Optimal state discrimination in general probabilistic theories

Kimura, Gen; Miyadera, Takayuki; Imai, Hideki

doi:10.1103/physreva.79.062306

Cited by 42 publications

(85 citation statements)

References 27 publications

(48 reference statements)

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“…Some fundamental aspects of information physics, such as the no-broadcasting principle and teleportation, are extensively studied within this general framework [2,6]. In [7,8], the authors investigated the state discrimination problems under such a general framework where they call it general probabilistic theories (GPT). They also studied the distinguishability measures and entropies in GPT [9,10].…”

Section: Introductionmentioning

confidence: 99%

Measurement interpretation and information measures in general probabilistic theory

Zhu

Zhang

2013

Open Physics

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Abstract:The incompatibility of dynamics postulate (unitary evolution) and the measurement postulate (wave-packet collapse) of quantum mechanics has recently been solved by Zurek from an information transfer perspective. Luo gave his derivation by relaxing the repeatability postulate. In this paper, we reconsider Luo's derivation in the setting of general probabilistic theory (GPT). We also introduce the concept of sub-and super-fidelity in GPT and discuss their properties. PACS

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Section: Introductionmentioning

confidence: 99%

Measurement interpretation and information measures in general probabilistic theory

Zhu

Zhang

2013

Open Physics

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“…Note that this was also mentioned in Ref. [27] in the context of generalized probability theories. Now, for the SO(3) states, however, it is not fulfilled that the states in (34) are pure, since tr[σ 2 0 ] = (3 + 4β 2 )/9 < 1 for all β ∈ (0, 1/ √ 2].…”

Section: Examples In High Dimensionsmentioning

confidence: 89%

Minimum-error state discrimination constrained by the no-signaling principle

Hwang

Bae

2010

Journal of Mathematical Physics

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We provide a bound on the minimum error when discriminating among quantum states, using the no-signaling principle. The bound is general in that it depends on neither dimensions nor specific structures of given quantum states to be discriminated among. We show that the bound is tight for the minimum-error state discrimination between symmetric (both pure and mixed) qubit states. Moreover, the bound can be applied to a set of quantum states for which the minimum-error state discrimination is not known yet. Finally, our results strengthen the quantitative connection between two no-go theorems, the no-signaling principle and the no perfect state estimation.

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“…We shall use a useful family of ensembles which have been introduced in Ref. [1] and is later shown to be closely related to an optimal state discrimination strategy. A set of N-numbers {p i ,…”

Section: Introductionmentioning

confidence: 99%

“…p and τ i are called Helstrom ratio and conjugate state to ρ i , respectively. It has been proved that [1] P opt ≤ p.…”

Section: Introductionmentioning

confidence: 99%

The minimum-error discrimination via Helstrom family of ensembles and convex optimization

Jafarizadeh

Mazhari

Aali

2010

Quantum Inf Process

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Using the convex optimization method and Helstrom family of ensembles introduced in Ref.[1], we have discussed optimal ambiguous discrimination in qubit systems. We have analyzed the problem of the optimal discrimination of N known quantum states and have obtained maximum success probability and optimal measurement for N known quantum states with equiprobable prior probabilities and equidistant from center of the Bloch ball, not all of which are on the one half of the Bloch ball and all of the conjugate states are pure. An exact solution has also been given for arbitrary three known quantum states. The given examples which use our method include: 1. Diagonal N mixed states; 2. N equiprobable states and equidistant from center of the Bloch ball which their corresponding Bloch vectors are inclined at the equal angle from z axis; 3. Three mirror-symmetric states; 4. States that have been prepared with equal prior probabilities on vertices of a Platonic solid.

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Optimal state discrimination in general probabilistic theories

Cited by 42 publications

References 27 publications

Measurement interpretation and information measures in general probabilistic theory

Measurement interpretation and information measures in general probabilistic theory

Minimum-error state discrimination constrained by the no-signaling principle

The minimum-error discrimination via Helstrom family of ensembles and convex optimization

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