12,487 research outputs found
Retrodiction of Generalised Measurement Outcomes
If a generalised measurement is performed on a quantum system and we do not
know the outcome, are we able to retrodict it with a second measurement? We
obtain a necessary and sufficient condition for perfect retrodiction of the
outcome of a known generalised measurement, given the final state, for an
arbitrary initial state. From this, we deduce that, when the input and output
Hilbert spaces have equal (finite) dimension, it is impossible to perfectly
retrodict the outcome of any fine-grained measurement (where each POVM element
corresponds to a single Kraus operator) for all initial states unless the
measurement is unitarily equivalent to a projective measurement. It also
enables us to show that every POVM can be realised in such a way that perfect
outcome retrodiction is possible for an arbitrary initial state when the number
of outcomes does not exceed the output Hilbert space dimension. We then
consider the situation where the initial state is not arbitrary, though it may
be entangled, and describe the conditions under which unambiguous outcome
retrodiction is possible for a fine-grained generalised measurement. We find
that this is possible for some state if the Kraus operators are linearly
independent. This condition is also necessary when the Kraus operators are
non-singular. From this, we deduce that every trace-preserving quantum
operation is associated with a generalised measurement whose outcome is
unambiguously retrodictable for some initial state, and also that a set of
unitary operators can be unambiguously discriminated iff they are linearly
independent. We then examine the issue of unambiguous outcome retrodiction
without entanglement. This has important connections with the theory of locally
linearly dependent and locally linearly independent operators.Comment: To appear in Physical Review
Thermalization of Squeezed States
Starting with a thermal squeezed state defined as a conventional thermal
state based on an appropriate hamiltonian, we show how an important physical
property, the signal-to-noise ratio, is degraded, and propose a simple model of
thermalization (Kraus thermalization).Comment: 7 pages, 1 table, 1 figure. Presented at ICSSUR 2005, Besancon,
Franc
Weak Values, Quantum Trajectories, and the Stony-Brook Cavity QED experiment
Weak values as introduced by Aharonov, Albert and Vaidman (AAV) are ensemble
average values for the results of weak measurements. They are interesting when
the ensemble is preselected on a particular initial state and postselected on a
particular final measurement result. I show that weak values arise naturally in
quantum optics, as weak measurements occur whenever an open system is monitored
(as by a photodetector). I use quantum trajectory theory to derive a
generalization of AAV's formula to include (a) mixed initial conditions, (b)
nonunitary evolution, (c) a generalized (non-projective) final measurement, and
(d) a non-back-action-evading weak measurement. I apply this theory to the
recent Stony-Brook cavity QED experiment demonstrating wave-particle duality
[G.T. Foster, L.A. Orozco, H.M. Castro-Beltran, and H.J. Carmichael, Phys. Rev.
Lett. {85}, 3149 (2000)]. I show that the ``fractional'' correlation function
measured in that experiment can be recast as a weak value in a form as simple
as that introduced by AAV.Comment: 6 pages, no figures. To be published in Phys. Rev.
The simplest demonstrations of quantum nonlocality
We investigate the complexity cost of demonstrating the key types of nonclassical correlations-Bell inequality violation, Einstein, Podolsky, Rosen (EPR)-steering, and entanglement-with independent agents, theoretically and in a photonic experiment. We show that the complexity cost exhibits a hierarchy among these three tasks, mirroring the recently discovered hierarchy for how robust they are to noise. For Bell inequality violations, the simplest test is the well-known Clauser-Horne-Shimony-Holt test, but for EPR-steering and entanglement the tests that involve the fewest number of detection patterns require nonprojective measurements. The simplest EPR-steering test requires a choice of projective measurement for one agent and a single nonprojective measurement for the other, while the simplest entanglement test uses just a single nonprojective measurement for each agent. In both of these cases, we derive our inequalities using the concept of circular two-designs. This leads to the interesting feature that in our photonic demonstrations, the correlation of interest is independent of the angle between the linear polarizers used by the two parties, which thus require no alignment
Total Widths And Slopes From Complex Regge Trajectories
Maximally complex Regge trajectories are introduced for which both Re
and Im grow as ( small and
positive). Our expression reduces to the standard real linear form as the
imaginary part (proportional to ) goes to zero. A scaling formula for
the total widths emerges: constant for large M, in very
good agreement with data for mesons and baryons. The unitarity corrections also
enhance the space-like slopes from their time-like values, thereby resolving an
old problem with the trajectory in charge exchange. Finally, the
unitarily enhanced intercept, , \nolinebreak is in
good accord with the Donnachie-Landshoff total cross section analysis.Comment: 9 pages, 3 Figure
Transitionless quantum drivings for the harmonic oscillator
Two methods to change a quantum harmonic oscillator frequency without
transitions in a finite time are described and compared. The first method, a
transitionless-tracking algorithm, makes use of a generalized harmonic
oscillator and a non-local potential. The second method, based on engineering
an invariant of motion, only modifies the harmonic frequency in time, keeping
the potential local at all times.Comment: 11 pages, 1 figure. Submitted for publicatio
Decoherence due to three-body loss and its effect on the state of a Bose-Einstein condensate
A Born-Markov master equation is used to investigate the decoherence of the
state of a macroscopically occupied mode of a cold atom trap due to three-body
loss. In the large number limit only coherent states remain pure for times
longer than the decoherence time: the time it takes for just three atoms to be
lost from the trap. For large numbers of atoms (N>10^4) the decoherence time is
found to be much faster than the phase collapse time caused by intra-trap
atomic collisions
Comment on ``Lyapunov Exponent of a Many Body System and Its Transport Coefficients''
In a recent Letter, Barnett, Tajima, Nishihara, Ueshima and Furukawa obtained
a theoretical expression for the maximum Lyapunov exponent of a
dilute gas. They conclude that is proportional to the cube root of
the self-diffusion coefficient , independent of the range of the interaction
potential. They validate their conjecture with numerical data for a dense
one-component plasma, a system with long-range forces. We claim that their
result is highly non-generic. We show in the following that it does not apply
to a gas of hard spheres, neither in the dilute nor in the dense phase.Comment: 1 page, Revtex - 1 PS Figs - Submitted to Physical Review Letter
Multivariate Granger Causality and Generalized Variance
Granger causality analysis is a popular method for inference on directed
interactions in complex systems of many variables. A shortcoming of the
standard framework for Granger causality is that it only allows for examination
of interactions between single (univariate) variables within a system, perhaps
conditioned on other variables. However, interactions do not necessarily take
place between single variables, but may occur among groups, or "ensembles", of
variables. In this study we establish a principled framework for Granger
causality in the context of causal interactions among two or more multivariate
sets of variables. Building on Geweke's seminal 1982 work, we offer new
justifications for one particular form of multivariate Granger causality based
on the generalized variances of residual errors. Taken together, our results
support a comprehensive and theoretically consistent extension of Granger
causality to the multivariate case. Treated individually, they highlight
several specific advantages of the generalized variance measure, which we
illustrate using applications in neuroscience as an example. We further show
how the measure can be used to define "partial" Granger causality in the
multivariate context and we also motivate reformulations of "causal density"
and "Granger autonomy". Our results are directly applicable to experimental
data and promise to reveal new types of functional relations in complex
systems, neural and otherwise.Comment: added 1 reference, minor change to discussion, typos corrected; 28
pages, 3 figures, 1 table, LaTe
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