22,667 research outputs found

### Deccoherent Histories and Measurement of Temporal Correlation Functions for Leggett-Garg Inequalities

We consider two protocols for the measurement of the temporal correlation
functions of a dichotomic variable Q appearing in Leggett-Garg type
inequalities. The protocols measure solely whether Q has the same or different
sign at the ends of a given time interval. They are inspired, in part, by a
decoherent histories analysis of the two-time histories of Q although the
protocols are ultimately expressed in macrorealistic form independent of
quantum theory. The first type involves an ancilla coupled to the system with
two sequential CNOT gates, and the two-time histories of the system are
determined in a single final time measurement of the ancilla. It is
non-invasive for special choices of initial system states and partially
invasive for more general choices. Modified Leggett-Garg type inequalities
which accommodate the partial invasiveness are discussed. The quantum picture
of the protocol shows that for certain choices of primary system initial state
the protocol is undetectable with respect to final system state measurements,
although it is still invasive at intermediate times. This invasiveness can be
reduced with different choices of ancilla states and the protocol is then
similar in flavour to a weak measurement. The second type of protocol is based
on the fact that the behaviour of Q over a time interval can be determined from
knowledge of the dynamics together with a measurement of certain initial (or
final) data. Its quantum version corresponds to the known fact that when sets
of histories are decoherent, their probabilities may be expressed in terms of a
record projector, hence the two-time histories in which Q has the same or
different sign can be determined by a single projective measurement. The
resulting protocol resembles the decay-type protocol proposed by Huelga and
collaborators (which is non-invasive but requires a stationarity assumption).Comment: 33 pages. Revised appendix on LG inequalities for partially invasive
measurements. Accepted for publication in Physical Review

### Arrival Times in Quantum Theory from an Irreversible Detector Model

We investigate a detector scheme designed to measure the arrival of a
particle at $x=0$ during a finite time interval. The detector consists of a two
state system which undergoes a transition from one state to the other when the
particle crosses $x=0$, and possesses the realistic feature that it is
effectively irreversible as a result of being coupled to a large environment.
The probabilities for crossing or not crossing $x=0$ thereby derived coincide
with earlier phenomenologically proposed expressions involving a complex
potential. The probabilities are compared with similar previously proposed
expressions involving sums over paths, and a connection with time operator
approaches is also indicated.Comment: 19 pages, plain Tex (Fourth revision). To appear in Prog.Th.Phys.
Vol. 102, No.

### The Leggett-Garg Inequalities and No-Signalling in Time: A Quasi-Probability Approach

The Leggett-Garg (LG) inequalities were proposed in order to assess whether
sets of pairs of sequential measurements on a single quantum system can be
consistent with an underlying notion of macrorealism. Here, the LG inequalities
are explored using a simple quasi-probability linear in the projection
operators to describe the properties of the system at two times. We show that
this quasi-probability is measurable, has the same correlation function as the
usual two-time measurement probability (for the bivalent variables considered
here) and has the key property that the probabilities for the later time are
independent of whether an earlier measurement was made, a generalization of the
no-signalling in time condition of Kofler and Brukner. We argue that this
quasi-probability, appropriately measured, provides a non-invasive measure of
macrorealism per se at the two time level. This measure, when combined with the
LG inequalities, provides a characterization of macrorealism more detailed than
that provided by the LG inequalities alone. When the quasi-probability is
non-negative, the LG system has a natural parallel with the EPRB system and
Fine's theorem. A simple spin model illustrating key features of the approach
is exhibited.Comment: 23 pages. Significant revisions. Change of titl

### An Operator Derivation of the Path Decomposition Expansion

The path decomposition expansion is a path integral technique for decomposing
sums over paths in configuration space into sums over paths in different
spatial regions. It leads to a decomposition of the configuration space
propagator across arbitrary surfaces in configuration space. It may be used,
for example, in calculations of the distribution of first crossing times. The
original proof relied heavily on the position representation and in particular
on the properties of path integrals. In this paper, an elementary proof of the
path decomposition expansion is given using projection operators. This leads to
a version of the path decomposition expansion more general than the
configuration space form previously given. The path decomposition expansion in
momentum space is given as an example.Comment: 9 pages Plain Te

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