Optimal probabilistic dense coding schemes

Abstract

Dense coding with non-maximally entangled states has been investigated in many different scenarios. We revisit this problem for protocols adopting the standard encoding scheme. In this case, the set of possible classical messages cannot be perfectly distinguished due to the non-orthogonality of the quantum states carrying them. So far, the decoding process has been approached in two ways: (i) The message is always inferred, but with an associated (minimum) error; (ii) the message is inferred without error, but only sometimes; in case of failure, nothing else is done. Here, we generalize on these approaches and propose novel optimal probabilistic decoding schemes. The first uses quantum-state separation to increase the distinguishability of the messages with an optimal success probability. This scheme is shown to include (i) and (ii) as special cases and continuously interpolate between them, which enables the decoder to trade-off between the level of confidence desired to identify the received messages and the success probability for doing so. The second scheme, called multistage decoding, applies only for qudits ($d$-level quantum systems with $d>2$) and consists of further attempts in the state identification process in case of failure in the first one. We show that this scheme is advantageous over (ii) as it increases the mutual information between the sender and receiver.

18 pages, 8 figures

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Cited by in corpus (5)

• Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies
• One-shot conclusive multiport quantum dense coding capacities
• Coherence based on positive operator-valued measures for standard and concatenated quantum state discrimination with inconclusive results
• Superiority in dense coding through non-Markovian stochasticity
• Experimental optimal discrimination of $N$ states of a qubit with fixed rates of inconclusive outcomes