344 research outputs found
Negativity and contextuality are equivalent notions of nonclassicality
Two notions of nonclassicality that have been investigated intensively are:
(i) negativity, that is, the need to posit negative values when representing
quantum states by quasiprobability distributions such as the Wigner
representation, and (ii) contextuality, that is, the impossibility of a
noncontextual hidden variable model of quantum theory (also known as the
Bell-Kochen-Specker theorem). Although both of these notions were meant to
characterize the conditions under which a classical explanation cannot be
provided, we demonstrate that they prove inadequate to the task and we argue
for a particular way of generalizing and revising them. With the refined
version of each in hand, it becomes apparent that they are in fact one and the
same. We also demonstrate the impossibility of noncontextuality or
nonnegativity in quantum theory with a novel proof that is symmetric in its
treatment of measurements and preparations.Comment: 5 pages, published version (modulo some supplementary material
Introduction
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68468/2/10.1177_107554708600800101.pd
Relaxed Bell inequalities and Kochen-Specker theorems
The combination of various physically plausible properties, such as no
signaling, determinism, and experimental free will, is known to be incompatible
with quantum correlations. Hence, these properties must be individually or
jointly relaxed in any model of such correlations. The necessary degrees of
relaxation are quantified here, via natural distance and information-theoretic
measures. This allows quantitative comparisons between different models in
terms of the resources, such as the number of bits, of randomness,
communication, and/or correlation, that they require. For example, measurement
dependence is a relatively strong resource for modeling singlet state
correlations, with only 1/15 of one bit of correlation required between
measurement settings and the underlying variable. It is shown how various
'relaxed' Bell inequalities may be obtained, which precisely specify the
complementary degrees of relaxation required to model any given violation of a
standard Bell inequality. The robustness of a class of Kochen-Specker theorems,
to relaxation of measurement independence, is also investigated. It is shown
that a theorem of Mermin remains valid unless measurement independence is
relaxed by 1/3. The Conway-Kochen 'free will' theorem and a result of Hardy are
less robust, failing if measurement independence is relaxed by only 6.5% and
4.5%, respectively. An appendix shows the existence of an outcome independent
model is equivalent to the existence of a deterministic model.Comment: 19 pages (including 3 appendices); v3: minor clarifications, to
appear in PR
On recognizing and formulating mathematical problems
When mathematics is used to help people cope with real-life situations, a three-stage intellectual process is involved. First, a person becomes aware of a problem-situation which stimulates him to generate a problem-statement, a verbal story-problem. This may be in writing, expressed orally, or merely thought and evidenced by other behavior. Second, he transforms the verbal problem-statement into a mathematical formulation. Third, he analyzes this mathematically stated problem into subproblems to which the solution is more immediate.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43864/1/11251_2004_Article_BF00052419.pd
Pre- and Post-selection paradoxes and contextuality in quantum mechanics
Many seemingly paradoxical effects are known in the predictions for outcomes
of intermediate measurements made on pre- and post-selected quantum systems.
Despite appearances, these effects do not demonstrate the impossibility of a
noncontextual hidden variable theory, since an explanation in terms of
measurement-disturbance is possible. Nonetheless, we show that for every
paradoxical effect wherein all the pre- and post- selected probabilities are 0
or 1 and the pre- and post-selected states are nonorthogonal, there is an
associated proof of contextuality. This proof is obtained by considering all
the measurements involved in the paradoxical effect -- the pre-selection, the
post-selection, and the alternative possible intermediate measurements -- as
alternative possible measurements at a single time.Comment: 5 pages, 1 figure. Submitted to Phys. Rev. Lett. v2.0 revised in the
light of referee comments, results unchange
The Free Will Theorem
On the basis of three physical axioms, we prove that if the choice of a
particular type of spin 1 experiment is not a function of the information
accessible to the experimenters, then its outcome is equally not a function of
the information accessible to the particles. We show that this result is
robust, and deduce that neither hidden variable theories nor mechanisms of the
GRW type for wave function collapse can be made relativistic. We also establish
the consistency of our axioms and discuss the philosophical implications.Comment: 31 pages, 6figure
Finding a state in a haystack
We consider the problem to single out a particular state among
orthogonal pure states. As it turns out, in general the optimal strategy is not
to measure the particles separately, but to consider joint properties of the
-particle system. The required number of propositions is . There exist
equivalent operational procedures to do so. We enumerate some
configurations for three particles, in particular the
Greenberger-Horne-Zeilinger (GHZ)- and W-states, which are specific cases of a
unitary transformation For the GHZ-case, an explicit physical meaning of the
projection operators is discussed.Comment: 11 page
Operationally Invariant Information in Quantum Measurements
A new measure of information in quantum mechanics is proposed which takes
into account that for quantum systems the only feature known before an
experiment is performed are the probabilities for various events to occur. The
sum of the individual measures of information for mutually complementary
observations is invariant under the choice of the particular set of
complementary observations and conserved if there is no information exchange
with an environment. That operational quantum information invariant results in
N bits of information for a system consisting of N qubits.Comment: 4 pages, 1 figur
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