Reduction theorems for optimal unambiguous state discrimination of density matrices

Raynal, Philippe; Lütkenhaus, Norbert; Enk, S. J. van

doi:10.1103/physreva.68.022308

Cited by 76 publications

(89 citation statements)

References 15 publications

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“…3) through USD, the measurement scheme becomes less practical involving photon number resolving detectors [29]. The USD of mixed quantum states is a much more subtle issue than that of pure states [30,31,32,33]. Nonetheless, for equal a priori probabilities (which is the FIG.…”

Section: Ultimate Boundsmentioning

confidence: 99%

Quantum repeaters using coherent-state communication

et al. 2008

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We investigate quantum repeater protocols based upon atomic qubit-entanglement distribution through optical coherent-state communication. Various measurement schemes for an optical mode entangled with two spatially separated atomic qubits are considered in order to nonlocally prepare conditional two-qubit entangled states. In particular, generalized measurements for unambiguous state discrimination enable one to completely eliminate spin-flip errors in the resulting qubit states, as they would occur in a homodyne-based scheme due to the finite overlap of the optical states in phase space. As a result, by using weaker coherent states, high initial fidelities can still be achieved for larger repeater spacing, at the expense of lower entanglement generation rates. In this regime, the coherent-state-based protocols start resembling single-photon-based repeater schemes.

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Section: Ultimate Boundsmentioning

confidence: 99%

Quantum repeaters using coherent-state communication

et al. 2008

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“…In Ref. [23], the authors consider the problem of unambiguous discrimination between two general density matrices.…”

Section: Introductionmentioning

confidence: 99%

Optimal quantum detectors for unambiguous detection of mixed states

2004

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We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient conditions for an optimal measurement that minimizes the probability of an inconclusive result. We show that the previous optimal measurements that were derived for certain special cases satisfy these optimality conditions. We then consider state sets with strong symmetry properties, and show that the optimal measurement operators for distinguishing between these states share the same symmetries, and can be computed very efficiently by solving a reduced size semidefinite program.

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“…III, we report the notion of parallel addition that leads to some useful relations for USD in connection with a reduction theorem of Ref. [12]. In Sec.IV, we derive the main result of this paper as a theorem: two necessary and sufficient conditions for the failure probability to reach the bounds are given.…”

Section: Introductionmentioning

confidence: 99%

“…Some special cases have been given for which the corresponding problem can be reduced to USD of pure state case, such as in state filtering [9,10,11] or state comparison [1,11]. The underlying reduction theorems have been stated in [12]. For the general case, necessary and sufficient conditions for the optimality of a POVM were derived in [13,14].…”

Section: Introductionmentioning

confidence: 99%

Optimal unambiguous state discrimination of two density matrices: Lower bound and class of exact solutions

Raynal

Lütkenhaus

2005

Phys. Rev. A

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Recently the problem of Unambiguous State Discrimination (USD) of mixed quantum states has attracted much attention. So far, bounds on the optimum success probability have been derived [1]. For two mixed states they are given in terms of the fidelity. Here we give tighter bounds as well as necessary and sufficient conditions for two mixed states to reach these bounds. Moreover we construct the corresponding optimal measurement strategies. With this result, we provide analytical solutions for unambiguous discrimination of a class of generic mixed states. This goes beyond known results which are all reducible to some pure state case. Additionally, we show that examples exist where the bounds cannot be reached.

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Reduction theorems for optimal unambiguous state discrimination of density matrices

Cited by 76 publications

References 15 publications

Quantum repeaters using coherent-state communication

Quantum repeaters using coherent-state communication

Optimal quantum detectors for unambiguous detection of mixed states

Optimal unambiguous state discrimination of two density matrices: Lower bound and class of exact solutions

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