23,553 research outputs found
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
Comment on ``Consistent Sets Yield Contrary Inferences in Quantum Theory''
In a recent paper Kent has pointed out that in consistent histories quantum
theory it is possible, given initial and final states, to construct two
different consistent families of histories, in each of which there is a
proposition that can be inferred with probability one, and such that the
projectors representing these two propositions are mutually orthogonal. In this
note we stress that, according to the rules of consistent history reasoning two
such propositions are not contrary in the usual logical sense namely, that one
can infer that if one is true then the other is false, and both could be false.
No single consistent family contains both propositions, together with the
initial and final states, and hence the propositions cannot be logically
compared. Consistent histories quantum theory is logically consistent,
consistent with experiment as far as is known, consistent with the usual
quantum predictions for measurements, and applicable to the most general
physical systems. It may not be the only theory with these properties, but in
our opinion, it is the most promising among present possibilities.Comment: 2pages, uses REVTEX 3.
Quantum Locality?
Robert Griffiths has recently addressed, within the framework of a
'consistent quantum theory' that he has developed, the issue of whether, as is
often claimed, quantum mechanics entails a need for faster-than-light transfers
of information over long distances. He argues that the putative proofs of this
property that involve hidden variables include in their premises some
essentially classical-physics-type assumptions that are fundamentally
incompatible with the precepts of quantum physics. One cannot logically prove
properties of a system by establishing, instead, properties of a system
modified by adding properties alien to the original system. Hence Griffiths'
rejection of hidden-variable-based proofs is logically warranted. Griffiths
mentions the existence of a certain alternative proof that does not involve
hidden variables, and that uses only macroscopically described observable
properties. He notes that he had examined in his book proofs of this general
kind, and concluded that they provide no evidence for nonlocal influences. But
he did not examine the particular proof that he cites. An examination of that
particular proof by the method specified by his 'consistent quantum theory'
shows that the cited proof is valid within that restrictive version of quantum
theory. An added section responds to Griffiths' reply, which cites general
possibilities of ambiguities that make what is to be proved ill-defined, and
hence render the pertinent 'consistent framework' ill defined. But the vagaries
that he cites do not upset the proof in question, which, both by its physical
formulation and by explicit identification, specify the framework to be used.
Griffiths confirms the validity of the proof insofar as that framework is used.
The section also shows, in response to Griffiths' challenge, why a putative
proof of locality that he has described is flawed.Comment: This version adds a response to Griffiths' reply to my original. It
notes that Griffiths confirms the validity of my argument if one uses the
framework that I use. Griffiths' objection that other frameworks exist is not
germaine, because I use the unique one that satisfies the explicitly stated
conditions that the choices be macroscopic choices of experiments and
outcomes in a specified orde
The effect of reionization on the COBE normalization
We point out that the effect of reionization on the microwave anisotropy
power spectrum is not necessarily negligible on the scales probed by COBE. It
can lead to an upward shift of the COBE normalization by more than the
one-sigma error quoted ignoring reionization. We provide a fitting function to
incorporate reionization into the normalization of the matter power spectrum.Comment: 3 pages LaTeX file with three figures incorporated (uses mn.sty and
epsf
Correlation inequalities for noninteracting Bose gases
For a noninteracting Bose gas with a fixed one-body Hamiltonian H^0
independent of the number of particles we derive the inequalities _N <
_{N+1}, _N _N _N for i\neq j, \partial
_N/\partial \beta >0 and ^+_N _N. Here N_i is the occupation
number of the ith eigenstate of H^0, \beta is the inverse temperature and the
superscript + refers to adding an extra level to those of H^0. The results
follow from the convexity of the N-particle free energy as a function of N.Comment: a further inequality adde
Atemporal diagrams for quantum circuits
A system of diagrams is introduced that allows the representation of various
elements of a quantum circuit, including measurements, in a form which makes no
reference to time (hence ``atemporal''). It can be used to relate quantum
dynamical properties to those of entangled states (map-state duality), and
suggests useful analogies, such as the inverse of an entangled ket. Diagrams
clarify the role of channel kets, transition operators, dynamical operators
(matrices), and Kraus rank for noisy quantum channels. Positive (semidefinite)
operators are represented by diagrams with a symmetry that aids in
understanding their connection with completely positive maps. The diagrams are
used to analyze standard teleportation and dense coding, and for a careful
study of unambiguous (conclusive) teleportation. A simple diagrammatic argument
shows that a Kraus rank of 3 is impossible for a one-qubit channel modeled
using a one-qubit environment in a mixed state.Comment: Minor changes in references. Latex 32 pages, 13 figures in text using
PSTrick
Two qubit copying machine for economical quantum eavesdropping
We study the mapping which occurs when a single qubit in an arbitrary state
interacts with another qubit in a given, fixed state resulting in some unitary
transformation on the two qubit system which, in effect, makes two copies of
the first qubit. The general problem of the quality of the resulting copies is
discussed using a special representation, a generalization of the usual Schmidt
decomposition, of an arbitrary two-dimensional subspace of a tensor product of
two 2-dimensional Hilbert spaces. We exhibit quantum circuits which can
reproduce the results of any two qubit copying machine of this type. A simple
stochastic generalization (using a ``classical'' random signal) of the copying
machine is also considered. These copying machines provide simple embodiments
of previously proposed optimal eavesdropping schemes for the BB84 and B92
quantum cryptography protocols.Comment: Minor changes. 26 pages RevTex including 7 PS figure
Optimal Eavesdropping in Quantum Cryptography. II. Quantum Circuit
It is shown that the optimum strategy of the eavesdropper, as described in
the preceding paper, can be expressed in terms of a quantum circuit in a way
which makes it obvious why certain parameters take on particular values, and
why obtaining information in one basis gives rise to noise in the conjugate
basis.Comment: 7 pages, 1 figure, Latex, the second part of quant-ph/970103
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