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理论物理通讯：英文版

Implementation of Positive Operator-Valued Measure in Passive Faraday Mirror Attack

Wang Wei, 高明, Zhi Ma

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

Passive Faraday-mirror(PFM) attack is based on imperfect Faraday mirrors in practical quantum cryptography systems and a set of three-dimensional Positive Operator-Valued Measure(POVM) operators plays an important role in this attack.In this paper,we propose a simple scheme to implement the POVM in PFM attack on an FaradayMichelson quantum cryptography system.Since the POVM can not be implemented directly with previous methods,in this scheme it needs to expand the states sent by Alice and the POVM operators in the attack into four-dimensional Hilbert space first,without changing the attacking effect by calculation.Based on the methods proposed by Ahnert and Payne,the linear-optical setup for implementing the POVM operators is derived.At last,the complete setup for realizing the PFM attack is presented with all parameters.Furthermore,our scheme can also be applied to realize PFM attack on a plug-and-play system by changing the parameters in the setup.

Related papers

Implementation of Positive Operator-Valued Measure in Passive Faraday Mirror Attack*

Weilong Wang, Ming Gao, Zhi Ma

Abstract Passive Faraday-mirror (PFM) attack is based on imperfect Faraday mirrors in practical quantum cryptography systems and a set of three-dimensional Positive Operator-Valued Measure (POVM) operators plays an important role in this attack. In this paper, we propose a simple scheme to implement the POVM in PFM attack on an Faraday–Michelson quantum cryptography system. Since the POVM can not be implemented directly with previous methods, in this scheme it needs to expand the states sent by Alice and the POVM operators in the attack into four-dimensional Hilbert space first, without changing the attacking effect by calculation. Based on the methods proposed by Ahnert and Payne, the linear-optical setup for implementing the POVM operators is derived. At last, the complete setup for realizing the PFM attack is presented with all parameters. Furthermore, our scheme can also be applied to realize PFM attack on a plug-and-play system by changing the parameters in the setup.

Communications in Theoretical Physics•Mar 1, 2015•0 citations

Passive Faraday-mirror attack in a practical two-way quantum-key-distribution system

Shi‐Hai Sun, Mu-Sheng Jiang, Lin-Mei Liang

The Faraday mirror (FM) plays a very important role in maintaining the stability of two-way plug-and-play quantum key distribution (QKD) systems. However, the practical FM is imperfect, which will not only introduce an additional quantum bit error rate (QBER) but also leave a loophole for Eve to spy the secret key. In this paper we propose a passive Faraday mirror attack in two-way QKD system based on the imperfection of FM. Our analysis shows that if the FM is imperfect, the dimension of Hilbert space spanned by the four states sent by Alice is three instead of two. Thus Eve can distinguish these states with a set of Positive Operator Valued Measure (POVM) operators belonging to three-dimension space, which will reduce the QBER induced by her attack. Furthermore, a relationship between the degree of the imperfection of FM and the transmittance of the practical QKD system is obtained. The results show that the probability that Eve loads her attack successfully depends on the degree of the imperfection of FM rapidly, but the QBER induced by Eve's attack changes slightly with the degree of the FM imperfection.

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A linear optical scheme to implement arbitrary positive operator valued measures

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Positive operator valued measurements (POVMs) play an important role in efficient quantum communication and computation. While optical systems are one of the strongest candidates for long distance quantum communication and information processing, efficient methods to implement POVMs in these systems are scarce. Here we propose an all-optical scheme to implement an arbitrary POVM using linear optical components on m-dimensional Hilbert space of internal degrees of freedom. Linear optical nature of the proposed scheme makes it efficient and robust. We show how the scheme can be applied for state tomography and for preparing arbitrary mixed states.

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In the quantum theory of measurement, the positive operator-valued measure (POVM) is an important concept, and its implementation can be useful. A POVM consists of a set of non-negative quantum-mechanical Hermitian operators that add up to the identity. The probability that a quantum system is in a particular state is given by the expectation value of the POVM operator corresponding to that state. Following a brief review of the mathematics and mention of the history of POVMs in quantum theory, a particular implementation of a POVM for use in the measurement of nonorthogonal photon polarization states is reviewed. The implementation consists simply of a Wollaston prism, a mirror, two beam splitters, a polarization rotator and three phototubes arranged in an interferometric configuration, and it is shown analytically that the device faithfully represents the POVM. Based on Neumark's extension theorem, the two-dimensional Hilbert space of the POVM implementation can be embedded in the three-dimensional Hilbert space of an ordinary projective-valued measure. Also, analytical expressions are given for the maximum Renyi information loss from the device to a disturbing probe, and for the error and inconclusive rates induced by the probe. Various aspects of the problem of probe optimization are elaborated.

