Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States

American Physical Society
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Journal article
Ying, Mingsheng, Duan, Runyao, and Yu, Nengkun 2012, 'Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States', Physical Review Letters, vol. 109, no. 2, pp. 020506-1-020506-5.
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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 4m 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.
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