- #1
- 24,775
- 792
Lucien Hardy is a prominent foundations of QM guy at Perimeter and he just came out with this paper
http://arxiv.org/abs/1104.2066
Reformulating and Reconstructing Quantum Theory
Lucien Hardy
159 pages. Many pictures
(Submitted on 11 Apr 2011)
"We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the following:
[Axiom 1] Operations correspond to operators.
[Axiom 2] Every complete set of positive operators corresponds to a complete set of operations.
The following operational postulates are shown to be equivalent to these mathematical axioms:
[P1] Definiteness. Associated with any given pure state is a unique maximal effect giving probability equal to one. This maximal effect does not give probability equal to one for any other pure state.
[P2] Information locality. A maximal measurement on a composite system is effected if we perform maximal measurements on each of the components.
[P3] Tomographic locality. The state of a composite system can be determined from the statistics collected by making measurements on the components.
[P4] Compound permutatability. There exists a compound reversible transformation on any system effecting any given permutation of any given maximal set of distinguishable states for that system.
[P5] Preparability. Filters are non-mixing and non-flattening.
Hence, from these postulates we can reconstruct all the usual features of quantum theory: States are represented by positive operators, transformations by completely positive trace non-increasing maps, and effects by positive operators. The Born rule (i.e. the trace rule) for calculating probabilities follows. A more detailed abstract is provided in the paper."
=========================
I don't know much about the subject, but I suspect others may be interested and want to check it out.
Being a non-standard approach to Quantum Theory, I thought it might belong in Beyond forum. But if somebody wants to move it to QM forum that's fine too.
http://arxiv.org/abs/1104.2066
Reformulating and Reconstructing Quantum Theory
Lucien Hardy
159 pages. Many pictures
(Submitted on 11 Apr 2011)
"We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the following:
[Axiom 1] Operations correspond to operators.
[Axiom 2] Every complete set of positive operators corresponds to a complete set of operations.
The following operational postulates are shown to be equivalent to these mathematical axioms:
[P1] Definiteness. Associated with any given pure state is a unique maximal effect giving probability equal to one. This maximal effect does not give probability equal to one for any other pure state.
[P2] Information locality. A maximal measurement on a composite system is effected if we perform maximal measurements on each of the components.
[P3] Tomographic locality. The state of a composite system can be determined from the statistics collected by making measurements on the components.
[P4] Compound permutatability. There exists a compound reversible transformation on any system effecting any given permutation of any given maximal set of distinguishable states for that system.
[P5] Preparability. Filters are non-mixing and non-flattening.
Hence, from these postulates we can reconstruct all the usual features of quantum theory: States are represented by positive operators, transformations by completely positive trace non-increasing maps, and effects by positive operators. The Born rule (i.e. the trace rule) for calculating probabilities follows. A more detailed abstract is provided in the paper."
=========================
I don't know much about the subject, but I suspect others may be interested and want to check it out.
Being a non-standard approach to Quantum Theory, I thought it might belong in Beyond forum. But if somebody wants to move it to QM forum that's fine too.