dorsal/arxiv
View SchemaDeterministic and Unambiguous Dense Coding
| Authors | Shengjun Wu, Scott M. Cohen, Yuqing Sun, Robert B. Griffiths |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512169 |
| URL | https://arxiv.org/abs/quant-ph/0512169 |
| DOI | 10.1103/PhysRevA.73.042311 |
| Journal | Phys. Rev. A 73, 042311 (2006) |
Abstract
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 $\tau_x$) Bob knows for sure that Alice sent message $x$, and when it fails (probability $1-\tau_x$) 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 $\tau_x>0$ for a set of $\bar D D$ messages, and a bound is obtained for the average $\lgl1/\tau\rgl$. A bound on the average $\lgl\tau\rgl$ requires an additional assumption of encoding by isometries (unitaries when $\bar D=D$) that are orthogonal for different messages. Both bounds are saturated when $\tau_x$ 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.
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"abstract": "Optimal dense coding using a partially-entangled pure state of Schmidt rank\n$\\bar D$ and a noiseless quantum channel of dimension $D$ is studied both in\nthe deterministic case where at most $L_d$ messages can be transmitted with\nperfect fidelity, and in the unambiguous case where when the protocol succeeds\n(probability $\\tau_x$) Bob knows for sure that Alice sent message $x$, and when\nit fails (probability $1-\\tau_x$) he knows it has failed. Alice is allowed any\nsingle-shot (one use) encoding procedure, and Bob any single-shot measurement.\nFor $\\bar D\\leq D$ a bound is obtained for $L_d$ in terms of the largest\nSchmidt coefficient of the entangled state, and is compared with published\nresults by Mozes et al. For $\\bar D \u003e D$ it is shown that $L_d$ is strictly\nless than $D^2$ unless $\\bar D$ is an integer multiple of $D$, in which case\nuniform (maximal) entanglement is not needed to achieve the optimal protocol.\nThe unambiguous case is studied for $\\bar D \\leq D$, assuming $\\tau_x\u003e0$ for a\nset of $\\bar D D$ messages, and a bound is obtained for the average\n$\\lgl1/\\tau\\rgl$. A bound on the average $\\lgl\\tau\\rgl$ requires an additional\nassumption of encoding by isometries (unitaries when $\\bar D=D$) that are\northogonal for different messages. Both bounds are saturated when $\\tau_x$ is a\nconstant independent of $x$, by a protocol based on one-shot entanglement\nconcentration. For $\\bar D \u003e D$ it is shown that (at least) $D^2$ messages can\nbe sent unambiguously. Whether unitary (isometric) encoding suffices for\noptimal protocols remains a major unanswered question, both for our work and\nfor previous studies of dense coding using partially-entangled states,\nincluding noisy (mixed) states.",
"arxiv_id": "quant-ph/0512169",
"authors": [
"Shengjun Wu",
"Scott M. Cohen",
"Yuqing Sun",
"Robert B. Griffiths"
],
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"quant-ph"
],
"doi": "10.1103/PhysRevA.73.042311",
"journal_ref": "Phys. Rev. A 73, 042311 (2006)",
"title": "Deterministic and Unambiguous Dense Coding",
"url": "https://arxiv.org/abs/quant-ph/0512169"
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