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Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information?
Department of Physics, Williams College, Williamstown, MA 01267, USA
Received: 21 June 2013; in revised form: 24 July 2013 / Accepted: 24 July 2013 / Published: 2 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
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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.
Wootters WK. Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information? Entropy. 2013; 15(8):3130-3147.
Wootters, William K. 2013. "Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information?" Entropy 15, no. 8: 3130-3147.