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

Torres-Ruiz, F. A.; Aguirre, J.F.; Delgado, A.; Lima, G.; Neves, Leonardo; Pádua, S.; Roa, Luis; Saavedra, C.

doi:10.1103/physreva.79.052113

Cited by 25 publications

(22 citation statements)

References 31 publications

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“…The experiment described in Ref. [20] was implemented by using a 351.1 nm singlemode Ar-ion laser pump with a 200 mW and 5-mm-thick BBO crystal, cut for type-II phase matching which allows a higher stability. Our proposed scheme for linearly independent pure-state decomposition and unambiguous quantum state discrimination could also be implemented with thit setup.…”

Section: Discussionmentioning

confidence: 99%

Linearly independent pure-state decomposition and quantum state discrimination

2011

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We put the pure-state decomposition mathematical property of a mixed state to a physical test. We begin by characterizing all the possible decompositions of a rank-two mixed state by means of the complex overlap between two involved states. The physical test proposes a scheme of quantum state recognition of one of the two linearly independent states which arise from the decomposition. We find that the two states associated with the balanced pure-state decomposition have the smaller overlap modulus and therefore the smallest probability of being discriminated conclusively, while in the nonconclusive scheme they have the highest probability of having an error. In addition, we design an experimental scheme which allows to discriminate conclusively and optimally two nonorthogonal states prepared with different a priori probabilities. Thus, we propose a physical implementation for this linearly independent pure-state decomposition and state discrimination test by using twin photons generated in the process of spontaneous parametric down conversion. The information-state is encoded in one photon polarization state whereas the second single-photon is used for heralded detection.

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Section: Discussionmentioning

confidence: 99%

Linearly independent pure-state decomposition and quantum state discrimination

2011

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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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“…The probabilistic cloning scheme is a particular example of this [10]. Recently, the mapping between sets of nonorthogonal states has been connected to the control of quantum state preparation, entanglement modification [11], and interference in the quantum eraser [12]. The role of majorization in describing quantum operations for probabilistic and deterministic dynamics of a system has been studied with respect to finding the conditions for mixing enhancement for all initial states [13].…”

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confidence: 99%

“…(11)], for η 1 = η 2 and different values of θ . We have assumed |α| = 1/ √ 3 and θ = f π/2, where f is indicated for each of the curves in the figure.…”

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Conclusive modification of the overlap between two quantum states

Roa¹,

Guevara²,

Delgado³

2010

Phys. Rev. A

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The task of changing the overlap between two quantum states cannot be performed by making use of unitary evolution only. However, by means of a unitary-reduction process, it could be modified. Here we study in detail the problem of mapping two known pure states onto two other states in such a way that the overlap between the outcome states is different from the one of the initial states. We show that the modulus of the overlap can be reduced only probabilistically, whereas it can be increased deterministically. Our analysis shows that the phases of the involved overlaps play an important role in the increase of the success probability of the desired process.The unambiguous state discrimination processes [1-9] can be viewed as probabilistic conclusive mappings connecting a set of initial states with nonvanishing overlap with a set of orthogonal final states. One can think in terms of a more general process consisting of a probabilistic conclusive mapping which connects two sets corresponding to initial and final states, each of them with different overlaps. The probabilistic cloning scheme is a particular example of this [10]. Recently, the mapping between sets of nonorthogonal states has been connected to the control of quantum state preparation, entanglement modification [11], and interference in the quantum eraser [12]. The role of majorization in describing quantum operations for probabilistic and deterministic dynamics of a system has been studied with respect to finding the conditions for mixing enhancement for all initial states [13]. Zhou et al. constructed the unitary implementation of state transformations in a composed system, obtaining the necessary and sufficient conditions for the existence of the desired maps [14].In this work, we study the conclusive mapping between two pairs of states with different overlaps. The transformation is performed by means of a unitary-reduction process on the primary and an ancillary system. We allow different a priori probabilities of the two initial states, and we take into account the complex nature of the overlap between the states. We find conditions that guarantee the existence of the mapping, and we obtain the optimal success probability. Also, we discuss the relation of the proposed mapping with some known quantum information protocols, such as quantum deleting and quantum cloning. We compare the optimal success probability of our scheme with the one obtained via an alternative scheme using the unambiguous state discrimination.Let us consider a system s described by a two-dimensional Hilbert space H s . This system is prepared randomly in one of the states |α i s (i = 1, 2), with a priori probabilities η i . Our aim is to map the states {|α i s } onto the states {|β i s }, where the overlaps α 1 | α 2 = α and β 1 | β 2 = β are different. The mapping must be implemented conclusively, that is, it must be known with certainty when it has been perfectly carried out, and with the highest possible success probability.In order to implement the mapping, we introduce an ...

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

Cited by 25 publications

References 31 publications

Linearly independent pure-state decomposition and quantum state discrimination

Linearly independent pure-state decomposition and quantum state discrimination

Quantum tomography via unambiguous state discrimination

Conclusive modification of the overlap between two quantum states

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