Non-optimality of unitary operations for dense coding

TL;DR

This paper challenges the assumption that unitary operations are always optimal for dense coding, providing numerical and analytical evidence that non-unitary operations can sometimes achieve higher classical information transmission.

Contribution

It demonstrates, through numerical and analytical methods, that non-unitary encoding can outperform unitary encoding in dense coding under certain conditions.

Findings

Non-unitary operations can encode more information than unitary ones in some dense coding scenarios.

Numerical evidence supports the existence of cases where non-unitary encoding is superior.

Analytical arguments explain the circumstances favoring non-unitary encoding.

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.