Quantum channels showing superadditivity in classical capacity

Sasaki, Masahide; Kato, Keizo; Izutsu, Masayuki; Hirota, Osamu

doi:10.1103/physreva.58.146

Cited by 124 publications

(140 citation statements)

References 22 publications

(36 reference statements)

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“…Two different approaches to the problem have been proposed. The first scenario, the ambiguous quantum state discrimination, has been analyzed by Holevo, Helstrom and others [6,7,8,9,10,11,12,13]. They considered discrimination of N mixed quantum states ρ j that are generated by Alice with the a-priori probabilities p j ,…”

Section: Introductionmentioning

confidence: 99%

Optimal discrimination of mixed quantum states involving inconclusive results

2003

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We propose a generalized discrimination scheme for mixed quantum states. In the present scenario we allow for certain fixed fraction of inconclusive results and we maximize the success rate of the quantum-state discrimination. This protocol interpolates between the Ivanovic-Dieks-Peres scheme and the Helstrom one. We formulate the extremal equations for the optimal positive operator valued measure describing the discrimination device and establish a criterion for its optimality. We also devise a numerical method for efficient solving of these extremal equations.

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Section: Introductionmentioning

confidence: 99%

Optimal discrimination of mixed quantum states involving inconclusive results

2003

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“…Unfortunately, attacking this problem by analytical means has chance to succeed only in the simplest cases (M = 2) [1], or cases with symmetric or linearly independent states [5,10,15,17,24]. In most situations one must resort to numerical methods.…”

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confidence: 99%

Finding optimal strategies for minimum-error quantum-state discrimination

2002

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We propose a numerical algorithm for finding optimal measurements for quantum-state discrimination. The theory of the semidefinite programming provides a simple check of the optimality of the numerically obtained results. With the help of our algorithm we calculate the minimum attainable error rate of a device discriminating among three particularly chosen non-symmetric qubit states.Nonorthogonality of quantum states is one of the basic features of quantum mechanics. Its deep consequences are reflected in all quantum protocols. For instance, it is well known that perfect decisions between two nonorthogonal states cannot be made. This has important implications for the information processing at the microscopic level since it sets a limit on the amount of information that can be encoded into a quantum system. Although perfect decisions between nonorthogonal quantum states are impossible, it is of importance to study measurement schemes performing this task in the optimum, though imperfect, way.Two conceptually different models of decision tasks have been studied. The first one is based on the minimization of the Bayesian cost function, which is nothing but a generalized error rate [1]. In the special case of linearly independent pure states, the second modelunambiguous discrimination of quantum states -makes an interesting alternative. The latter scheme combines the error-less discrimination with a certain fraction of inconclusive results [2][3][4].Ambiguous as well as unambiguous discrimination schemes have been intensively studied over the past few years. In consequence, the optimal measurements distinguishing between pair, trine, tetrad states, and linearly independent symmetric states are now well understood [5,7,6,[8][9][10][11][12][13][14][15][16][17]. Many of the theoretically discovered optimal devices have already been realized experimentally, mainly with polarized light [18][19][20][21]. As an example of the practical importance of the optimal decision schemes let us mention their use for the eavesdropping on quantum cryptosystems [22,23].The purpose of this paper is to develop universal method for optimizing ambiguous discrimination between generic quantum states.Assume that Alice sets up M different sources of quantum systems living in p-dimensional Hilbert space. The complete quantum-mechanical description of each source * e-mail: rehacek@phoenix.inf.upol.cz is provided by its density matrix. Alice chooses one of the sources at random using a chance device and sends the generated quantum system to Bob. Bob is also given M numbers {ξ i } specifying probabilities that i-th source is selected by the chance device. Bob is then required to tell which of the M sources {ρ i } generated the quantum system he had obtained from Alice. In doing this he should make as few mistakes as possible.It is well known [1] that each Bob's strategy can be described in terms of an M -component probability operator measure (POM) {Π j }, 0 < Π i < 1, j Π j = 1. Each POM element corresponds to one output channel of Bob's discri...

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“…The quantum information picture allows one to optimize not only over encodings, but also detection apparatus and states used in the protocol. Quantum measurements may be collective, i.e., performed on the outputs of a large number of channel uses, which in principle can enhance the communication performance over the best single-shot strategy, the phenomenon known as output superadditivity [18,20,31]. Therefore, a valid quantity describing communication performance is a regularized mutual information optimized over (possibly collective) output measurements…”

Section: Communication Theorymentioning

confidence: 99%

“…In that picture many fundamental results have been obtained concerning both specific transmission protocols [2][3][4][5][6][7] and general optimal bounds [8][9][10][11][12][13]. The application of laws of quantum mechanics has allowed for a deeper analysis of communication [14][15][16][17] and showing such effects as output and input superadditivity [18][19][20] or finite optimal rates even for noiseless channels, emerging from nonclassical phenomena such as entanglement or the Heisenberg uncertainty principle.…”

Section: Introductionmentioning

confidence: 99%

Classical capacity per unit cost for quantum channels

Jarzyna

2017

Phys. Rev. A

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In most communication scenarios, sending a symbol encoded in a quantum state requires spending resources such as energy, which can be quantified by a cost of communication. A standard approach in this context is to quantify the performance of communication protocol by classical capacity, quantifying the maximal amount of information that can be transmitted through a quantum channel per single use of the channel. However, different figures of merit are also possible, and a particularly well-suited one is the classical capacity per unit cost, which quantifies the maximal amount of information that can be transmitted per unit cost. I generalize this concept to account for the quantum nature of the information carriers and communication channels and show that if there exists a state with cost equal to zero, e.g. a vacuum state, the capacity per unit cost can be expressed by a simple formula containing maximization of the relative entropy between two quantum states. This enables me to analyze the behavior of photon information efficiency for general communication tasks and show simple bounds on the capacity per unit cost in terms of quantities familiar from quantum estimation theory. I calculate also the capacity per unit cost for general Gaussian quantum channels.

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Quantum channels showing superadditivity in classical capacity

Cited by 124 publications

References 22 publications

Optimal discrimination of mixed quantum states involving inconclusive results

Optimal discrimination of mixed quantum states involving inconclusive results

Finding optimal strategies for minimum-error quantum-state discrimination

Classical capacity per unit cost for quantum channels

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