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arXiv 0709.0563quant-ph
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确定性密集编码与纠缠熵

Deterministic dense coding and entanglement entropy

P. S. Bourdon, E. Gerjuoy, J. P. McDonald, H. T. Williams

摘要:

本文对标准的两方确定性密码协议进行了分析研究,在该协议下,完全可区分的消息通过一对纯态非最大纠缠量子点的量子点进行通信|S>.我们的结果包括:(i)我们证明了一个状态是可能的,|S>具有较低的纠缠熵,以支持发送比具有较高的纠缠熵的更大数量的完全可区分的消息,证实了在Mozes等人[Phys.Rev.A71012311(2005)]中通过数值分析提出的结果。(ii)通过显式构造局域幺正算子族,我们验证了Mozes等人关于d = 3和d=4维情况下支持d + j个信息发送的最小纠缠熵的猜想,j = 2,. d-1;此外,我们证明了猜想的j=2和j= d-1的情况在所有维度上都是有效的。(iii)鉴于|S>允许发送K个消息,并且具有c的平方屋顶作为其最大施密特系数,我们证明了由Wu等人[Phys.Rev.A73,042311(2006)]建立的不等式c <= d/K,如果K = d+1,而我们的局部么正结构表明,当K = d+2或K = 2d-1时,等式是可以实现的.

英文摘要:

We present an analytical study of the standard two-party deterministic dense-coding protocol, under which communication of perfectly distinguishable messages takes place via a qudit from a pair of non-maximally entangled qudits in pure state |S>. Our results include the following: (i) We prove that it is possible for a state |S> with lower entanglement entropy to support the sending of a greater number of perfectly distinguishable messages than one with higher entanglement entropy, confirming a result suggested via numerical analysis in Mozes et al. [Phys. Rev. A 71 012311 (2005)]. (ii) By explicit construction of families of local unitary operators, we verify, for dimensions d = 3 and d=4, a conjecture of Mozes et al. about the minimum entanglement entropy that supports the sending of d + j messages, j = 2, ..., d-1; moreover, we show that the j=2 and j= d-1 cases of the conjecture are valid in all dimensions. (iii) Given that |S> allows the sending of K messages and has the square roof of c as its largest Schmidt coefficient, we show that the inequality c <= d/K, established by Wu et al. [ Phys. Rev. A 73, 042311 (2006)], must actually take the form c < d/K if K = d+1, while our constructions of local unitaries show that equality can be realized if K = d+2 or K = 2d-1.

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