3,487 research outputs found
Universal Uncertainty Principle in the Measurement Operator Formalism
Heisenberg's uncertainty principle has been understood to set a limitation on
measurements; however, the long-standing mathematical formulation established
by Heisenberg, Kennard, and Robertson does not allow such an interpretation.
Recently, a new relation was found to give a universally valid relation between
noise and disturbance in general quantum measurements, and it has become clear
that the new relation plays a role of the first principle to derive various
quantum limits on measurement and information processing in a unified
treatment. This paper examines the above development on the noise-disturbance
uncertainty principle in the model-independent approach based on the
measurement operator formalism, which is widely accepted to describe a class of
generalized measurements in the field of quantum information. We obtain
explicit formulas for the noise and disturbance of measurements given by the
measurement operators, and show that projective measurements do not satisfy the
Heisenberg-type noise-disturbance relation that is typical in the gamma-ray
microscope thought experiments. We also show that the disturbance on a Pauli
operator of a projective measurement of another Pauli operator constantly
equals the square root of 2, and examine how this measurement violates the
Heisenberg-type relation but satisfies the new noise-disturbance relation.Comment: 11 pages. Based on the author's invited talk at the 9th International
Conference on Squeezed States and Uncertainty Relations (ICSSUR'2005),
Besancon, France, May 2-6, 200
Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
The Heisenberg uncertainty principle states that the product of the noise in
a position measurement and the momentum disturbance caused by that measurement
should be no less than the limit set by Planck's constant, hbar/2, as
demonstrated by Heisenberg's thought experiment using a gamma-ray microscope.
Here I show that this common assumption is false: a universally valid trade-off
relation between the noise and the disturbance has an additional correlation
term, which is redundant when the intervention brought by the measurement is
independent of the measured object, but which allows the noise-disturbance
product much below Planck's constant when the intervention is dependent. A
model of measuring interaction with dependent intervention shows that
Heisenberg's lower bound for the noise-disturbance product is violated even by
a nearly nondisturbing, precise position measuring instrument. An experimental
implementation is also proposed to realize the above model in the context of
optical quadrature measurement with currently available linear optical devices.Comment: Revtex, 6 page
Instruments and channels in quantum information theory
While a positive operator valued measure gives the probabilities in a quantum
measurement, an instrument gives both the probabilities and the a posteriori
states. By interpreting the instrument as a quantum channel and by using the
typical inequalities for the quantum and classical relative entropies, many
bounds on the classical information extracted in a quantum measurement, of the
type of Holevo's bound, are obtained in a unified manner.Comment: 12 pages, revtex
Solution to the Mean King's problem with mutually unbiased bases for arbitrary levels
The Mean King's problem with mutually unbiased bases is reconsidered for
arbitrary d-level systems. Hayashi, Horibe and Hashimoto [Phys. Rev. A 71,
052331 (2005)] related the problem to the existence of a maximal set of d-1
mutually orthogonal Latin squares, in their restricted setting that allows only
measurements of projection-valued measures. However, we then cannot find a
solution to the problem when e.g., d=6 or d=10. In contrast to their result, we
show that the King's problem always has a solution for arbitrary levels if we
also allow positive operator-valued measures. In constructing the solution, we
use orthogonal arrays in combinatorial design theory.Comment: REVTeX4, 4 page
Elastic and total reaction cross sections of oxygen isotopes in Glauber theory
We systematically calculate the total reaction cross sections of oxygen
isotopes, O, on a C target at high energies using the Glauber
theory. The oxygen isotopes are described with Slater determinants generated
from a phenomenological mean-field potential. The agreement between theory and
experiment is generally good, but a sharp increase of the reaction cross
sections from ^{21}O to ^{23}O remains unresolved. To examine the sensitivity
of the diffraction pattern of elastic scattering to the nuclear surface, we
study the differential elastic-scattering cross sections of proton-^{20,21,23}O
at the incident energy of 300 MeV by calculating the full Glauber amplitude.Comment: 9 pages, 8 figure
There exist non orthogonal quantum measurements that are perfectly repeatable
We show that, contrarily to the widespread belief, in quantum mechanics
repeatable measurements are not necessarily described by orthogonal
projectors--the customary paradigm of "observable". Nonorthogonal
repeatability, however, occurs only for infinite dimensions. We also show that
when a non orthogonal repeatable measurement is performed, the measured system
retains some "memory" of the number of times that the measurement has been
performed.Comment: 4 pages, 1 figure, revtex4, minor change
Contractive Schroedinger cat states for a free mass
Contractive states for a free quantum particle were introduced by Yuen [Yuen
H P 1983 Phys. Rev. Lett. 51, 719] in an attempt to evade the standard quantum
limit for repeated position measurements. We show how appropriate families of
two- and three component ``Schroedinger cat states'' are able to support
non-trivial correlations between the position and momentum observables leading
to contractive behavior. The existence of contractive Schroedinger cat states
is suggestive of potential novel roles of non-classical states for precision
measurement schemes.Comment: 24 pages, 7 encapsulated eps color figures, REVTeX4 style. Published
online in New Journal of Physics 5 (2003) 5.1-5.21. Higher-resolution figures
available in published version. (accessible at http://www.njp.org/
Quantum Nondemolition Monitoring of Universal Quantum Computers
The halt scheme for quantum Turing machines, originally proposed by Deutsch,
is reformulated precisely and is proved to work without spoiling the
computation. The ``conflict'' pointed out recently by Myers in the definition
of a universal quantum computer is shown to be only apparent. In the context of
quantum nondemolition (QND) measurement, it is also shown that the output
observable, an observable representing the output of the computation, is a QND
observable and that the halt scheme is equivalent to the QND monitoring of the
output observable.Comment: 5 pages, RevTeX, no figures, revised, to appear in Phys. Rev. Let
Quantum noise in ideal operational amplifiers
We consider a model of quantum measurement built on an ideal operational
amplifier operating in the limit of infinite gain, infinite input impedance and
null output impedance and with a feddback loop. We evaluate the intensity and
voltage noises which have to be added to the classical amplification equations
in order to fulfill the requirements of quantum mechanics. We give a
description of this measurement device as a quantum network scattering quantum
fluctuations from input to output ports.Comment: 4 pages, 2 figures, RevTe
General Framework for the Behaviour of Continuously Observed Open Quantum Systems
We develop the general quantum stochastic approach to the description of
quantum measurements continuous in time. The framework, that we introduce,
encompasses the various particular models for continuous-time measurements
condsidered previously in the physical and the mathematical literature.Comment: 30 pages, no figure
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