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General implementation of all possible positive-operator-value measurements of single-photon polarization states

Sebastian E. Ahnert, Mike C. Payne

Positive-operator-value measures (POVM's) are the most general class of quantum measurements. We propose a setup in which all possible POVM's of a single-photon polarization state (corresponding to all possible sets of two-dimensional Kraus operators) can be implemented easily using linear optics elements. This method makes it possible to experimentally realize any projective orthogonal, projective nonorthogonal or nonprojective sets of any number of POVM operators. Furthermore, our implementation only requires vacuum ancillas and is deterministic rather than probabilistic. Thus it realizes every POVM with the correct set of output states. We give the settings required to implement two different well-known nonorthogonal projective POVM's.

arXiv:quant-ph/0408011•Physical Review A•Jan 20, 2005•51 citations
Passive Faraday-mirror(PFM) attack is based on imperfect Faraday mirrors in practical quantum cryptography systems and a set of three-dimensional Positive Operator-Valued Measure(POVM) operators plays an important role in this attack.In this paper,we propose a simple scheme to implement the POVM in PFM attack on an FaradayMichelson quantum cryptography system.Since the POVM can not be implemented directly with previous methods,in this scheme it needs to expand the states sent by Alice and the POVM operators in the attack into four-dimensional Hilbert space first,without changing the attacking effect by calculation.Based on the methods proposed by Ahnert and Payne,the linear-optical setup for implementing the POVM operators is derived.At last,the complete setup for realizing the PFM attack is presented with all parameters.Furthermore,our scheme can also be applied to realize PFM attack on a plug-and-play system by changing the parameters in the setup.
Abstract Passive Faraday-mirror (PFM) attack is based on imperfect Faraday mirrors in practical quantum cryptography systems and a set of three-dimensional Positive Operator-Valued Measure (POVM) operators plays an important role in this attack. In this paper, we propose a simple scheme to implement the POVM in PFM attack on an Faraday–Michelson quantum cryptography system. Since the POVM can not be implemented directly with previous methods, in this scheme it needs to expand the states sent by Alice and the POVM operators in the attack into four-dimensional Hilbert space first, without changing the attacking effect by calculation. Based on the methods proposed by Ahnert and Payne, the linear-optical setup for implementing the POVM operators is derived. At last, the complete setup for realizing the PFM attack is presented with all parameters. Furthermore, our scheme can also be applied to realize PFM attack on a plug-and-play system by changing the parameters in the setup.
The Faraday mirror (FM) plays a very important role in maintaining the stability of two-way plug-and-play quantum key distribution (QKD) systems. However, the practical FM is imperfect, which will not only introduce an additional quantum bit error rate (QBER) but also leave a loophole for Eve to spy the secret key. In this paper we propose a passive Faraday mirror attack in two-way QKD system based on the imperfection of FM. Our analysis shows that if the FM is imperfect, the dimension of Hilbert space spanned by the four states sent by Alice is three instead of two. Thus Eve can distinguish these states with a set of Positive Operator Valued Measure (POVM) operators belonging to three-dimension space, which will reduce the QBER induced by her attack. Furthermore, a relationship between the degree of the imperfection of FM and the transmittance of the practical QKD system is obtained. The results show that the probability that Eve loads her attack successfully depends on the degree of the imperfection of FM rapidly, but the QBER induced by Eve's attack changes slightly with the degree of the FM imperfection.
Positive operator valued measurements (POVMs) play an important role in efficient quantum communication and computation. While optical systems are one of the strongest candidates for long distance quantum communication and information processing, efficient methods to implement POVMs in these systems are scarce. Here we propose an all-optical scheme to implement an arbitrary POVM using linear optical components on m-dimensional Hilbert space of internal degrees of freedom. Linear optical nature of the proposed scheme makes it efficient and robust. We show how the scheme can be applied for state tomography and for preparing arbitrary mixed states.
In the quantum theory of measurement, the positive operator-valued measure (POVM) is an important concept, and its implementation can be useful. A POVM consists of a set of non-negative quantum-mechanical Hermitian operators that add up to the identity. The probability that a quantum system is in a particular state is given by the expectation value of the POVM operator corresponding to that state. Following a brief review of the mathematics and mention of the history of POVMs in quantum theory, a particular implementation of a POVM for use in the measurement of nonorthogonal photon polarization states is reviewed. The implementation consists simply of a Wollaston prism, a mirror, two beam splitters, a polarization rotator and three phototubes arranged in an interferometric configuration, and it is shown analytically that the device faithfully represents the POVM. Based on Neumark's extension theorem, the two-dimensional Hilbert space of the POVM implementation can be embedded in the three-dimensional Hilbert space of an ordinary projective-valued measure. Also, analytical expressions are given for the maximum Renyi information loss from the device to a disturbing probe, and for the error and inconclusive rates induced by the probe. Various aspects of the problem of probe optimization are elaborated.
Positive operator valued measurements (POVMs) play an important role in efficient quantum communication and computation. While optical systems are one of the strongest candidates for long distance quantum communication and information processing, efficient methods to implement POVMs in these systems are scarce. Here we propose an all-optical scheme to implement an arbitrary POVM using linear optical components on mmm-dimensional Hilbert space of internal degrees of freedom. Linear optical nature of the proposed scheme makes it efficient and robust. We show how the scheme can be applied for state tomography and for preparing arbitrary mixed states.
Positive-operator-value measures (POVM's) are the most general class of quantum measurements. We propose a setup in which all possible POVM's of a single-photon polarization state (corresponding to all possible sets of two-dimensional Kraus operators) can be implemented easily using linear optics elements. This method makes it possible to experimentally realize any projective orthogonal, projective nonorthogonal or nonprojective sets of any number of POVM operators. Furthermore, our implementation only requires vacuum ancillas and is deterministic rather than probabilistic. Thus it realizes every POVM with the correct set of output states. We give the settings required to implement two different well-known nonorthogonal projective POVM's.