918 research outputs found
A Quantum-Bayesian Route to Quantum-State Space
In the quantum-Bayesian approach to quantum foundations, a quantum state is
viewed as an expression of an agent's personalist Bayesian degrees of belief,
or probabilities, concerning the results of measurements. These probabilities
obey the usual probability rules as required by Dutch-book coherence, but
quantum mechanics imposes additional constraints upon them. In this paper, we
explore the question of deriving the structure of quantum-state space from a
set of assumptions in the spirit of quantum Bayesianism. The starting point is
the representation of quantum states induced by a symmetric informationally
complete measurement or SIC. In this representation, the Born rule takes the
form of a particularly simple modification of the law of total probability. We
show how to derive key features of quantum-state space from (i) the requirement
that the Born rule arises as a simple modification of the law of total
probability and (ii) a limited number of additional assumptions of a strong
Bayesian flavor.Comment: 7 pages, 1 figure, to appear in Foundations of Physics; this is a
condensation of the argument in arXiv:0906.2187v1 [quant-ph], with special
attention paid to making all assumptions explici
Efficient measurements, purification, and bounds on the mutual information
When a measurement is made on a quantum system in which classical information
is encoded, the measurement reduces the observers average Shannon entropy for
the encoding ensemble. This reduction, being the {\em mutual information}, is
always non-negative. For efficient measurements the state is also purified;
that is, on average, the observers von Neumann entropy for the state of the
system is also reduced by a non-negative amount. Here we point out that by
re-writing a bound derived by Hall [Phys. Rev. A {\bf 55}, 100 (1997)], which
is dual to the Holevo bound, one finds that for efficient measurements, the
mutual information is bounded by the reduction in the von Neumann entropy. We
also show that this result, which provides a physical interpretation for Hall's
bound, may be derived directly from the Schumacher-Westmoreland-Wootters
theorem [Phys. Rev. Lett. {\bf 76}, 3452 (1996)]. We discuss these bounds, and
their relationship to another bound, valid for efficient measurements on pure
state ensembles, which involves the subentropy.Comment: 4 pages, Revtex4. v3: rewritten and reinterpreted somewha
Continuous variable quantum cryptography
We propose a quantum cryptographic scheme in which small phase and amplitude
modulations of CW light beams carry the key information. The presence of EPR
type correlations provides the quantum protection.Comment: 8 pages, 3 figure
Quantum-Limited Measurement and Information in Mesoscopic Detectors
We formulate general conditions necessary for a linear-response detector to
reach the quantum limit of measurement efficiency, where the
measurement-induced dephasing rate takes on its minimum possible value. These
conditions are applicable to both non-interacting and interacting systems. We
assess the status of these requirements in an arbitrary non-interacting
scattering based detector, identifying the symmetries of the scattering matrix
needed to reach the quantum limit. We show that these conditions are necessary
to prevent the existence of information in the detector which is not extracted
in the measurement process.Comment: 13 pages, 1 figur
Quantum copying: Fundamental inequalities
How well one can copy an arbitrary qubit? To answer this question we consider
two arbitrary vectors in a two-dimensional state space and an abstract copying
transformation which will copy these two vectors. If the vectors are
orthogonal, then perfect copies can be made. If they are not, then errors will
be introduced. The size of the error depends on the inner product of the two
original vectors. We derive a lower bound for the amount of noise induced by
quantum copying. We examine both copying transformations which produce one copy
and transformations which produce many, and show that the quality of each copy
decreases as the number of copies increases.Comment: 5 pages + 1 figure, LaTeX with revtex, epsfig submitted to Phys. Rev.
D-Branes on K3-Fibrations
B-type D-branes are constructed on two different K3-fibrations over IP_1
using boundary conformal field theory at the rational Gepner points of these
models. The microscopic CFT charges are compared with the Ramond charges of
D-branes wrapped on holomorphic cycles of the corresponding Calabi-Yau
manifold. We study in particular D4-branes and bundles localized on the K3
fibers, and find from CFT that each irreducible component of a bundle on K3
gains one modulus upon fibration over IP_1. This is in agreement with
expectations and so provides a further test of the boundary CFT.Comment: 16p, harvmac, tables.tex; typos corrected, refs added, discussion
about moduli spaces improve
Universality of optimal measurements
We present optimal and minimal measurements on identical copies of an unknown
state of a qubit when the quality of measuring strategies is quantified with
the gain of information (Kullback of probability distributions). We also show
that the maximal gain of information occurs, among isotropic priors, when the
state is known to be pure. Universality of optimal measurements follows from
our results: using the fidelity or the gain of information, two different
figures of merits, leads to exactly the same conclusions. We finally
investigate the optimal capacity of copies of an unknown state as a quantum
channel of information.Comment: Revtex, 5 pages, no figure
Minimal Informationally Complete Measurements for Pure States
We consider measurements, described by a positive-operator-valued measure
(POVM), whose outcome probabilities determine an arbitrary pure state of a
D-dimensional quantum system. We call such a measurement a pure-state
informationally complete (PSI-complete) POVM. We show that a measurement with
2D-1 outcomes cannot be PSI-complete, and then we construct a POVM with 2D
outcomes that suffices, thus showing that a minimal PSI-complete POVM has 2D
outcomes. We also consider PSI-complete POVMs that have only rank-one POVM
elements and construct an example with 3D-2 outcomes, which is a generalization
of the tetrahedral measurement for a qubit. The question of the minimal number
of elements in a rank-one PSI-complete POVM is left open.Comment: 2 figures, submitted for the Asher Peres festschrif
Glass transition in the quenched and annealed version of the frustrated lattice gas model
In this paper we study the 3d frustrated lattice gas model in the annealed
version, where the disorder is allowed to evolve in time with a suitable
kinetic constraint. Although the model does not exhibit any thermodynamic
transition it shows a diverging peak at some characteristic time in the
dynamical non-linear susceptibility, similar to the results on the p-spin model
in mean field and Lennard-Jones mixture recently found by Donati et al.
[cond-mat/9905433]. Comparing these results to those obtained in the model with
quenched interactions, we conclude that the critical behavior of the dynamical
susceptibility is reminiscent of the thermodynamic transition present in the
quenched model, and signaled by the divergence of the static non-linear
susceptibility, suggesting therefore a similar mechanism also in supercooled
glass-forming liquids.Comment: 8 pages, 14 figure
A toy model for quantum mechanics
The toy model used by Spekkens [R. Spekkens, Phys. Rev. A 75, 032110 (2007)]
to argue in favor of an epistemic view of quantum mechanics is extended by
generalizing his definition of pure states (i.e. states of maximal knowledge)
and by associating measurements with all pure states. The new toy model does
not allow signaling but, in contrast to the Spekkens model, does violate
Bell-CHSH inequalities. Negative probabilities are found to arise naturally
within the model, and can be used to explain the Bell-CHSH inequality
violations.Comment: in which the author breaks his vow to never use the words "ontic" and
"epistemic" in publi
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