Deterministic dense coding and entanglement entropy

Abstract

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.Comment: 19 pages, 2 figures. Published versio

Augmented message-matrix approach to deterministic dense-coding theory

“…Solving for λ 0 produces Saturation has been demonstrated in [6] for the WCSG bound for K = d+2 and K = 2d−1. Generalization of the argument of this section for other K values is easily constructed, but shows that an improvement in the WCSG bound comes only for the case K = d + 1 shown above.…”

“…The deterministic dense coding protocol, first described by Bennett and Wiesner [1] in 1992, has been the subject of numerous investigations ( [2]- [6] and references therein). Here, therefore, we describe the protocol and its associated formalism only briefly.…”

Conditions for Bipartite General Bell States

“…Liu et al studied multi-parties in the d-dimensional case, 13,14 and it has been demonstrated experimentally. 15,16 Quantum dense coding can be described as follows.…”

Optimal probabilistic dense coding schemes

“…In the first, one optimizes the encoding/decoding processes while trying to transmit the same amount of information that would be possible with a maximally entangled state [5][6][7][8][9][10][11][12]. In the second, one seeks to maximize the number of perfectly distinguishable messages that can be encoded and transmitted through the shared entangled state [13][14][15][16][17]. 1 Our work follows the first line of investigation and, in this context, we assume that Alice's encoding scheme will be the standard one presented in the original dense coding proposal [4].…”