2005/12/31 by Shengjun Wu, Scott M. Cohen, Yuqing Sun +1
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physreva.73.042311
published as Phys. Rev. A 73, 042311 (2006) · Short new section VII added. Latex 23 pages, 1 PSTricks figure in text
arxiv created 2006/02/14 · openalex publication_date 2006/04/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 Ld messages can be transmitted with perfect fidelity, and in the unambiguous case where when the protocol succeeds (probability \ensuremathτx) Bob knows for sure that Alice sent message x, and when it fails (probability 1\ensuremath-\ensuremathτx) he knows it has failed. Alice is allowed any single-shot (one use) encoding procedure, and Bob any single-shot measurement. For D\ensuremath\leqslantD a bound is obtained for Ld 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 Ld is strictly less than D2 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\ensuremath\leqslantD, assuming \ensuremathτx>0 for a set of DD messages, and a bound is obtained for the average ⟨1∕\ensuremathτ⟩. A bound on the average ⟨\ensuremathτ⟩ requires an additional assumption of encoding by isometries (unitaries when D=D) that are orthogonal for different messages. Both bounds are saturated when \ensuremathτx is a constant independent of x, by a protocol based on one-shot entanglement concentration. For D>D it is shown that (at least) D2 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.