dorsal/arxiv
View SchemaQuantum Information and Spacetime Structure
| Authors | Igor V. Volovich |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0207050 |
| URL | https://arxiv.org/abs/quant-ph/0207050 |
Abstract
In modern quantum information theory one deals with an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime. Therefore such basic notions in quantum information theory as qubit, channel, composite systems and entangled states should be formulated in space and time. In this paper some basic notions of quantum information theory are considered from the point of view of quantum field theory and general relativity. It is pointed out an important fact that in quantum field theory there is a statistical dependence between two regions in spacetime even if they are spacelike separated. A classical probabilistic representation for a family of correlation functions in quantum field theory is obtained. A noncommutative generalization of von Neumann`s spectral theorem is discussed. We suggest a new physical principle describing a relation between the mathematical formalism of Hilbert space and quantum physical phenomena which goes beyond the superselection rules. Entangled states and the change of state associated with the measurement process in space and time are discussed including the black hole and the cosmological spacetime. It is shown that any reasonable state in relativistic quantum field theory becomes disentangled at large spacelike distances if one makes local observations. As a result a violation of Bell`s inequalities can be observed without inconsistency with principles of relativistic quantum theory only if the distance between detectors is rather small. We suggest a further experimental study of entangled states in spacetime by studying the dependence of the correlation functions on the distance between detectors.
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"abstract": "In modern quantum information theory one deals with an idealized situation\nwhen the spacetime dependence of quantum phenomena is neglected. However the\ntransmission and processing of (quantum) information is a physical process in\nspacetime. Therefore such basic notions in quantum information theory as qubit,\nchannel, composite systems and entangled states should be formulated in space\nand time. In this paper some basic notions of quantum information theory are\nconsidered from the point of view of quantum field theory and general\nrelativity. It is pointed out an important fact that in quantum field theory\nthere is a statistical dependence between two regions in spacetime even if they\nare spacelike separated. A classical probabilistic representation for a family\nof correlation functions in quantum field theory is obtained. A noncommutative\ngeneralization of von Neumann`s spectral theorem is discussed. We suggest a new\nphysical principle describing a relation between the mathematical formalism of\nHilbert space and quantum physical phenomena which goes beyond the\nsuperselection rules. Entangled states and the change of state associated with\nthe measurement process in space and time are discussed including the black\nhole and the cosmological spacetime.\n It is shown that any reasonable state in relativistic quantum field theory\nbecomes disentangled at large spacelike distances if one makes local\nobservations. As a result a violation of Bell`s inequalities can be observed\nwithout inconsistency with principles of relativistic quantum theory only if\nthe distance between detectors is rather small. We suggest a further\nexperimental study of entangled states in spacetime by studying the dependence\nof the correlation functions on the distance between detectors.",
"arxiv_id": "quant-ph/0207050",
"authors": [
"Igor V. Volovich"
],
"categories": [
"quant-ph",
"gr-qc",
"hep-th"
],
"title": "Quantum Information and Spacetime Structure",
"url": "https://arxiv.org/abs/quant-ph/0207050"
},
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