On the Chernoff Distance for Asymptotic LOCC Discrimination of Bipartite Quantum States

• Published in: Communications in mathematical physics Vol. 285; no. 1; pp. 161 - 174
• Main Authors: Matthews, William, Winter, Andreas
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.01.2009; Springer
• Subjects: Classical and Quantum Gravitation; Complex Systems; Exact sciences and technology; Mathematical and Computational Physics; Mathematical methods in physics; Mathematical Physics; Other topics in mathematical methods in physics; Physics; Physics and Astronomy; Quantum Physics; Relativity Theory; Theoretical; Pure State; Error Probability; Bipartite State; Werner State; Positive Partial Transpose; Lower bound; Linear programming; Probability distribution; Error estimation; Mathematical physics; State constraint
• ISSN: 0010-3616; 1432-0916
• DOI: 10.1007/s00220-008-0582-6

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  × 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.