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

• Main Author: William K. Wootters
• Format: Article
• Language: English
• Published: MDPI AG 2013-08-01
• Series: Entropy
• Subjects: optimal communication; quantum foundations; real probability amplitudes
• Online Access: http://www.mdpi.com/1099-4300/15/8/3130

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.