Four locally indistinguishable ququad-ququad orthogonal maximally entangled states

• Published in: Physical review letters Vol. 109; no. 2; p. 020506
• Main Authors: Yu, Nengkun, Duan, Runyao, Ying, Mingsheng
• Format: Journal Article
• Language: English
• Published: United States 13.07.2012
• ISSN: 1079-7114
• DOI: 10.1103/PhysRevLett.109.020506

We explicitly exhibit a set of four ququad-ququad orthogonal maximally entangled states that cannot be perfectly distinguished by means of local operations and classical communication. Before our work, it was unknown whether there is a set of d locally indistinguishable d⊗d orthogonal maximally entangled states for some positive integer d. We further show that a 2⊗2 maximally entangled state can be used to locally distinguish this set of states without being consumed, thus demonstrate a novel phenomenon of entanglement discrimination catalysis. Based on this set of states, we construct a new set K consisting of four locally indistinguishable states such that K(⊗m) (with 4(m) members) is locally distinguishable for some m greater than one. As an immediate application, we construct a noisy quantum channel with one sender and two receivers whose local zero-error classical capacity can achieve the full dimension of the input space but only with a multi-shot protocol.