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Realization of positive-operator-valued measures using measurement-assisted programmable quantum processors

Mário Ziman, Vladimír Bužek

We study possible realizations of generalized quantum measurements on measurement-assisted programmable quantum processors. We focus our attention on the realization of von Neumann measurements and informationally complete positive-operator-valued measures. Nielsen and Chuang [Phys. Rev. Lett. 79, 321 (1997)] have shown that two unitary transformations implementable by the same programmable processor require mutually orthogonal states. We show that two different von Neumann measurements can be encoded into nonorthogonal program states. Nevertheless, given the dimension of a Hilbert space of the program register the number of implementable von Neumann measurements is still limited. As an example of a programmable processor we use the so-called quantum-information distributor.We study possible realizations of generalized quantum measurements on measurement-assisted programmable quantum processors. We focus our attention on the realization of von Neumann measurements and informationally complete positive-operator-valued measures. Nielsen and Chuang [Phys. Rev. Lett. 79, 321 (1997)] have shown that two unitary transformations implementable by the same programmable processor require mutually orthogonal states. We show that two different von Neumann measurements can be encoded into nonorthogonal program states. Nevertheless, given the dimension of a Hilbert space of the program register the number of implementable von Neumann measurements is still limited. As an example of a programmable processor we use the so-called quantum-information distributor.

arXiv:quant-ph/0411135Physical Review AAug 29, 200527 citations

Quantum Measurement with a Positive Operator-Valued Measure

Howard E. Brandt

Acta Physica Hungarica B) Quantum ElectronicsJan 1, 20041 citation

Quantum Instruments and Positive Operator Valued Measures

Andrei Yu. Khrennikov

Springer eBooksJan 1, 20230 citations

Universality and optimality of programmable quantum processors

Mário Ziman, Buzek, V

We analyze and compare the optimality of approximate and probabilistic universal programmable quantum processors. We define several characteristics how to quantify the optimality and we study in detail performance of three types of programmable quantum processors based on (1) the C-NOT gate, (2) the SWAP operation, and (3) the model of the quantum information distributor - the QID processor. We show under which conditions the measurement assisted QID processor is optimal. We also investigate optimality of the so-called U-processors and we also compare the optimal approximative implementation of U(1) qubit rotations with the known probabilistic implementation as introduced by Vidal, Masanes and Cirac [ {\\em Phys. Rev. Lett.} {\\bf 88}, 047905 (2002)].We analyze and compare the optimality of approximate and probabilistic universal programmable quantum processors. We define several characteristics how to quantify the optimality and we study in detail performance of three types of programmable quantum processors based on (1) the C-NOT gate, (2) the SWAP operation, and (3) the model of the quantum information distributor - the QID processor. We show under which conditions the measurement assisted QID processor is optimal. We also investigate optimality of the so-called U-processors and we also compare the optimal approximative implementation of U(1) qubit rotations with the known probabilistic implementation as introduced by Vidal, Masanes and Cirac [ {\\em Phys. Rev. Lett.} {\\bf 88}, 047905 (2002)].

Dec 28, 20062 citations

Universal programmable unambiguous discrimination of two unknown states with two copies

Shouya Wang, Wen‐Hai Zhang

We investigate the universal programmable unambiguous discrimination of two unknown quantum states with two copies. We first present the optimal positive-operator valued measure (POVM) elements that determine the individual success probabilities. In terms of the positivity of an inconclusive operator, we derive the average success probability, which is higher than the average success probability of discriminating two unknown states with one copy given in the reference [Bergou and Hillery, Phys. Rev. Lett. 94, 160501 (2005)].We investigate the universal programmable unambiguous discrimination of two unknown quantum states with two copies. We first present the optimal positive-operator valued measure (POVM) elements that determine the individual success probabilities. In terms of the positivity of an inconclusive operator, we derive the average success probability, which is higher than the average success probability of discriminating two unknown states with one copy given in the reference [Bergou and Hillery, Phys. Rev. Lett. 94, 160501 (2005)].

AIP AdvancesOct 1, 20240 citations

Construction of Positive-Operator Valued Measures via Wavefunctions of Physical Systems

Xuehong Wang, Yan Li, Hong-Yi Su +1 more

International Journal of Theoretical PhysicsOct 9, 20120 citations

Publisher's Note: Realization of positive-operator-valued measures using measurement-assisted programmable quantum processors [Phys. Rev.72, 022343 (2005)]

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Publisher's Note: Realization of positive-operator-valued measures using measurement-assisted programmable quantum processors [Phys. Rev.72, 022343 (2005)]

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