Physics – Quantum Physics
Scientific paper
2010-08-26
Phys. Rev. A 83, 032107 (2011)
Physics
Quantum Physics
Added a lemma on the dynamical properties of the set S that solves some bugs in the proof of the theorem in section IV
Scientific paper
10.1103/PhysRevA.83.032107
Recently we have presented a hidden variable model of measurements for a qubit where the hidden variable state space dimension is one-half the quantum state manifold dimension. The absence of a short memory (Markov) dynamics is the price paid for this dimensional reduction. The conflict between having the Markov property and achieving the dimensional reduction was proved in [A. Montina, Phys. Rev. A, 77, 022104 (2008)] using an additional hypothesis of trajectory relaxation. Here we analyze in more detail this hypothesis introducing the concept of invertible process and report a proof that makes clearer the role played by the topology of the hidden variable space. This is accomplished by requiring suitable properties of regularity of the conditional probability governing the dynamics. In the case of minimal dimension the set of continuous hidden variables is identified with an object living an N-dimensional Hilbert space, whose dynamics is described by the Schr\"odinger equation. A method for generating the economical non-Markovian model for the qubit is also presented.
No associations
LandOfFree
State space dimensionality in short memory hidden variable theories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with State space dimensionality in short memory hidden variable theories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and State space dimensionality in short memory hidden variable theories will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-703520