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Entropy 2013, 15(8), 3130-3147; doi:10.3390/e15083220
Article

Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information?

Received: 21 June 2013; in revised form: 24 July 2013 / Accepted: 24 July 2013 / Published: 2 August 2013
(This article belongs to the Special Issue Quantum Information 2012)
Download PDF [440 KB, uploaded 21 August 2013]
Abstract: 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, θ, but her only means of conveying this value is by sending Bob a coin in which the value of θ 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.
Keywords: optimal communication; quantum foundations; real probability amplitudes optimal communication; quantum foundations; real probability amplitudes
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Wootters, W.K. Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information? Entropy 2013, 15, 3130-3147.

AMA Style

Wootters WK. Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information? Entropy. 2013; 15(8):3130-3147.

Chicago/Turabian Style

Wootters, William K. 2013. "Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information?" Entropy 15, no. 8: 3130-3147.


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