Deterministic and Unambiguous Dense Coding
| dc.creator | Wu, Shengjun | |
| dc.creator | Cohen, Scott M. | |
| dc.creator | Sun, Yuqing | |
| dc.creator | Griffiths, Robert B. | |
| dc.date | 2005-12-20 | |
| dc.date | 2006-02-14 | |
| dc.date.accessioned | 2026-07-07T06:56:40Z | |
| dc.date.available | 2026-07-07T06:56:40Z | |
| dc.description | Optimal dense coding using a partially-entangled pure state of Schmidt rank $\bar D$ and a noiseless quantum channel of dimension $D$ is studied both in the deterministic case where at most $L_d$ messages can be transmitted with perfect fidelity, and in the unambiguous case where when the protocol succeeds (probability $τ_x$) Bob knows for sure that Alice sent message $x$, and when it fails (probability $1-τ_x$) he knows it has failed. Alice is allowed any single-shot (one use) encoding procedure, and Bob any single-shot measurement. For $\bar D\leq D$ a bound is obtained for $L_d$ in terms of the largest Schmidt coefficient of the entangled state, and is compared with published results by Mozes et al. For $\bar D > D$ it is shown that $L_d$ is strictly less than $D^2$ unless $\bar D$ 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 $\bar D \leq D$, assuming $τ_x>0$ for a set of $\bar D D$ messages, and a bound is obtained for the average $\lgl1/τ\rgl$. A bound on the average $\lglτ\rgl$ requires an additional assumption of encoding by isometries (unitaries when $\bar D=D$) that are orthogonal for different messages. Both bounds are saturated when $τ_x$ is a constant independent of $x$, by a protocol based on one-shot entanglement concentration. For $\bar D > D$ it is shown that (at least) $D^2$ 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. | |
| dc.description | Short new section VII added. Latex 23 pages, 1 PSTricks figure in text | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0512169 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0512169 | |
| dc.identifier | Phys. Rev. A 73, 042311 (2006) | |
| dc.identifier | doi:10.1103/PhysRevA.73.042311 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106729 | |
| dc.subject | Quantum Physics | |
| dc.title | Deterministic and Unambiguous Dense Coding | |
| dc.type | text |