TY - GEN

T1 - On the Chernoff distance for asymptotic LOCC discrimination of bipartite quantum states

AU - Matthews, William

AU - Winter, Andreas

PY - 2008

Y1 - 2008

N2 - Motivated by the recent discovery of a quantum Chernoff theorem for asymptotic state discrimination, we investigate the distinguishability of two bipartite mixed states under the constraint of local operations and classical communication (LOCC), in the limit of many copies. While for two pure states a result of Walgate et al. shows that LOCC is just as powerful as global measurements, data hiding states (DiVincenzo et al.) show that locality can impose severe restrictions on the distinguishability of even orthogonal states. Here we determine the optimal error probability and measurement to discriminate many copies of particular data hiding states (extremal d x d Werner states) by a linear programming approach. Surprisingly, the single-copy optimal measurement remains optimal for n copies, in the sense that the best strategy is measuring each copy separately, followed by a simple classical decision rule. We also put a lower bound on the bias with which states can be distinguished by separable operations. This is a shortened version of a paper [1] recently submitted to Communications in Mathematical Physics; here the proofs have been omitted.

AB - Motivated by the recent discovery of a quantum Chernoff theorem for asymptotic state discrimination, we investigate the distinguishability of two bipartite mixed states under the constraint of local operations and classical communication (LOCC), in the limit of many copies. While for two pure states a result of Walgate et al. shows that LOCC is just as powerful as global measurements, data hiding states (DiVincenzo et al.) show that locality can impose severe restrictions on the distinguishability of even orthogonal states. Here we determine the optimal error probability and measurement to discriminate many copies of particular data hiding states (extremal d x d Werner states) by a linear programming approach. Surprisingly, the single-copy optimal measurement remains optimal for n copies, in the sense that the best strategy is measuring each copy separately, followed by a simple classical decision rule. We also put a lower bound on the bias with which states can be distinguished by separable operations. This is a shortened version of a paper [1] recently submitted to Communications in Mathematical Physics; here the proofs have been omitted.

UR - http://www.scopus.com/inward/record.url?scp=52149090732&partnerID=8YFLogxK

U2 - 10.1109/ITW.2008.4578687

DO - 10.1109/ITW.2008.4578687

M3 - Conference contribution

AN - SCOPUS:52149090732

SN - 9781424422708

T3 - 2008 IEEE Information Theory Workshop, ITW

SP - 364

EP - 367

BT - 2008 IEEE Information Theory Workshop, ITW

T2 - 2008 IEEE Information Theory Workshop, ITW

Y2 - 5 May 2008 through 9 May 2008

ER -