213 research outputs found
Simple Derivation of the Lindblad Equation
The Lindblad equation is an evolution equation for the density matrix in
quantum theory. It is the general linear, Markovian, form which ensures that
the density matrix is hermitian, trace 1, positive and completely positive.
Some elementary examples of the Lindblad equation are given. The derivation of
the Lindblad equation presented here is "simple" in that all it uses is the
expression of a hermitian matrix in terms of its orthonormal eigenvectors and
real eigenvalues. Thus, it is appropriate for students who have learned the
algebra of quantum theory. Where helpful, arguments are first given in a
two-dimensional hilbert space.Comment: To be published in the European Journal of Physic
Consciousness and the Wigner's friend problem
It is generally agreed that decoherence theory is, if not a complete answer,
at least a great step forward towards a solution of the quantum measurement
problem. It is shown here however that in the cases in which a sentient being
is explicitly assumed to take cognizance of the outcome the reasons we have for
judging this way are not totally consistent, so that the question has to be
considered anew. It is pointed out that the way the Broglie-Bohm model solves
the riddle suggests a possible clue, consisting in assuming that even very
simple systems may have some sort of a proto-consciousness, but that their
``internal states of consciousness'' are not predictive. It is, next, easily
shown that if we imagine the systems get larger, in virtue of decoherence their
internal states of consciousness progressively gain in predictive value. So
that, for macro-systems, they may be identified (in practice) with the
predictive states of consciousness on which we ground our observational
predictions. The possibilities of carrying over this idea to standard quantum
mechanics are then investigated. Conditions of conceptual consistency are
considered and found rather strict, and, finally, two solutions emerge,
differing conceptually very much from one another but in both of which the,
possibly non-predictive, generalized internal states of consciousness play a
crucial role
Choice of Consistent Family, and Quantum Incompatibility
In consistent history quantum theory, a description of the time development
of a quantum system requires choosing a framework or consistent family, and
then calculating probabilities for the different histories which it contains.
It is argued that the framework is chosen by the physicist constructing a
description of a quantum system on the basis of questions he wishes to address,
in a manner analogous to choosing a coarse graining of the phase space in
classical statistical mechanics. The choice of framework is not determined by
some law of nature, though it is limited by quantum incompatibility, a concept
which is discussed using a two-dimensional Hilbert space (spin half particle).
Thus certain questions of physical interest can only be addressed using
frameworks in which they make (quantum mechanical) sense. The physicist's
choice does not influence reality, nor does the presence of choices render the
theory subjective. On the contrary, predictions of the theory can, in
principle, be verified by experimental measurements. These considerations are
used to address various criticisms and possible misunderstandings of the
consistent history approach, including its predictive power, whether it
requires a new logic, whether it can be interpreted realistically, the nature
of ``quasiclassicality'', and the possibility of ``contrary'' inferences.Comment: Minor revisions to bring into conformity with published version.
Revtex 29 pages including 1 page with figure
Anomalies of weakened decoherence criteria for quantum histories
The theory of decoherent histories is checked for the requirement of
statistical independence of subsystems. Strikingly, this is satisfied only when
the decoherence functional is diagonal in both its real a n d imaginary parts.
