194 research outputs found
Towards a Neo-Copenhagen Interpretation of Quantum Mechanics
The Copenhagen interpretation is critically considered. A number of
ambiguities, inconsistencies and confusions are discussed. It is argued that it
is possible to purge the interpretation so as to obtain a consistent and
reasonable way to interpret the mathematical formalism of quantum mechanics,
which is in agreement with the way this theory is dealt with in experimental
practice. In particular, the essential role attributed by the Copenhagen
interpretation to measurement is acknowledged. For this reason it is proposed
to refer to it as a neo-Copenhagen interpretation
On the feasibility and usefulness of applying the `Schr\"odinger c.q. Liouville-von Neumann equation' to quantum measurement
The present paper is a sequel to papers dealing with recent developments on
the issue of `quantum measurement'. In this paper `measurement within the
domain of application of quantum mechanics' is treated as a \emph{quantum
mechanical} \emph{interaction} of a `(sub)microscopic object ' and an
`equally (sub)microscopic part of the measuring instrument being
sensitive to the (sub)microscopic information', that interaction to be
described by a Schr\"odinger equation. The Stern-Gerlach experiment is used as
a paradigmatic example. An alternative to the Heisenberg inequality is found,
exhibiting the \emph{independent} contributions of `preparation of the initial
state of object ' \emph{and} `interaction of object \emph{and}
measuring instrument/probe '. Applicability of the Liouville-von Neumann
equation is stressed
The Haroche-Ramsey experiment as a generalized measurement
A number of atomic beam experiments, related to the Ramsey experiment and a
recent experiment by Brune et al., are studied with respect to the question of
complementarity. Three different procedures for obtaining information on the
state of the incoming atom are compared. Positive operator-valued measures are
explicitly calculated. It is demonstrated that, in principle, it is possible to
choose the experimental arrangement so as to admit an interpretation as a joint
non-ideal measurement yielding interference and ``which-way'' information.
Comparison of the different measurements gives insight into the question of
which information is provided by a (generalized) quantum mechanical
measurement. For this purpose the subspaces of Hilbert-Schmidt space, spanned
by the operators of the POVM, are determined for different measurement
arrangements and different values of the parameters.Comment: REVTeX, 22 pages, 5 figure
Quantum state tomography using a single apparatus
The density matrix of a two-level system (spin, atom) is usually determined
by measuring the three non-commuting components of the Pauli vector. This
density matrix can also be obtained via the measurement data of two commuting
variables, using a single apparatus. This is done by coupling the two-level
system to a mode of radiation field, where the atom-field interaction is
described with the Jaynes--Cummings model. The mode starts its evolution from a
known coherent state. The unknown initial state of the atom is found by
measuring two commuting observables: the population difference of the atom and
the photon number of the field. We discuss the advantages of this setup and its
possible applications.Comment: 7 pages, 8 figure, Phys. Rev.
Simultaneous measurement of two non-commuting quantum variables: Solution of a dynamical model
The possibility of performing simultaneous measurements in quantum mechanics
is investigated in the context of the Curie-Weiss model for a projective
measurement. Concretely, we consider a spin- system simultaneously
interacting with two magnets, which act as measuring apparatuses of two
different spin components. We work out the dynamics of this process and
determine the final state of the measuring apparatuses, from which we can find
the probabilities of the four possible outcomes of the measurements. The
measurement is found to be non-ideal, as (i) the joint statistics do not
coincide with the one obtained by separately measuring each spin component, and
(ii) the density matrix of the spin does not collapse in either of the measured
observables. However, we give an operational interpretation of the process as a
generalised quantum measurement, and show that it is fully informative: The
expected value of the measured spin components can be found with arbitrary
precision for sufficiently many runs of the experiment.Comment: 24 pages, 9 figures; close to published versio
Joint measurements of spin, operational locality and uncertainty
Joint, or simultaneous, measurements of non-commuting observables are
possible within quantum mechanics, if one accepts an increase in the variances
of the jointly measured observables. In this paper, we discuss joint
measurements of a spin 1/2 particle along any two directions. Starting from an
operational locality principle, it is shown how to obtain a bound on how sharp
the joint measurement can be. We give a direct interpretation of this bound in
terms of an uncertainty relation.Comment: Accepted for publication in Phys. Rev.
Channel kets, entangled states, and the location of quantum information
The well-known duality relating entangled states and noisy quantum channels
is expressed in terms of a channel ket, a pure state on a suitable tripartite
system, which functions as a pre-probability allowing the calculation of
statistical correlations between, for example, the entrance and exit of a
channel, once a framework has been chosen so as to allow a consistent set of
probabilities. In each framework the standard notions of ordinary (classical)
information theory apply, and it makes sense to ask whether information of a
particular sort about one system is or is not present in another system.
Quantum effects arise when a single pre-probability is used to compute
statistical correlations in different incompatible frameworks, and various
constraints on the presence and absence of different kinds of information are
expressed in a set of all-or-nothing theorems which generalize or give a
precise meaning to the concept of ``no-cloning.'' These theorems are used to
discuss: the location of information in quantum channels modeled using a
mixed-state environment; the (classical-quantum) channels introduced by
Holevo; and the location of information in the physical carriers of a quantum
code. It is proposed that both channel and entanglement problems be classified
in terms of pure states (functioning as pre-probabilities) on systems of parts, with mixed bipartite entanglement and simple noisy channels belonging
to the category , a five-qubit code to the category , etc.; then by
the dimensions of the Hilbert spaces of the component parts, along with other
criteria yet to be determined.Comment: Latex 32 pages, 4 figures in text using PSTricks. Version 3: Minor
typographical errors correcte
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