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 nonmaximally entangled qudits in a pure state vertical bar psi >. Our results include the following: (i) We prove that it is possible for a state vertical bar psi > 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 [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 about the minimum entanglement entropy that supports the sending of d+j messages, 2 <= j <= 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 vertical bar psi > allows the sending of K messages and has root lambda(0) as its largest Schmidt coefficient, we show that the inequality lambda(0)<= d/K, established by Wu [Phys. Rev. A 73, 042311 (2006)], must actually take the form lambda(0)< 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.
原文链接
分享
引用
