Deterministic and unambiguous dense coding
- Physics Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213 (United States)
Optimal dense coding using a partially-entangled pure state of Schmidt rank D and a noiseless quantum channel of dimension D is studied both in the deterministic case where at most L{sub d} messages can be transmitted with perfect fidelity, and in the unambiguous case where when the protocol succeeds (probability {tau}{sub x}) Bob knows for sure that Alice sent message x, and when it fails (probability 1-{tau}{sub x}) he knows it has failed. Alice is allowed any single-shot (one use) encoding procedure, and Bob any single-shot measurement. For D{<=}D a bound is obtained for L{sub d} in terms of the largest Schmidt coefficient of the entangled state, and is compared with published results by Mozes et al. [Phys. Rev. A71, 012311 (2005)]. For D>D it is shown that L{sub d} is strictly less than D{sup 2} unless D is an integer multiple of D, in which case uniform (maximal) entanglement is not needed to achieve the optimal protocol. The unambiguous case is studied for D{<=}D, assuming {tau}{sub x}>0 for a set of DD messages, and a bound is obtained for the average <1/{tau}>. A bound on the average <{tau}> requires an additional assumption of encoding by isometries (unitaries when D=D) that are orthogonal for different messages. Both bounds are saturated when {tau}{sub x} is a constant independent of x, by a protocol based on one-shot entanglement concentration. For D>D it is shown that (at least) D{sup 2} messages can be sent unambiguously. Whether unitary (isometric) encoding suffices for optimal protocols remains a major unanswered question, both for our work and for previous studies of dense coding using partially-entangled states, including noisy (mixed) states.
- OSTI ID:
- 20787084
- Journal Information:
- Physical Review. A, Vol. 73, Issue 4; Other Information: DOI: 10.1103/PhysRevA.73.042311; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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