dorsal/arxiv
View SchemaQuantum processes on phase space
| Authors | Charis Anastopoulos |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0205132 |
| URL | https://arxiv.org/abs/quant-ph/0205132 |
| DOI | 10.1016/S0003-4916(03)00006-X |
| Journal | Annals Phys. 303 (2003) 275-320 |
Abstract
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for histories; this object is the decoherence functional of the consistent histories approach. If we take phases as well as probabilities as primitive elements of our theory, we abandon Kolmogorov probability and can describe quantum theory in terms of fundamental commutative observables, without being obstructed by Bell's and related theorems. Generalising the theory of stochastic processes, we develop the description of relative phases and probabilities for paths on the classical phase space. This description provides a theory of quantum processes. We identify a number of basic postulates and study its corresponding properties. We strongly emphasise the notion of conditioning and are able to write ``quantum differential equations'' as analogous to stochastic differential equations. These can be interpreted as referring to individual systems. We, then, show the sense in which quantum theory is equivalent to a quantum process on phase space (using coherent states). Conversely, starting from quantum processes on phase space we recover standard quantum theory on Hilbert space from the requirement that the process satisfies (the Markov property together with time reversibility. The statistical predictions of our theory are identical to the ones of standard quantum theory, but the ``logic'' of events is Boolean; events are not represented by projectors any more. We discuss some implication of this fact for the interpretation of quantum theory, emphasising that it makes plausible the existence of realist theories for individual quantum systems.
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"abstract": "Quantum theory predicts probabilities as well as relative phases between\ndifferent alternatives of the system. A unified description of both\nprobabilities and phases comes through a generalisation of the notion of a\ndensity matrix for histories; this object is the decoherence functional of the\nconsistent histories approach. If we take phases as well as probabilities as\nprimitive elements of our theory, we abandon Kolmogorov probability and can\ndescribe quantum theory in terms of fundamental commutative observables,\nwithout being obstructed by Bell\u0027s and related theorems. Generalising the\ntheory of stochastic processes, we develop the description of relative phases\nand probabilities for paths on the classical phase space. This description\nprovides a theory of quantum processes. We identify a number of basic\npostulates and study its corresponding properties. We strongly emphasise the\nnotion of conditioning and are able to write ``quantum differential equations\u0027\u0027\nas analogous to stochastic differential equations. These can be interpreted as\nreferring to individual systems. We, then, show the sense in which quantum\ntheory is equivalent to a quantum process on phase space (using coherent\nstates). Conversely, starting from quantum processes on phase space we recover\nstandard quantum theory on Hilbert space from the requirement that the process\nsatisfies (the Markov property together with time reversibility. The\nstatistical predictions of our theory are identical to the ones of standard\nquantum theory, but the ``logic\u0027\u0027 of events is Boolean; events are not\nrepresented by projectors any more. We discuss some implication of this fact\nfor the interpretation of quantum theory, emphasising that it makes plausible\nthe existence of realist theories for individual quantum systems.",
"arxiv_id": "quant-ph/0205132",
"authors": [
"Charis Anastopoulos"
],
"categories": [
"quant-ph",
"gr-qc"
],
"doi": "10.1016/S0003-4916(03)00006-X",
"journal_ref": "Annals Phys. 303 (2003) 275-320",
"title": "Quantum processes on phase space",
"url": "https://arxiv.org/abs/quant-ph/0205132"
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