Optimal Eavesdropping in Quantum Cryptography with Six States

Bruß, Dagmar

doi:10.1103/physrevlett.81.3018

Cited by 741 publications

(537 citation statements)

References 13 publications

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“…Security may be improved by using three bases (Bruß, 1998;Bechmann-Pasquinucci and Gisin, 1999), and even more by going to higher dimensions (Bechmann-Pasquinucci and Peres, 2000;Bruß and Macchiavello 2002). Gisin, Ribordy, Tittel and Zbinden (2002) recently reviewed theoretical and experimental results in quantum cryptography.…”

Section: F the Essence Of Quantum Informationmentioning

confidence: 99%

Quantum information and relativity theory

2004

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Quantum mechanics, information theory, and relativity theory are the basic foundations of theoretical physics. The acquisition of information from a quantum system is the interface of classical and quantum physics. Essential tools for its description are Kraus matrices and positive operator valued measures (POVMs). Special relativity imposes severe restrictions on the transfer of information between distant systems. Quantum entropy is not a Lorentz covariant concept. Lorentz transformations of reduced density matrices for entangled systems may not be completely positive maps. Quantum field theory, which is necessary for a consistent description of interactions, implies a fundamental trade-off between detector reliability and localizability. General relativity produces new, counterintuitive effects, in particular when black holes (or more generally, event horizons) are involved. Most of the current concepts in quantum information theory may then require a reassessment.

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Section: F the Essence Of Quantum Informationmentioning

confidence: 99%

Quantum information and relativity theory

2004

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“…When considering some specific protocols, there can be other, more efficient ways to obtain i.i.d. Specifically, for the BB84 [24] and the six-state protocol [25,26,27], suitable symmetries can be implemented in the protocol itself by random but coordinated bit-and phase flips [28,29]. Security bounds against general attacks can be computed by considering i.i.d.…”

Section: Security Analysis Against General Attacksmentioning

confidence: 99%

Security Bounds for Quantum Cryptography with Finite Resources

Scarani

Renner

2008

Lecture Notes in Computer Science

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Abstract. A practical quantum key distribution (QKD) protocol necessarily runs in finite time and, hence, only a finite amount of communication is exchanged. This is in contrast to most of the standard results on the security of QKD, which only hold in the limit where the number of transmitted signals approaches infinity. Here, we analyze the security of QKD under the realistic assumption that the amount of communication is finite. At the level of the general formalism, we present new results that help simplifying the actual implementation of QKD protocols: in particular, we show that symmetrization steps, which are required by certain security proofs (e.g., proofs based on de Finetti's representation theorem), can be omitted in practical implementations. Also, we demonstrate how two-way reconciliation protocols can be taken into account in the security analysis. At the level of numerical estimates, we present the bounds with finite resources for "device-independent security" against collective attacks.

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“…In this scheme, Alice prepares a qubit in one of the following six quantum states: {|0 , |1 , |± = 1/ √ 2(|0 ± |1 ), |± = 1/ √ 2(|0 ± i|1 ), and sends it to Bob [19]. On the receiving side, Bob measures each incoming signal by projecting it onto one of the three possible bases.…”

Section: Six-state Protocolmentioning

confidence: 99%

“…With this separability criterion, Refs. [4,13] analysed three well-known qubit-based QKD schemes, and provided a compact description of a minimal verification set of EWs (i.e, one that does not contain any redundant EW) for the four-state [18] and the six-state [19] QKD protocols, and a reduced verification set of EWs (i.e., one which may still include some redundant EWs) for the two-state [20] QKD scheme, respectively. These verification sets of EWs allow a systematic search for quantum correlations in p ij .…”

Section: Introductionmentioning

confidence: 99%

Single-photon quantum key distribution in the presence of loss

Curty

Moroder

2007

Phys. Rev. A

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We investigate two-way and one-way single-photon quantum key distribution (QKD) protocols in the presence of loss introduced by the quantum channel. Our analysis is based on a simple precondition for secure QKD in each case. In particular, the legitimate users need to prove that there exists no separable state (in the case of two-way QKD), or that there exists no quantum state having a symmetric extension (one-way QKD), that is compatible with the available measurements results. We show that both criteria can be formulated as a convex optimisation problem known as a semidefinite program, which can be efficiently solved. Moreover, we prove that the solution to the dual optimisation corresponds to the evaluation of an optimal witness operator that belongs to the minimal verification set of them for the given two-way (or one-way) QKD protocol. A positive expectation value of this optimal witness operator states that no secret key can be distilled from the available measurements results. We apply such analysis to several well-known single-photon QKD protocols under losses.

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Optimal Eavesdropping in Quantum Cryptography with Six States

Cited by 741 publications

References 13 publications

Quantum information and relativity theory

Quantum information and relativity theory

Security Bounds for Quantum Cryptography with Finite Resources

Single-photon quantum key distribution in the presence of loss

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