Deterministic dense coding and entanglement entropy
- Department of Mathematics, Washington and Lee University, Lexington, Virginia 24450 (United States)
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 |{psi}>. Our results include the following: (i) We prove that it is possible for a state |{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 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, 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 |{psi}> allows the sending of K messages and has {radical}({lambda}{sub 0}) as its largest Schmidt coefficient, we show that the inequality {lambda}{sub 0}{<=}d/K, established by Wu et al. [Phys. Rev. A 73, 042311 (2006)], must actually take the form {lambda}{sub 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.
- OSTI ID:
- 21140450
- Journal Information:
- Physical Review. A, Vol. 77, Issue 2; Other Information: DOI: 10.1103/PhysRevA.77.022305; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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