dorsal/arxiv
View SchemaNonlinearity without Superluminality
| Authors | Adrian Kent |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0204106 |
| URL | https://arxiv.org/abs/quant-ph/0204106 |
| DOI | 10.1103/PhysRevA.72.012108 |
| Journal | Phys. Rev. A 72, 012108 (2005) |
Abstract
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signalling. As Czachor, Gisin and Polchinski pointed out, this is not true for general nonlinear modifications of the Schroedinger equation. Excluding superluminal signalling has thus been taken to rule out most nonlinear versions of quantum theory. The no superluminal signalling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by non-relativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localised pure states need not allow superluminal signalling, provided that the devices display the values of the states of entangled subsystems as defined in a non-standard, but natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality.
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"abstract": "Quantum theory is compatible with special relativity. In particular, though\nmeasurements on entangled systems are correlated in a way that cannot be\nreproduced by local hidden variables, they cannot be used for superluminal\nsignalling. As Czachor, Gisin and Polchinski pointed out, this is not true for\ngeneral nonlinear modifications of the Schroedinger equation. Excluding\nsuperluminal signalling has thus been taken to rule out most nonlinear versions\nof quantum theory. The no superluminal signalling constraint has also been used\nfor alternative derivations of the optimal fidelities attainable for imperfect\nquantum cloning and other operations.\n These results apply to theories satisfying the rule that their predictions\nfor widely separated and slowly moving entangled systems can be approximated by\nnon-relativistic equations of motion with respect to a preferred time\ncoordinate. This paper describes a natural way in which this rule might fail to\nhold. In particular, it is shown that quantum readout devices which display the\nvalues of localised pure states need not allow superluminal signalling,\nprovided that the devices display the values of the states of entangled\nsubsystems as defined in a non-standard, but natural, way. It follows that any\nlocally defined nonlinear evolution of pure states can be made consistent with\nMinkowski causality.",
"arxiv_id": "quant-ph/0204106",
"authors": [
"Adrian Kent"
],
"categories": [
"quant-ph",
"gr-qc"
],
"doi": "10.1103/PhysRevA.72.012108",
"journal_ref": "Phys. Rev. A 72, 012108 (2005)",
"title": "Nonlinearity without Superluminality",
"url": "https://arxiv.org/abs/quant-ph/0204106"
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