We prove the unconditional security of the standard six-state scheme for quantum key distribution (QKD). We demonstrate its unconditional security up to a bit error rate of 12.7 percents, by allowing only one-way classical communications in the error correction/privacy amplification procedure between Alice and Bob. This shows a clear advantage of the six-state scheme over another standard scheme---BB84, which has been proven to be secure up to only about 11 percents, if only one-way classical communications are allowed. Our proof technique is a generalization of that of Shor-Preskill's proof of security of BB84. We show that a advantage of the six-state scheme lies in the Alice and Bob's ability to establish rigorously from their test sample the non-trivial mutual information between the bit-flip and phase error patterns. A modified version of the degenerate quantum codes studied by DiVincenzo, Shor and Smolin is employed in our proof.We prove the unconditional security of the standard six-state scheme for quantum key distribution (QKD). We demonstrate its unconditional security up to a bit error rate of 12.7 percents, by allowing only one-way classical communications in the error correction/privacy amplification procedure between Alice and Bob. This shows a clear advantage of the six-state scheme over another standard scheme---BB84, which has been proven to be secure up to only about 11 percents, if only one-way classical communications are allowed. Our proof technique is a generalization of that of Shor-Preskill's proof of security of BB84. We show that a advantage of the six-state scheme lies in the Alice and Bob's ability to establish rigorously from their test sample the non-trivial mutual information between the bit-flip and phase error patterns. A modified version of the degenerate quantum codes studied by DiVincenzo, Shor and Smolin is employed in our proof.

arXiv:quant-ph/0102138Feb 27, 20013 citations

Unconditional Security of a Three State Quantum Key Distribution Protocol

Jean-Christian Boileau, Kiyoshi Tamaki, Jamie Batuwantudawe +2 more

Quantum key distribution (QKD) protocols are cryptographic techniques with security based only on the laws of quantum mechanics. Two prominent QKD schemes are the Bennett-Brassard 1984 and Bennett 1992 protocols that use four and two quantum states, respectively. In 2000, Phoenix et al. proposed a new family of three-state protocols that offers advantages over the previous schemes. Until now, an error rate threshold for security of the symmetric trine spherical code QKD protocol has been shown only for the trivial intercept-resend eavesdropping strategy. In this Letter, we prove the unconditional security of the trine spherical code QKD protocol, demonstrating its security up to a bit error rate of 9.81%. We also discuss how this proof applies to a version of the trine spherical code QKD protocol where the error rate is evaluated from the number of inconclusive events.Quantum key distribution (QKD) protocols are cryptographic techniques with security based only on the laws of quantum mechanics. Two prominent QKD schemes are the Bennett-Brassard 1984 and Bennett 1992 protocols that use four and two quantum states, respectively. In 2000, Phoenix et al. proposed a new family of three-state protocols that offers advantages over the previous schemes. Until now, an error rate threshold for security of the symmetric trine spherical code QKD protocol has been shown only for the trivial intercept-resend eavesdropping strategy. In this Letter, we prove the unconditional security of the trine spherical code QKD protocol, demonstrating its security up to a bit error rate of 9.81%. We also discuss how this proof applies to a version of the trine spherical code QKD protocol where the error rate is evaluated from the number of inconclusive events.

arXiv:quant-ph/0408085Physical Review LettersJan 31, 200584 citations

Security of six-state quantum key distribution protocol with threshold detectors

Go Kato, Kiyoshi Tamaki

The security of quantum key distribution (QKD) is established by a security proof, and the security proof puts some assumptions on the devices consisting of a QKD system. Among such assumptions, security proofs of the six-state protocol assume the use of photon number resolving (PNR) detector, and as a result the bit error rate threshold for secure key generation for the six-state protocol is higher than that for the BB84 protocol. Unfortunately, however, this type of detector is demanding in terms of technological level compared to the standard threshold detector, and removing the necessity of such a detector enhances the feasibility of the implementation of the six-state protocol. Here, we develop the security proof for the six-state protocol and show that we can use the threshold detector for the six-state protocol. Importantly, the bit error rate threshold for the key generation for the six-state protocol (12.611%) remains almost the same as the one (12.619%) that is derived from the existing security proofs assuming the use of PNR detectors. This clearly demonstrates feasibility of the six-state protocol with practical devices.The security of quantum key distribution (QKD) is established by a security proof, and the security proof puts some assumptions on the devices consisting of a QKD system. Among such assumptions, security proofs of the six-state protocol assume the use of photon number resolving (PNR) detector, and as a result the bit error rate threshold for secure key generation for the six-state protocol is higher than that for the BB84 protocol. Unfortunately, however, this type of detector is demanding in terms of technological level compared to the standard threshold detector, and removing the necessity of such a detector enhances the feasibility of the implementation of the six-state protocol. Here, we develop the security proof for the six-state protocol and show that we can use the threshold detector for the six-state protocol. Importantly, the bit error rate threshold for the key generation for the six-state protocol (12.611%) remains almost the same as the one (12.619%) that is derived from the existing security proofs assuming the use of PNR detectors. This clearly demonstrates feasibility of the six-state protocol with practical devices.

