product of coherent states of light, such that a complex phase of each pulse is rotated by the corresponding phase rotation. The encoding of iii-th bit of the key r=r1…rℓr=r_1 \dots r_\ellr=r1​…rℓ​ is done by further performing phase rotation riπr_i πri​π (with ri=0,1r_i = 0,1ri​=0,1) on the iii-th coherent state pulse. In order to protect the protocol against the man-in-the-middle attack, we introduce a verification procedure, and analyse the protocol's security using the Holevo bound. We also analyse the possibility of beam splitting-like and of collective attacks, showing the impossibility of the former and, in the case of our protocol, the inadequacy of the latter. While we cannot prove full perfect security against the most general attacks allowed by the laws of quantum mechanics, our protocol achieves faster quantum key distribution, over larger distances and with lower costs, than the single-photon counterparts, maintaining at least practical security against the current and the near future technologies.
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.
Abstract Quantum cryptography or, more precisely, quantum key distribution (QKD), is one of the advanced areas in the field of quantum technologies. The confidentiality of keys distributed with the use of QKD protocols is guaranteed by the fundamental laws of quantum mechanics. This paper is devoted to the decoy state method, a countermeasure against vulnerabilities caused by the use of coherent states of light for QKD protocols whose security is proved under the assumption of single-photon states. We give a formal security proof of the decoy state method against all possible attacks. We compare two widely known attacks on multiphoton pulses: photon-number splitting and beam splitting. Finally, we discuss the equivalence of polarization and phase coding.
We propose a secure quantum key distribution (QKD) protocol using a single not-so-weak coherent qubit. With two preprocesses for random rotation and compensation, a key bit is encoded to a randomly polarized not-so-weak coherent qubit. We analyze the security of the QKD protocol, which counters the photon number splitting and the impersonation attacks. The estimated mean number of photon, which is less than 6.0, guarantees security. Additionally, we discuss the possibility of quantum secure direct communication.
Standard security proofs of quantum-key-distribution (QKD) protocols often rely on symmetry arguments. In this paper, we prove the security of a three-state protocol that does not possess rotational symmetry. The three-state QKD protocol we consider involves three qubit states, where the first two states $\ensuremath{\mid}{0}_{z}⟩$ and $\ensuremath{\mid}{1}_{z}⟩$ can contribute to key generation, and the third state $\ensuremath{\mid}+⟩=(\ensuremath{\mid}{0}_{z}⟩+\ensuremath{\mid}{1}_{z}⟩)∕\sqrt{2}$ is for channel estimation. This protocol has been proposed and implemented experimentally in some frequency-based QKD systems where the three states can be prepared easily. Thus, by founding on the security of this three-state protocol, we prove that these QKD schemes are, in fact, unconditionally secure against any attacks allowed by quantum mechanics. The main task in our proof is to upper bound the phase error rate of the qubits given the bit error rates observed. Unconditional security can then be proved not only for the ideal case of a single-photon source and perfect detectors, but also for the realistic case of a phase-randomized weak coherent light source and imperfect threshold detectors. Our result in the phase error rate upper bound is independent of the loss in the channel. Also, we compare the three-state protocol with the Bennett-Brassard 1984 (BB84) protocol. For the single-photon source case, our result proves that the BB84 protocol strictly tolerates a higher quantum bit error rate than the three-state protocol, while for the coherent-source case, the BB84 protocol achieves a higher key generation rate and secure distance than the three-state protocol when a decoy-state method is used.
State-of-the-art Quantum Key Distribution (QKD) is based on the uncertainty principle of qubits on quantum measurements and is theoretically proven to be unconditionally secure. Over the past three decades, QKD has been explored with single photons as the information carrier. More recently, attention has shifted towards using weak coherent laser pulses as the information carrier. In this paper, we propose a novel quantum key distribution mechanism over a pure optical channel using randomized Glauber states. The proposed mechanism closely resembles a quantum mechanical implementation of the public key envelope idea. The core idea can be described in five steps as follows: 1. A user (Bob) generates a Glauber state as a quantum public key envelope (QPKE) by randomly modulating a secret phase φr, known only to Bob, and transmits it over an optical channel to the other user (Alice). 2. Alice modulates a key phase φk into the QPKE based on a random key and selected modulation scheme and returns it to Bob. 3. For the returning QPKE, Bob derandomizes it with his private key or the phase -φr and then 4. passes it to a coherent receiver to measure the key phase φk. 5. For better security, differential phase-shift keying (DPSK) technique with a reference list is applied to extract keys. For the proposed solution, we explore physical countermeasures to provide path authentication and to avoid man-in-the-middle attacks. Other attack vectors can also be effectively mitigated by leveraging the QPKE, the uncertainty principle and the DPSK modulation technique.