Experimental scheme for unambiguous discrimination of linearly independent symmetric states

Jiménez, Omar; Sanchez-Lozano, X.; Burgos-Inostroza, E.; Delgado, A.; Saavedra, C.

doi:10.1103/physreva.76.062107

Cited by 22 publications

(26 citation statements)

References 38 publications

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“…These probabilities were plotted as a function of the magnitude of either nonvanishing failure-state coefficient in Eq. (40). As expected, the MC measurement gives us greater confidence than the ME measurement, except for C j = 1/ √ 2.…”

Section: A Smc Measurements For the Discrimination Of Four Symmetricsupporting

confidence: 73%

“…In the present work our goal is to extend this study to individual D-dimensional quantum systems (with D > 2), i.e., qudits. The nonorthogonal symmetric states of qudits are known to play an important role in QSD [26,34,40] and many other quantum information protocols [15,17,21,22]. Motivated by this fact, we study the MC strategy applied to a set of N linearly dependent symmetric qudit states, prepared with equal prior probabilities.…”

Section: Introductionmentioning

confidence: 99%

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Maximum-confidence discrimination among symmetric qudit states

et al. 2011

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We study the maximum-confidence (MC) measurement strategy for discriminating among nonorthogonal symmetric qudit states. Restricting to linearly dependent and equally likely pure states, we find the optimal positive operator valued measure (POVM) that maximizes our confidence in identifying each state in the set and minimizes the probability of obtaining inconclusive results. The physical realization of this POVM is completely determined and it is shown that after an inconclusive outcome, the input states may be mapped into a new set of equiprobable symmetric states, restricted, however, to a subspace of the original qudit Hilbert space. By applying the MC measurement again onto this new set, we can still gain some information about the input states, although with less confidence than before. This leads us to introduce the concept of "sequential maximum-confidence" (SMC) measurements, where the optimized MC strategy is iterated in as many stages as allowed by the input set, until no further information can be extracted from an inconclusive result. Within each stage of this measurement our confidence in identifying the input states is the highest possible, although it decreases from one stage to the next. In addition, the more stages we accomplish within the maximum allowed, the higher will be the probability of correct identification. We will discuss an explicit example of the optimal SMC measurement applied in the discrimination among four symmetric qutrit states and propose an optical network to implement it.Comment: 14 pages, 4 figures. Published versio

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Section: A Smc Measurements For the Discrimination Of Four Symmetricsupporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Maximum-confidence discrimination among symmetric qudit states

et al. 2011

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“…The generalization of the results here reported and the case of higher dimensional systems seems feasible considering recent advances in integrated waveguide quantum circuits [29] and considering protocols like the one proposed by Jiménez et al [13].…”

Section: Discussionmentioning

confidence: 99%

“…USD at the IDP limit was experimentally achieved via a free-space interferometer which recorded conclusive and inconclusive events [11] and has also been experimentally studied in the context of three non-orthogonal linearly independent states [12]. Recently, a proposal for doing the conclusive discrimination of 2 M (with M integer) symmetric states, considering only linear optics, was reported [13]. Today, USD plays an important role in quantum communication and quantum computing, being at the core of many quantum cryptographic schemes and probabilistic quantum algorithms [14].…”

Section: Introductionmentioning

confidence: 99%

Unambiguous modification of nonorthogonal single- and two-photon polarization states

et al. 2009

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In this work we propose a probabilistic method which allows an unambiguous modification of two non-orthogonal quantum states. We experimentally implement this protocol by using two-photon polarization states generated in the process of spontaneous parametric down conversion. In the experiment, for codifying initial quantum states, we consider single photon states and heralded detection. We show that the application of this protocol to entangled states, it allows a fine control of the amount of entanglement of the initial state.

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“…We now assume that the unitary transformation U sa of Eq. (6) can be experimentally realized [37][38][39][40][41] and applied to the state ρ s |A a A|. This generates a new bipartite state ρ sa given by…”

Section: Qubit Tomography Via Optimal Unambiguous State Discriminmentioning

confidence: 99%

Quantum tomography via unambiguous state discrimination

Salazar

Delgado

2012

Phys. Rev. A

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We study the determination of an unknown mixed state of a d-dimensional quantum system by means of unambiguous state discrimination. We show that optimal and nonoptimal unambiguous state discrimination can be used to reconstruct unknown states of a qubit. This result is extended to the case of a qudit by a sequence of reconstructions in two-dimensional subspaces. The total number of projections scales approximately as 2d 2 for d large; this is twice as much as in the case of tomography based on mutually unbiased bases or symmetric informationally complete positive-operator-valued measures, and less than the d 3 projections required by standard tomography.

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Experimental scheme for unambiguous discrimination of linearly independent symmetric states

Cited by 22 publications

References 38 publications

Maximum-confidence discrimination among symmetric qudit states

Maximum-confidence discrimination among symmetric qudit states

Unambiguous modification of nonorthogonal single- and two-photon polarization states

Quantum tomography via unambiguous state discrimination

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