353,043 research outputs found
Operational Theory of Homodyne Detection
We discuss a balanced homodyne detection scheme with imperfect detectors in
the framework of the operational approach to quantum measurement. We show that
a realistic homodyne measurement is described by a family of operational
observables that depends on the experimental setup, rather than a single field
quadrature operator. We find an explicit form of this family, which fully
characterizes the experimental device and is independent of a specific state of
the measured system. We also derive operational homodyne observables for the
setup with a random phase, which has been recently applied in an ultrafast
measurement of the photon statistics of a pulsed diode laser. The operational
formulation directly gives the relation between the detected noise and the
intrinsic quantum fluctuations of the measured field. We demonstrate this on
two examples: the operational uncertainty relation for the field quadratures,
and the homodyne detection of suppressed fluctuations in photon statistics.Comment: 7 pages, REVTe
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
Contextuality under weak assumptions
The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements could not be viewed as deterministically revealing pre-existing properties of the system. More precisely, no model can assign deterministic outcomes to the projectors of a quantum measurement in a way that depends only on the projector and not the context (the full set of projectors) in which it appeared, despite the fact that the Born rule probabilities associated with projectors are independent of the context. A more general, operational definition of contextuality introduced by Spekkens, which we will term "probabilistic contextuality", drops the assumption of determinism and allows for operations other than measurements to be considered contextual. Even two-dimensional quantum mechanics can be shown to be contextual under this generalised notion. Probabilistic noncontextuality represents the postulate that elements of an operational theory that cannot be distinguished from each other based on the statistics of arbitrarily many repeated experiments (they give rise to the same operational probabilities) are ontologically identical. In this paper, we introduce a framework that enables us to distinguish between different noncontextuality assumptions in terms of the relationships between the ontological representations of objects in the theory given a certain relation between their operational representations. This framework can be used to motivate and define a "possibilistic" analogue, encapsulating the idea that elements of an operational theory that cannot be unambiguously distinguished operationally can also not be unambiguously distinguished ontologically. We then prove that possibilistic noncontextuality is equivalent to an alternative notion of noncontextuality proposed by Hardy. Finally, we demonstrate that these weaker noncontextuality assumptions are sufficient to prove alternative versions of known "no-go" theorems that constrain ψ-epistemic models for quantum mechanics
Different instances of time as different quantum modes: quantum states across space-time for continuous variables
Space-time is one of the most essential, yet most mysterious concepts in
physics. In quantum mechanics it is common to understand time as a marker of
instances of evolution and define states around all the space but at one time;
while in general relativity space-time is taken as a combinator, curved around
mass. Here we present a unified approach on both space and time in quantum
theory, and build quantum states across spacetime instead of only on spatial
slices. We no longer distinguish measurements on the same system at different
times with measurements on different systems at one time and construct
spacetime states upon these measurement statistics. As a first step towards
non-relativistic quantum field theory, we consider how to approach this in the
continuous-variable multi-mode regime. We propose six possible definitions for
spacetime states in continuous variables, based on four different measurement
processes: quadratures, displaced parity operators, position measurements and
weak measurements. The basic idea is to treat different instances of time as
different quantum modes. They are motivated by the pseudo-density matrix
formulation among indefinite causal structures and the path integral formalism.
We show that these definitions lead to desirable properties, and raise the
differences and similarities between spatial and temporal correlations. An
experimental proposal for tomography is presented, construing the operational
meaning of the spacetime states.Comment: 28 pages, comments welcom
A Wigner quasiprobability distribution of work
In this article we introduce a quasiprobability distribution of work that is
based on the Wigner function. This construction rests on the idea that the work
done on an isolated system can be coherently measured by coupling the system to
a quantum measurement apparatus. In this way, a quasiprobability distribution
of work can be defined in terms of the Wigner function of the apparatus. This
quasidistribution contains the information of the work statistics and also
holds a clear operational definition. Moreover, it is shown that the presence
of quantum coherence in the energy eigenbasis is related with the appearance of
characteristics related to non-classicality in the Wigner function such as
negativity and interference fringes. On the other hand, from this
quasiprobability distribution it is straightforward to obtain the standard
two-point measurement probability distribution of work and also the difference
in average energy for initial states with coherences.Comment: 11 pages, 3 figure
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