arXiv:quant-ph/0506205

Distinguishing sets of quantum states

Rahul Jain

Published Jun 24, 2005• 4 citations

Abstract

Given two sets finite $S_0$ and $S_1$ of quantum states. We show necessary and sufficient conditions for distinguishing them by a measurement.

DOI: 10.48550/arxiv.quant-ph/0506205

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arXiv:quant-ph/0506205

Distinguishing sets of quantum states

Rahul Jain

Published Jun 24, 2005• 4 citations

arXiv HTML PDF

Abstract

Given two sets finite

S_0

and

S_1

of quantum states. We show necessary and sufficient conditions for distinguishing them by a measurement.

Given two sets finite $S_0$ and $S_1$ of quantum states. We show necessary and sufficient conditions for distinguishing them by a measurement.

DOI: 10.48550/arxiv.quant-ph/0506205

Related papers

On the conditions for discrimination between quantum states with minimum error

Stephen M Barnett, Sarah Croke

We provide a simple proof for the necessity of conditions for discriminating with minimum error between a known set of quantum states.

arXiv:0810.1919Journal of Physics A Mathematical and TheoreticalJan 14, 200958 citations

On a measure of distance for quantum strategies

Gus Gutoski

The present paper studies an operator norm that captures the distinguishability of quantum strategies in the same sense that the trace norm captures the distinguishability of quantum states or the diamond norm captures the distinguishability of quantum channels. Characterizations of its unit ball and dual norm are established via strong duality of a semidefinite optimization problem. A full, formal proof of strong duality is presented for the semidefinite optimization problem in question. This norm and its properties are employed to generalize a state discrimination result of Gutoski and Watrous [In Proceedings of the 22nd Symposium on Theoretical Aspects of Computer Science (STACS’05), Lecture Notes in Computer Science, Vol. 3404 (Springer, 2005), pp. 605–616. The generalized result states that for any two convex sets S0, S1 of strategies there exists a fixed interactive measurement scheme that successfully distinguishes any choice of S0 ∈ S0 from any choice of S1 ∈ S1 with bias proportional to the minimal distance between the sets S0 and S1 as measured by this norm. A similar discrimination result for channels then follows as a special case.The present paper studies an operator norm that captures the distinguishability of quantum strategies in the same sense that the trace norm captures the distinguishability of quantum states or the diamond norm captures the distinguishability of quantum channels. Characterizations of its unit ball and dual norm are established via strong duality of a semidefinite optimization problem. A full, formal proof of strong duality is presented for the semidefinite optimization problem in question. This norm and its properties are employed to generalize a state discrimination result of Gutoski and Watrous [In Proceedings of the 22nd Symposium on Theoretical Aspects of Computer Science (STACS’05), Lecture Notes in Computer Science, Vol. 3404 (Springer, 2005), pp. 605–616. The generalized result states that for any two convex sets S0, S1 of strategies there exists a fixed interactive measurement scheme that successfully distinguishes any choice of S0 ∈ S0 from any choice of S1 ∈ S1 with bias proportional to the minimal distance between the sets S0 and S1 as measured by this norm. A similar discrimination result for channels then follows as a special case.

arXiv:1008.4636Journal of Mathematical PhysicsMar 1, 201243 citations

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Tatiana Alieva, André M. Barbé

Examples of different pure quantum states which are not distinguishable by the finite set of their marginal distributions are presented.

Journal of Physics A Mathematical and GeneralOct 2, 19980 citations

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David A. Crosby, Jens C. Zorn

The static dipole polarizability of helium atoms in the metastable $2^{3}S_{1}$ and $2^{1}S_{0}$ states has been determined by measuring the deflection of a beam of excited helium atoms that is caused by an inhomogeneous electric field of known properties. The necessary velocity distribution information is obtained from time-of-flight measurements, and a resonance quenching technique made it possible to distinguish the singlet and triplet components of the beam. The results, $\ensuremath{\alpha}(2^{3}S_{1})=(44.6\ifmmode\pm\else\textpm\fi{}3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{3}$ and $\ensuremath{\alpha}(2^{1}S_{0})=(108\ifmmode\pm\else\textpm\fi{}13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{3}$ , agree with the theoretical value that has been used to calibrate earlier polarizability measurements of the alkali metals and the heavier noble gases.The static dipole polarizability of helium atoms in the metastable $2^{3}S_{1}$ and $2^{1}S_{0}$ states has been determined by measuring the deflection of a beam of excited helium atoms that is caused by an inhomogeneous electric field of known properties. The necessary velocity distribution information is obtained from time-of-flight measurements, and a resonance quenching technique made it possible to distinguish the singlet and triplet components of the beam. The results, $\ensuremath{\alpha}(2^{3}S_{1})=(44.6\ifmmode\pm\else\textpm\fi{}3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{3}$ and $\ensuremath{\alpha}(2^{1}S_{0})=(108\ifmmode\pm\else\textpm\fi{}13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{3}$, agree with the theoretical value that has been used to calibrate earlier polarizability measurements of the alkali metals and the heavier noble gases.

Physical Review AAug 1, 197725 citations

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William Matthews, Stephanie Wehner, Andreas Winter

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Jonathan Walgate, Lucién Hardy

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arXiv:quant-ph/0202034Physical Review LettersSep 16, 2002276 citations

Given two sets finite

S_0

and

S_1

of quantum states. We show necessary and sufficient conditions for distinguishing them by a measurement.

The static dipole polarizability of helium atoms in the metastable

2^{3}S_{1}

and

2^{1}S_{0}

states has been determined by measuring the deflection of a beam of excited helium atoms that is caused by an inhomogeneous electric field of known properties. The necessary velocity distribution information is obtained from time-of-flight measurements, and a resonance quenching technique made it possible to distinguish the singlet and triplet components of the beam. The results, $\ensuremath{\alpha}(2^{3}S_{1})=(44.6\ifmmode\pm\else\textpm\fi{}3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$

{\mathrm{cm}}^{3}

and $\ensuremath{\alpha}(2^{1}S_{0})=(108\ifmmode\pm\else\textpm\fi{}13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$

{\mathrm{cm}}^{3}

, agree with the theoretical value that has been used to calibrate earlier polarizability measurements of the alkali metals and the heavier noble gases.