Optimal probabilistic dense coding schemes
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Universidade Federal de Minas Gerais
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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.
Abstract
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Teoria da codificação
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Dense coding, Quantum-state separation, Maximum-confidence measurements, Multistage decoding
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https://link.springer.com/article/10.1007/s11128-017-1545-7#citeas