In particular, the condition of consistency (or weak decoherence) required for
the assignment of probabilities appears to be ruled out. The same conclusion is
obtained independently, by claiming a plausible dynamical robustness of
decoherent histories.Comment: 3pp, submitted to Phys. Rev. Let
Self-induced decoherence approach: Strong limitations on its validity in a simple spin bath model and on its general physical relevance
The "self-induced decoherence" (SID) approach suggests that (1) the
expectation value of any observable becomes diagonal in the eigenstates of the
total Hamiltonian for systems endowed with a continuous energy spectrum, and
(2), that this process can be interpreted as decoherence. We evaluate the first
claim in the context of a simple spin bath model. We find that even for large
environments, corresponding to an approximately continuous energy spectrum,
diagonalization of the expectation value of random observables does in general
not occur. We explain this result and conjecture that SID is likely to fail
also in other systems composed of discrete subsystems. Regarding the second
claim, we emphasize that SID does not describe a physically meaningful
decoherence process for individual measurements, but only involves destructive
interference that occurs collectively within an ensemble of presupposed
"values" of measurements. This leads us to question the relevance of SID for
treating observed decoherence effects.Comment: 11 pages, 4 figures. Final published versio
EPR, Bell, and Quantum Locality
Maudlin has claimed that no local theory can reproduce the predictions of
standard quantum mechanics that violate Bell's inequality for Bohm's version
(two spin-half particles in a singlet state) of the Einstein-Podolsky-Rosen
problem. It is argued that, on the contrary, standard quantum mechanics itself
is a counterexample to Maudlin's claim, because it is local in the appropriate
sense (measurements at one place do not influence what occurs elsewhere there)
when formulated using consistent principles in place of the inconsistent
appeals to "measurement" found in current textbooks. This argument sheds light
on the claim of Blaylock that counterfactual definiteness is an essential
ingredient in derivations of Bell's inequality.Comment: Minor revisions to previous versio
Insolubility Theorems and EPR Argument
I wish to thank in particular Arthur Fine for very perceptive comments on a previous draft of this paper. Many thanks also to Theo Nieuwenhuizen for inspiration, to Max Schlosshauer for correspondence, to two anonymous referees for shrewd observations, and to audiences at Aberdeen, Cagliari and Oxford (in particular to Harvey Brown, Elise Crull, Simon Saunders, Chris Timpson and David Wallace) for stimulating questions. This paper was written during my tenure of a Leverhulme Grant on âThe Einstein Paradoxâ: The Debate on Nonlocality and Incompleteness in 1935 (Project Grant nr. F/00 152/AN), and it was revised for publication during my tenure of a Visiting Professorship in the Doctoral School of Philosophy and Epistemology, University of Cagliari (Contract nr. 268/21647).Peer reviewedPostprin
Genuine Multipartite Entanglement in Quantum Phase Transitions
We demonstrate that the Global Entanglement (GE) measure defined by Meyer and
Wallach, J. Math. Phys. 43, 4273 (2002), is maximal at the critical point for
the Ising chain in a transverse magnetic field. Our analysis is based on the
equivalence of GE to the averaged linear entropy, allowing the understanding of
multipartite entanglement (ME) features through a generalization of GE for
bipartite blocks of qubits. Moreover, in contrast to GE, the proposed ME
measure can distinguish three paradigmatic entangled states: ,
, and . As such the generalized measure can detect
genuine ME and is maximal at the critical point.Comment: 4 pages, 3 figures. Replaced with final published versio
Spatial Degrees of Freedom in Everett Quantum Mechanics
Stapp claims that, when spatial degrees of freedom are taken into account,
Everett quantum mechanics is ambiguous due to a "core basis problem." To
examine an aspect of this claim I generalize the ideal measurement model to
include translational degrees of freedom for both the measured system and the
measuring apparatus. Analysis of this generalized model using the Everett
interpretation in the Heisenberg picture shows that it makes unambiguous
predictions for the possible results of measurements and their respective
probabilities. The presence of translational degrees of freedom for the
measuring apparatus affects the probabilities of measurement outcomes in the
same way that a mixed state for the measured system would. Examination of a
measurement scenario involving several observers illustrates the consistency of
the model with perceived spatial localization of the measuring apparatus.Comment: 34 pp., no figs. Introduction, discussion revised. Material
tangential to main point remove
A model of quantum reduction with decoherence
The problem of reduction (wave packet reduction) is reexamined under two
simple conditions: Reduction is a last step completing decoherence. It acts in
commonplace circumstances and should be therefore compatible with the
mathematical frame of quantum field theory and the standard model.
These conditions lead to an essentially unique model for reduction.
Consistency with renormalization and time-reversal violation suggest however a
primary action in the vicinity of Planck's length. The inclusion of quantum
gravity and the uniqueness of space-time point moreover to generalized quantum
theory, first proposed by Gell-Mann and Hartle, as a convenient framework for
developing this model into a more complete theory.Comment: 20 pages. To be published in Physical Review
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