Overcoming a limitation of deterministic dense coding with a nonmaximally entangled initial state

Journal Article · Mon Feb 15 04:00:00 EST 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.022314· OSTI ID:21408205

Bourdon, P S; Gerjuoy, E ^[1]

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1. Department of Mathematics, Washington and Lee University, Lexington, Virginia 24450 (United States)

Under two-party deterministic dense coding, Alice communicates (perfectly distinguishable) messages to Bob via a qudit from a pair of entangled qudits in pure state |{Psi}>. If |{Psi}> represents a maximally entangled state (i.e., each of its Schmidt coefficients is {radical}(1/d)), then Alice can convey to Bob one of d{sup 2} distinct messages. If |{Psi}> 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{sup 2}-1 messages. Encoding d{sup 2}-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 |{Psi}> is not maximally entangled, the communications limit of d{sup 2}-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 |{Psi}> is sufficiently close to {radical}(1/d). In this protocol, d{sup 2}-2 of the messages are encoded via unitary operations on Alice's qudit, and the final (d{sup 2}-1)-th message is encoded via a non-trace-preserving quantum operation.

• OSTI ID: 21408205
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 2 Vol. 81; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

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