Scientific ReportsJul 22, 201611 citations

A simpler security proof for 6-state quantum key distribution

Kaan Akyuz, Boris Škorić

Six-state Quantum Key Distribution (QKD) achieves the highest key rate in the class of qubit-based QKD schemes. The standard security proof, which has been developed since 2005, invokes complicated theorems involving smooth R\'{e}nyi entropies. In this paper we present a simpler security proof for 6-state QKD that entirely avoids R\'{e}nyi entropies. This is achieved by applying state smoothing directly in the Bell basis. We obtain the well known asymptotic rate, but with slightly more favorable finite-size terms. We furthermore show that the same proof technique can be used for 6-state quantum key recycling.Six-state Quantum Key Distribution (QKD) achieves the highest key rate in the class of qubit-based QKD schemes. The standard security proof, which has been developed since 2005, invokes complicated theorems involving smooth R\'{e}nyi entropies. In this paper we present a simpler security proof for 6-state QKD that entirely avoids R\'{e}nyi entropies. This is achieved by applying state smoothing directly in the Bell basis. We obtain the well known asymptotic rate, but with slightly more favorable finite-size terms. We furthermore show that the same proof technique can be used for 6-state quantum key recycling.

arXiv:2305.03940Quantum Information and ComputationSep 1, 20231 citation

Experimentally feasible quantum-key-distribution scheme using qubit-like qudits and its comparison with existing qubit- and qudit-based protocols

H. F. Chau, Qinan Wang, Cardythy Wong

Recently, Chau [Phys. Rev. A 92, 062324 (2015)] introduced an experimentally feasible qudit-based quantum-key-distribution (QKD) scheme. In that scheme, one bit of information is phase encoded in the prepared state in a ${2}^{n}$ -dimensional Hilbert space in the form $(|i\ensuremath{\rangle}\ifmmode\pm\else\textpm\fi{}|j\ensuremath{\rangle})/\sqrt{2}$ with $n\ensuremath{\ge}2$. For each qudit prepared and measured in the same two-dimensional Hilbert subspace, one bit of raw secret key is obtained in the absence of transmission error. Here we show that by modifying the basis announcement procedure, the same experimental setup can generate $n$ bits of raw key for each qudit prepared and measured in the same basis in the noiseless situation. The reason is that in addition to the phase information, each qudit also carries information on the Hilbert subspace used. The additional $(n\ensuremath{-}1)$ bits of raw key comes from a clever utilization of this extra piece of information. We prove the unconditional security of this modified protocol and compare its performance with other existing provably secure qubit- and qudit-based protocols on market in the one-way classical communication setting. Interestingly, we find that for the case of $n=2$ , the secret key rate of this modified protocol using nondegenerate random quantum code to perform one-way entanglement distillation is equal to that of the six-state scheme.Recently, Chau [Phys. Rev. A 92, 062324 (2015)] introduced an experimentally feasible qudit-based quantum-key-distribution (QKD) scheme. In that scheme, one bit of information is phase encoded in the prepared state in a ${2}^{n}$-dimensional Hilbert space in the form $(|i\ensuremath{\rangle}\ifmmode\pm\else\textpm\fi{}|j\ensuremath{\rangle})/\sqrt{2}$ with $n\ensuremath{\ge}2$. For each qudit prepared and measured in the same two-dimensional Hilbert subspace, one bit of raw secret key is obtained in the absence of transmission error. Here we show that by modifying the basis announcement procedure, the same experimental setup can generate $n$ bits of raw key for each qudit prepared and measured in the same basis in the noiseless situation. The reason is that in addition to the phase information, each qudit also carries information on the Hilbert subspace used. The additional $(n\ensuremath{-}1)$ bits of raw key comes from a clever utilization of this extra piece of information. We prove the unconditional security of this modified protocol and compare its performance with other existing provably secure qubit- and qudit-based protocols on market in the one-way classical communication setting. Interestingly, we find that for the case of $n=2$, the secret key rate of this modified protocol using nondegenerate random quantum code to perform one-way entanglement distillation is equal to that of the six-state scheme.

arXiv:1603.02370Physical Review AFeb 7, 20177 citations

{2}^{n}

-dimensional Hilbert space in the form $(|i\ensuremath{\rangle}\ifmmode\pm\else\textpm\fi{}|j\ensuremath{\rangle})/\sqrt{2}$ with $n\ensuremath{\ge}2$. For each qudit prepared and measured in the same two-dimensional Hilbert subspace, one bit of raw secret key is obtained in the absence of transmission error. Here we show that by modifying the basis announcement procedure, the same experimental setup can generate

n

bits of raw key for each qudit prepared and measured in the same basis in the noiseless situation. The reason is that in addition to the phase information, each qudit also carries information on the Hilbert subspace used. The additional $(n\ensuremath{-}1)$ bits of raw key comes from a clever utilization of this extra piece of information. We prove the unconditional security of this modified protocol and compare its performance with other existing provably secure qubit- and qudit-based protocols on market in the one-way classical communication setting. Interestingly, we find that for the case of

n=2

, the secret key rate of this modified protocol using nondegenerate random quantum code to perform one-way entanglement distillation is equal to that of the six-state scheme.