Non-optimality of unitary operations for dense coding

Abstract

One of the primary goals of information theory is to provide limits on the amount of information it is possible to send through various types of communication channels, and to understand the encoding methods that will allow one to achieve such limits. An early surprise in the study of \textit{quantum} information theory was the discovery of dense coding, which demonstrated that it is possible to achieve higher rates for communicating classical information by transmitting quantum systems, rather than classical ones. To achieve the highest possible rate, the transmitted quantum system must initially be maximally entangled with another that is held by the receiver, and the sender can achieve this rate by encoding her messages with unitary operations. The situation where these two systems are not maximally entangled has been intensively studied in recent years, and to date it has appeared as though unitary encoding might well be optimal in all cases. Indeed, this optimality of unitary operations for quantum communication protocols has been found to hold under far more general conditions, extending well beyond the special case of dense coding. Nonetheless, we here present strong numerical evidence supported by analytical arguments that indicate there exist circumstances under which one can encode strictly more classical information using dense coding with non-unitary, as opposed to unitary, operations.

10 pages, 1 figure, comments welcome

References in corpus (5)

• Perfect Teleportation and Superdense Coding With W-States
• Not So SuperDense Coding - Deterministic Dense Coding with Partially Entangled States
• Deterministic and Unambiguous Dense Coding
• Deterministic dense coding and entanglement entropy
• Boundary effect of deterministic dense coding

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• Optimal probabilistic dense coding schemes
• Phase boundaries in deterministic dense coding
• Superiority in dense coding through non-Markovian stochasticity
• Overcoming a limitation of deterministic dense coding with a non-maximally entangled initial state
• POVMs are equivalent to projections for perfect state exclusion of three pure states in three dimensions
• When quantum memory is useful for dense coding