The optimal approximation of qubit states with limited quantum states

Zhang, Li-qiang; Yu, Deng-hui; Yu, Chang-shui

doi:10.1016/j.physleta.2021.127286

Cited by 5 publications

(5 citation statements)

References 33 publications

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“…The optimal approximation of a quantum state with limited states has been addressed in various cases. [47][48][49][50][51][52] In refs. [47,48], optimally approximating an unavailable quantum state 𝜌 (quantum channel Φ) by the convex mixing of states (channels) drawn from a set of available states {v i } (channels {Ψ i }) was considered.…”

Section: Introductionmentioning

confidence: 99%

“…Later, the disposable quantum state set was extended from the eigenstates of the Pauli matrix to the eigenstates of any quantum logic gate, [51] and then to arbitrary quantum states without any restriction. [52] Up to now, all the relevant contributions have been only restricted to the qubit states. It remains open whether such an optimal problem could have a closed solution for a general high-dimensional state.…”

Section: Introductionmentioning

confidence: 99%

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The Best Approximation of an Objective State With a Given Set of Quantum States

Zhang

Zhou

2021

Annalen der Physik

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Approximating a quantum state by the convex mixing of some given states has strong experimental significance and provides alternative understandings of quantum resource theory. It is essentially a complex optimal problem which, up to now, has only partially solved for qubit states. Here, the most general case is focused on that the approximation of a d-dimensional objective quantum state by the given state set consisting of any number of (mixed-) states. The problem is thoroughly solved with a closed solution of the minimal distance in the sense of l 2 norm between the objective state and the set. In particular, the minimal number of states in the given set is presented to achieve the optimal distance. The validity of this closed solution is further verified numerically by several randomly generated quantum states.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Best Approximation of an Objective State With a Given Set of Quantum States

Zhang

Zhou

2021

Annalen der Physik

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“…The optimal approximation of a quantum state with limited states has been addressed in various cases [47][48][49][50][51][52]. In Refs.…”

Section: Introductionmentioning

confidence: 99%

“…[50]. Later, the disposable quantum state set was extended from the eigenstates of the Pauli matrix to the eigenstates of any quantum logic gate [51], and then to arbitrary quantum states without any restriction [52]. Up to now all the relevant contributions have been only restricted to the qubit states.…”

Section: Introductionmentioning

confidence: 99%

The best approximation of an objective state with a given set of quantum states

Zhang,

Zhou,

2021

Preprint

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Approximating a quantum state by the convex mixing of some given states has strong experimental significance and provides potential applications in quantum resource theory. Here we find a closed form of the minimal distance in the sense of l2 norm between a given d-dimensional objective quantum state and the state convexly mixed by those restricted in any given (mixed-) state set. In particular, we present the minimal number of the states in the given set to achieve the optimal distance. The validity of our closed solution is further verified numerically by several randomly generated quantum states.

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“…This study depends not only on the set of available states but also on the distance measures between quantum states. There were some work based on the trace norm [12][13][14][15]17] and fidelity [16].…”

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confidence: 99%

Optimal convex approximation of qubit states and geometry of completely represented states

Zhou¹,

Gao²,

Yan³

2021

EPL

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We investigate the optimal convex approximation, optimally approximating a desired and unavailable qubit state by the convex mixing of a given set of available states. When the available states are the eigenvectors of three Pauli matrices, we present the complete exact solution for the optimal convex approximation of an arbitrary qubit state based on the fidelity distance. By the comparison of optimal states based on fidelity and trace norm, the advantages and disadvantages of the optimal convex approximation are identified. Several examples are provided to support this. We also analyze the geometrical properties of the target states which can be completely represented by a set of available states. Using the feature of convex combination, we derive the maximum range of completely represented states and clearly illustrate that any qubit state can be optimally prepared by at most three available states in known useable states.

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The optimal approximation of qubit states with limited quantum states

Cited by 5 publications

References 33 publications

The Best Approximation of an Objective State With a Given Set of Quantum States

The Best Approximation of an Objective State With a Given Set of Quantum States

The best approximation of an objective state with a given set of quantum states

Optimal convex approximation of qubit states and geometry of completely represented states

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