dorsal/arxiv
View SchemaNo-signalling-based version of Zurek's derivation of quantum probabilities: A note on "Environment-assisted invariance, entanglement, and probabilities in quantum physics"
| Authors | Howard Barnum |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0312150 |
| URL | https://arxiv.org/abs/quant-ph/0312150 |
Abstract
Zurek has derived the quantum probabilities for Schmidt basis states of bipartite quantum systems in pure joint states, from the assumption that they should be not be affected by one party's action if the action can be undone by the other party (``envariance of probability'') and an auxiliary assumption. We argue that a natural generalization of the auxiliary assumption is actually strong enough to yield the Born rule itself, but that Zurek's argument and protocol can be adapted to do without this assumption, at the cost of using envariance of probability in both directions. We consider alternative motivations for envariance, one based on the no-signalling constraint that actions on one subsystem of a quantum system not allow signalling to another subsystem entirely distinct from the first, and another which is perhaps strongest in the context of a relative-state interpretation of quantum mechanics. In part because of this, we argue that the relative appeal of our version and the original version of Zurek's argument depends in part upon whether one interprets the quantum formalism in terms of relative states or definite measurement outcomes.
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"abstract": "Zurek has derived the quantum probabilities for Schmidt basis states of\nbipartite quantum systems in pure joint states, from the assumption that they\nshould be not be affected by one party\u0027s action if the action can be undone by\nthe other party (``envariance of probability\u0027\u0027) and an auxiliary assumption. We\nargue that a natural generalization of the auxiliary assumption is actually\nstrong enough to yield the Born rule itself, but that Zurek\u0027s argument and\nprotocol can be adapted to do without this assumption, at the cost of using\nenvariance of probability in both directions. We consider alternative\nmotivations for envariance, one based on the no-signalling constraint that\nactions on one subsystem of a quantum system not allow signalling to another\nsubsystem entirely distinct from the first, and another which is perhaps\nstrongest in the context of a relative-state interpretation of quantum\nmechanics. In part because of this, we argue that the relative appeal of our\nversion and the original version of Zurek\u0027s argument depends in part upon\nwhether one interprets the quantum formalism in terms of relative states or\ndefinite measurement outcomes.",
"arxiv_id": "quant-ph/0312150",
"authors": [
"Howard Barnum"
],
"categories": [
"quant-ph"
],
"title": "No-signalling-based version of Zurek\u0027s derivation of quantum probabilities: A note on \"Environment-assisted invariance, entanglement, and probabilities in quantum physics\"",
"url": "https://arxiv.org/abs/quant-ph/0312150"
},
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