2,145 research outputs found
On the complementarity of the quadrature observables
In this paper we investigate the coupling properties of pairs of quadrature
observables, showing that, apart from the Weyl relation, they share the same
coupling properties as the position-momentum pair. In particular, they are
complementary. We determine the marginal observables of a covariant phase space
observable with respect to an arbitrary rotated reference frame, and observe
that these marginal observables are unsharp quadrature observables. The related
distributions constitute the Radon tranform of a phase space distribution of
the covariant phase space observable. Since the quadrature distributions are
the Radon transform of the Wigner function of a state, we also exhibit the
relation between the quadrature observables and the tomography observable, and
show how to construct the phase space observable from the quadrature
observables. Finally, we give a method to measure together with a single
measurement scheme any complementary pair of quadrature observables.Comment: Dedicated to Peter Mittelstaedt in honour of his eightieth birthda
Complementarity and the algebraic structure of 4-level quantum systems
The history of complementary observables and mutual unbiased bases is
reviewed. A characterization is given in terms of conditional entropy of
subalgebras. The concept of complementarity is extended to non-commutative
subalgebras. Complementary decompositions of a 4-level quantum system are
described and a characterization of the Bell basis is obtained.Comment: 19 page
Maximal Accuracy and Minimal Disturbance in the Arthurs-Kelly Simultaneous Measurement Process
The accuracy of the Arthurs-Kelly model of a simultaneous measurement of
position and momentum is analysed using concepts developed by Braginsky and
Khalili in the context of measurements of a single quantum observable. A
distinction is made between the errors of retrodiction and prediction. It is
shown that the distribution of measured values coincides with the initial state
Husimi function when the retrodictive accuracy is maximised, and that it is
related to the final state anti-Husimi function (the P representation of
quantum optics) when the predictive accuracy is maximised. The disturbance of
the system by the measurement is also discussed. A class of minimally
disturbing measurements is characterised. It is shown that the distribution of
measured values then coincides with one of the smoothed Wigner functions
described by Cartwright.Comment: 12 pages, 0 figures. AMS-Latex. Earlier version replaced with final
published versio
Electromagnetism in terms of quantum measurements
We consider the question whether electromagnetism can be derived from quantum
physics of measurements. It turns out that this is possible, both for quantum
and classical electromagnetism, if we use more recent innovations such as
smearing of observables and simultaneous measurability. In this way we justify
the use of von Neumann-type measurement models for physical processes.
We apply operational quantum measurement theory to gain insight in
fundamental aspects of quantum physics. Interactions of von Neumann type make
the Heisenberg evolution of observables describable using explicit operator
deformations. In this way one can obtain quantized electromagnetism as a
measurement of a system by another. The relevant deformations (Rieffel
deformations) have a mathematically well-defined "classical" limit which is
indeed classical electromagnetism for our choice of interaction
On the nature of continuous physical quantities in classical and quantum mechanics
Within the traditional Hilbert space formalism of quantum mechanics, it is
not possible to describe a particle as possessing, simultaneously, a sharp
position value and a sharp momentum value. Is it possible, though, to describe
a particle as possessing just a sharp position value (or just a sharp momentum
value)? Some, such as Teller (Journal of Philosophy, 1979), have thought that
the answer to this question is No -- that the status of individual continuous
quantities is very different in quantum mechanics than in classical mechanics.
On the contrary, I shall show that the same subtle issues arise with respect to
continuous quantities in classical and quantum mechanics; and that it is, after
all, possible to describe a particle as possessing a sharp position value
without altering the standard formalism of quantum mechanics.Comment: 26 pages, LaTe
Neumark Operators and Sharp Reconstructions, the finite dimensional case
A commutative POV measure with real spectrum is characterized by the
existence of a PV measure (the sharp reconstruction of ) with real
spectrum such that can be interpreted as a randomization of . This paper
focuses on the relationships between this characterization of commutative POV
measures and Neumark's extension theorem. In particular, we show that in the
finite dimensional case there exists a relation between the Neumark operator
corresponding to the extension of and the sharp reconstruction of . The
relevance of this result to the theory of non-ideal quantum measurement and to
the definition of unsharpness is analyzed.Comment: 37 page
Born-Oppenheimer Approximation near Level Crossing
We consider the Born-Oppenheimer problem near conical intersection in two
dimensions. For energies close to the crossing energy we describe the wave
function near an isotropic crossing and show that it is related to generalized
hypergeometric functions 0F3. This function is to a conical intersection what
the Airy function is to a classical turning point. As an application we
calculate the anomalous Zeeman shift of vibrational levels near a crossing.Comment: 8 pages, 1 figure, Lette
On Quantum State Observability and Measurement
We consider the problem of determining the state of a quantum system given
one or more readings of the expectation value of an observable. The system is
assumed to be a finite dimensional quantum control system for which we can
influence the dynamics by generating all the unitary evolutions in a Lie group.
We investigate to what extent, by an appropriate sequence of evolutions and
measurements, we can obtain information on the initial state of the system. We
present a system theoretic viewpoint of this problem in that we study the {\it
observability} of the system. In this context, we characterize the equivalence
classes of indistinguishable states and propose algorithms for state
identification
Macroscopic limit of a solvable dynamical model
The interaction between an ultrarelativistic particle and a linear array made
up of two-level systems (^^ ^^ AgBr" molecules) is studied by making use of
a modified version of the Coleman-Hepp Hamiltonian. Energy-exchange processes
between the particle and the molecules are properly taken into account, and the
evolution of the total system is calculated exactly both when the array is
initially in the ground state and in a thermal state. In the macroscopic limit
(), the system remains solvable and leads to interesting
connections with the Jaynes-Cummings model, that describes the interaction of a
particle with a maser. The visibility of the interference pattern produced by
the two branch waves of the particle is computed, and the conditions under
which the spin array in the limit behaves as a ^^ ^^
detector" are investigated. The behavior of the visibility yields good insights
into the issue of quantum measurements: It is found that, in the
thermodynamical limit, a superselection-rule space appears in the description
of the (macroscopic) apparatus. In general, an initial thermal state of the ^^
^^ detector" provokes a more substantial loss of quantum coherence than an
initial ground state. It is argued that a system decoheres more as the
temperature of the detector increases. The problem of ^^ ^^ imperfect
measurements" is also shortly discussed.Comment: 30 pages, report BA-TH/93-13
- …