Discriminating<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>-qudit states using geometric structure

Ha, Donghoon; Kwon, Younghun

doi:10.1103/physreva.90.022330

Cited by 27 publications

(23 citation statements)

References 28 publications

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“…When only conclusive results are allowed, one possible strategy is to maximize Bob’s guessing probability. This strategy is called minimum error discrimination 1 – 5 . Meanwhile, when the quantum states of Alice are linearly independent, it is possible for Bob to develop a strategy whereby he can trust his conclusive result 6 , 7 .…”

Section: Introductionmentioning

confidence: 99%

Sequential state discrimination of coherent states

Namkung

Kwon

2018

Sci Rep

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Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum states when N receivers are separately located. In this report, we propose optical designs that can perform sequential state discrimination of two coherent states. For this purpose, we consider not only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior probabilities. Since our optical designs do not include electric feedback, they can be implemented without difficulty. Furthermore, we analyze our proposal for the case of photon loss. We also demonstrate that sequential state discrimination of two coherent states performs better than the probabilistic quantum cloning strategy. This proposal can facilitate multiparty QKD based on coherent states.

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Section: Introductionmentioning

confidence: 99%

Sequential state discrimination of coherent states

Namkung

Kwon

2018

Sci Rep

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“…Apart from studying some general features of the optimal measurement [3,4], in the beginning mainly the minimum-error discrimination of states obeying certain symmetry properties or of two mixed states was investigated, see e. g. [5][6][7][8][9][10][11][12]. The minimum-error discrimination of more than two states that are arbitrary has gained renewed interest only recently [13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Optimal measurements for the discrimination of quantum states with a fixed rate of inconclusive results

Herzog

2015

Phys. Rev. A

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We study the discrimination of N mixed quantum states in an optimal measurement that maximizes the probabihty of correct results while the probability of inconclusive results is fixed at a given value. After considering the discrimination of N states in a d -dimensional Hilbert space, we focus on the discrimination of qubit states. We develop a method to determine an optimal measurement for discriminating arbitrary qubit states, taking into account that often the optimal measurement is not unique and the maximum probabihty of correct results can be achieved by several different measurements. Analytical results are derived for a number of examples, mostly for the discrimination between qubit states which possess a partial symmetry, but also for discriminating N equiprobable qubit states and for the dicrimination between a pure and a uniformly mixed state in d dimensions.In the special case where the fixed rate of inconclusive results is equal to zero, our method provides a treatment for the minimum-error discrimination of arbitrary qubit states which differs from previous approaches.

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“…The diagonal elements of the matrix G 1 2 W can be made non-negative by appropriately fixing the phases of the |w i vectors in the following way: right-multiply W with a diagonal unitary W ′ , whose diagonal elements will be phases. From equation (15) it is seen that right-multiplying W with W ′ merely changes the phases of the ONB vectors |w i , and that they will still satisfy equation (16). We can vary the phases in W ′ so that the diagonals of G 1 2 W W ′ are non-negative.…”

Section: Rotationally Invariant Necessary and Sufficient Conditions Fmentioning

confidence: 99%

Minimum error discrimination for an ensemble of linearly independent pure states

Singal¹,

Ghosh²

2016

J. Phys. A: Math. Theor.

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Inspired by the work done by Belavkin [BelavkinV.P.,Stochastics,1,315(1975)], and independently by Mochon, [Phys.Rev.A73,032328,(2006)], we formulate the problem of minimum error discrimination of any ensemble of n linearly independent pure states by stripping the problem of its rotational covariance and retaining only the rotationally invariant aspect of the problem. This is done by embedding the optimal conditions in a matrix equality as well as matrix inequality. Employing the implicit function theorem in these conditions we get a set of first-order coupled ordinary non-linear differential equations which can be used to drag the solution from an initial point (where solution is known) to another point (whose solution is sought). This way of obtaining the solution can be done through a simple Taylor series expansion and analytic continuation when required. Thus, we complete the work done by Belavkin and Mochon by ultimately leading their theory to a solution for the minimum error discrimination problem of linearly independent pure state ensembles. We also compare the computational complexity of our technique with a barrier-type interior point method of SDP and show that our technique is computationally as efficient as (actually, a bit more than) the SDP algorithm, with the added advantage of being much simpler to implement.

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DiscriminatingN-qudit states using geometric structure

Cited by 27 publications

References 28 publications

Sequential state discrimination of coherent states

Sequential state discrimination of coherent states

Optimal measurements for the discrimination of quantum states with a fixed rate of inconclusive results

Minimum error discrimination for an ensemble of linearly independent pure states

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