Optimal Quantum Measurements for Two Pure and Mixed States

Levitin, Lev B.

doi:10.1007/978-1-4899-1391-3_43

Cited by 39 publications

(41 citation statements)

References 16 publications

(26 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It may be related to the conjecture [11,4] that the optimal accessible information for two arbitrary density matrices can always be achieved by a von Neumann measurement. This has been proved in two dimensions [11], and is supported by numerical studies in higher dimensions [4]. We thus conjecture: Conjecture 2 C 1,A = C 1,1 for two mixed states in arbitrary dimensions.…”

Section: The Upper Bound On C 11mentioning

confidence: 99%

The adaptive classical capacity of a quantum channel, or Information capacities of three symmetric pure states in three dimensions

Shor

2004

IBM J. Res. & Dev.

View full text Add to dashboard Cite

We investigate the capacity of three symmetric quantum states in three real dimensions to carry classical information. Several such capacities have already been defined, depending on what operations are allowed in the sending and receiving protocols. These include the C 1,1 capacity, which is the capacity achievable if separate measurements must be used for each of the received states, and the C 1,∞ capacity, which is the capacity achievable if joint measurements are allowed on the tensor product of all the received states. We discover a new classical information capacity of quantum channels, the adaptive capacity C 1,A , which lies strictly between the C 1,1 and the C 1,∞ capacities. The adaptive capacity allows what is known as the LOCC (local operations and classical communication) model of quantum operations for decoding the channel outputs. This model requires each of the signals to be measured by a separate apparatus, but allows the quantum states of these signals to be measured in stages, with the first stage partially reducing their quantum states, and where measurements in subsequent stages may depend on the results of a classical computation taking as input the outcomes of the first round of measurements. We also show that even in three dimensions, with the information carried by an ensemble containing three pure states, achieving the C 1,1 capacity may require a POVM with six outcomes.

show abstract

Section: The Upper Bound On C 11mentioning

confidence: 99%

The adaptive classical capacity of a quantum channel, or Information capacities of three symmetric pure states in three dimensions

Shor

2004

IBM J. Res. & Dev.

View full text Add to dashboard Cite

show abstract

“…For ensembles below this boundary, optimal discrimination requires three measurement vectors-but vectors different than the three optimal regime B measurement vectors 6 . In the case of binary ensembles E(1, θ), the same measurement is already known to be optimal for both accessible information and minimum-error discrimination 11 . Interestingly, there are many other ensembles (all those in regime C with q ≥ b D (θ)-see Figure 3) for which the same measurement serves optimally for both purposes.…”

Section: Accessible Information In E(q θ)mentioning

confidence: 98%

“…The sum in (11) can be viewed as an expectation E[J(Σ)] where Σ is a random variable with values σ m ∈ [0, 1] and corresponding probabilities w m = P (Σ = σ m ). Then the accessible information in E is…”

Section: Accessible Information In Z-symmetric Ensemblesmentioning

confidence: 99%

Information accessible by measurement in mirror-symmetric ensembles of qubit states

Frey

2006

SPIE Proceedings

View full text Add to dashboard Cite

We formulate an expression for the accessible information in mirror-symmetric ensembles of real qubit states. This expression is used to make a detailed study of optimum quantum measurements for extracting the accessible information in three-state, mirror-symmetric ensembles. Distinct measurement regimes are identified for these ensembles with optimal measurement strategies involving different numbers of measurement operators, similar to results found for minimum error discrimination. Our resultsgeneralize known results for the accessible information in two pure states and in the trine ensemble.

show abstract

“…[7,26], but totally from a different viewpoint. Note that Fuchs's quantumness measure [7] is naturally compatible with the definition of quantum discord.…”

mentioning

confidence: 99%

Quantum discord of ensemble of quantum states

Yao

Huang

Zou

et al. 2014

Quantum Inf Process

View full text Add to dashboard Cite

We highlight an information-theoretic meaning of quantum discord as the gap between the accessible information and the Holevo bound in the framework of ensemble of quantum states. This complementary relationship implies that a large amount of pre-existing arguments about the evaluation of quantum discord can be directly applied to the accessible information and vice versa. For an ensemble of two pure qubit states, we show that one can evade the optimization problem with the help of the Koashi-Winter relation. Further, for the general case (two mixed qubit states), we recover the main results presented by Fuchs and Caves [Phys. Rev. Lett. 73, 3047 (1994)], but totally from the perspective of quantum discord. Following this line of thought, we also investigate the geometric discord as an indicator of quantumness of ensembles in detail. Finally, we give an example to elucidate the difference between quantum discord and geometric discord with respect to optimal measurement strategies. Introduction. Since its introduction in 2001, the concept of quantum discord [1, 2] has been gradually recognized and used as an indicator of the quantumness of composite quantum systems. Most recently, it is arousing increasing interest in its quantification and applications (for a recent review see [3] and references therein). Quantum discord originates from the inequivalence of two classically identical expressions of mutual information in the quantum realm. For a composite bipartite system ρ ab , the quantum mutual information is defined as

show abstract

Optimal Quantum Measurements for Two Pure and Mixed States

Cited by 39 publications

References 16 publications

The adaptive classical capacity of a quantum channel, or Information capacities of three symmetric pure states in three dimensions

The adaptive classical capacity of a quantum channel, or Information capacities of three symmetric pure states in three dimensions

Information accessible by measurement in mirror-symmetric ensembles of qubit states

Quantum discord of ensemble of quantum states

Contact Info

Product

Resources

About