Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information?
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 probabiliti...
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| Format: | Article |
| Language: | English |
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MDPI AG
2013-08-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/15/8/3130 |
| _version_ | 1798041972425883648 |
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| author | William K. Wootters |
| author_facet | William K. Wootters |
| author_sort | William K. Wootters |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T22:29:02Z |
| format | Article |
| id | doaj.art-0e0d9359a67046faa639817f97fb2b55 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:29:02Z |
| publishDate | 2013-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0e0d9359a67046faa639817f97fb2b552022-12-22T03:59:33ZengMDPI AGEntropy1099-43002013-08-011583130314710.3390/e15083220Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information?William K. WoottersA 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.http://www.mdpi.com/1099-4300/15/8/3130optimal communicationquantum foundationsreal probability amplitudes |
| spellingShingle | William K. Wootters Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information? Entropy optimal communication quantum foundations real probability amplitudes |
| title | Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information? |
| title_full | Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information? |
| title_fullStr | Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information? |
| title_full_unstemmed | Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information? |
| title_short | Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information? |
| title_sort | communicating through probabilities does quantum theory optimize the transfer of information |
| topic | optimal communication quantum foundations real probability amplitudes |
| url | http://www.mdpi.com/1099-4300/15/8/3130 |
| work_keys_str_mv | AT williamkwootters communicatingthroughprobabilitiesdoesquantumtheoryoptimizethetransferofinformation |