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Communicating through probabilities: does quantum theory optimize the transfer of information? (English) Zbl 1335.81048

Summary: A quantum measurement can be regarded as a communication channel, in which the parameters of the state are expressed only in the probabilities of the outcomes of the measurement. We begin this paper by considering, in a non-quantum-mechanical setting, the problem of communicating through probabilities. For example, a sender, Alice, wants to convey to a receiver, Bob, the value of a continuous variable, \(\theta\), but her only means of conveying this value is by sending Bob a coin in which the value of\(\theta\) is encoded in the probability of heads. We ask what the optimal encoding is when Bob will be allowed to flip the coin only a finite number of times. As the number of tosses goes to infinity, we find that the optimal encoding is the same as what nature would do if we lived in a world governed by real-vector-space quantum theory. We then ask whether the problem might be modified, so that the optimal communication strategy would be consistent with standard, complex-vector-space quantum theory.

MSC:

81P45 Quantum information, communication, networks (quantum-theoretic aspects)
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References:

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