arXiv:quant-ph/0306148 · Physical Review A

Comment II on “Dense coding in entangled states”

Omid Akhavan, A. T. Rezakhani

Published Jul 9, 2003• 11 citations

Abstract

In a recent Brief Report, L. Lee, D. Ahn, and S. W. Hwang [Phys. Rev. A 66, 024304 (2002)] have claimed that using pairwise entangled qubits gives rise to an exponentially more efficient dense coding when two parties are involved than using maximally entangled qubits shared among N parties. Here we show that their claim is not true.

DOI: 10.1103/physreva.68.016302

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arXiv:quant-ph/0306148 · Physical Review A

Comment II on “Dense coding in entangled states”

Omid Akhavan, A. T. Rezakhani

Published Jul 9, 2003• 11 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreva.68.016302

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arXiv:0906.0384Physical Review AFeb 16, 20104 citations

Recently, Yan and Gao [Phys. Rev. A 72, 012304 (2005)] presented a quantum secret sharing protocol which allows a secret message to be shared between two groups of parties (

m

parties in group 1 and

n

parties in group 2). Their protocol is claimed to be secure that, except with the cooperation of the entire group 1 or group 2, no subgroup of either group 1 or group 2 can extract the secret message. However, this study points out that the

m\text{th}

party (the last party to process the quantum state) of group 1 can maliciously replace the secret message with an arbitrary message without the detection of the other parties.

\sqrt{1/d}

), then Alice can convey to Bob one of

{d}^{2}

distinct messages. If $|\ensuremath{\Psi}\ensuremath{\rangle}$ is not maximally entangled, then Ji et al. [Phys. Rev. A 73, 034307 (2006)] have shown that under the original deterministic dense-coding protocol, in which messages are encoded by unitary operations performed on Alice's qudit, it is impossible to encode ${d}^{2}\ensuremath{-}1$ messages. Encoding ${d}^{2}\ensuremath{-}2$ messages is possible; see, for example, the numerical studies by Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. Answering a question raised by Wu et al. [Phys. Rev. A 73, 042311 (2006)], we show that when $|\ensuremath{\Psi}\ensuremath{\rangle}$ is not maximally entangled, the communications limit of ${d}^{2}\ensuremath{-}2$ messages persists even when the requirement that Alice encode by unitary operations on her qudit is weakened to allow encoding by more general quantum operators. We then describe a dense-coding protocol that can overcome this limitation with high probability, assuming the largest Schmidt coefficient of $|\ensuremath{\Psi}\ensuremath{\rangle}$ is sufficiently close to

\sqrt{1/d}

. In this protocol, ${d}^{2}\ensuremath{-}2$ of the messages are encoded via unitary operations on Alice's qudit, and the final $({d}^{2}\ensuremath{-}1)$-th message is encoded via a non-trace-preserving quantum operation.