dorsal/arxiv
View SchemaConditional Density Operators and the Subjectivity of Quantum Operations
| Authors | M. S. Leifer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0611233 |
| URL | https://arxiv.org/abs/quant-ph/0611233 |
| DOI | 10.1063/1.2713456 |
| Journal | G. Adenier, C. A. Fuchs and A. Yu. Khrennikov (eds.), Foundations of Probability and Physics - 4, AIP Conference Proceedings vol. 889, (AIP 2007), pp. 172-186 |
Abstract
Assuming that quantum states, including pure states, represent subjective degrees of belief rather than objective properties of systems, the question of what other elements of the quantum formalism must also be taken as subjective is addressed. In particular, we ask this of the dynamical aspects of the formalism, such as Hamiltonians and unitary operators. Whilst some operations, such as the update maps corresponding to a complete projective measurement, must be subjective, the situation is not so clear in other cases. Here, it is argued that all trace preserving completely positive maps, including unitary operators, should be regarded as subjective, in the same sense as a classical conditional probability distribution. The argument is based on a reworking of the Choi-Jamiolkowski isomorphism in terms of "conditional" density operators and trace preserving completely positive maps, which mimics the relationship between conditional probabilities and stochastic maps in classical probability.
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"abstract": "Assuming that quantum states, including pure states, represent subjective\ndegrees of belief rather than objective properties of systems, the question of\nwhat other elements of the quantum formalism must also be taken as subjective\nis addressed. In particular, we ask this of the dynamical aspects of the\nformalism, such as Hamiltonians and unitary operators. Whilst some operations,\nsuch as the update maps corresponding to a complete projective measurement,\nmust be subjective, the situation is not so clear in other cases. Here, it is\nargued that all trace preserving completely positive maps, including unitary\noperators, should be regarded as subjective, in the same sense as a classical\nconditional probability distribution. The argument is based on a reworking of\nthe Choi-Jamiolkowski isomorphism in terms of \"conditional\" density operators\nand trace preserving completely positive maps, which mimics the relationship\nbetween conditional probabilities and stochastic maps in classical probability.",
"arxiv_id": "quant-ph/0611233",
"authors": [
"M. S. Leifer"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.2713456",
"journal_ref": "G. Adenier, C. A. Fuchs and A. Yu. Khrennikov (eds.), Foundations\n of Probability and Physics - 4, AIP Conference Proceedings vol. 889, (AIP\n 2007), pp. 172-186",
"title": "Conditional Density Operators and the Subjectivity of Quantum Operations",
"url": "https://arxiv.org/abs/quant-ph/0611233"
},
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