864 research outputs found
Continuous-variable quantum non-demolishing interaction at a distance
A feasible setup of continuous-variable (CV) quantum non-demolishing (QND)
interaction at a distance is proposed. If two distant experimentalists are able
to locally perform identical QND interactions then the proposed realization
requires only a single quantum channel and classical communication between
them. A possible implementation of the proposed setup in recent quantum optical
laboratories is discussed and an influence of Gaussian noise in the quantum
channel on a quality of the implementation is analyzed. An efficient
realization of the QND interaction at a distance can be a basic step to
possible distributed quantum CV experiments between the distant laboratories.Comment: 5 pages, 2 figure
Standard Quantum Limits for broadband position measurement
I utilize the Caves-Milburn model for continuous position measurements to
formulate a broadband version of the Standard Quantum Limit (SQL) for
monitoring the position of a free mass, and illustrate the use of Kalman
filtering to recover the SQL for estimating a weak classical force that acts on
a quantum-mechanical test particle under continuous observation. These
derivations are intended to clarify the interpretation of SQL's in the context
of continuous quantum measurement.Comment: Replaced version: changed title, fixed algebra error at the very end,
conclusions modified accordingly. Four pages, one eps figur
Quantum probabilities as Bayesian probabilities
In the Bayesian approach to probability theory, probability quantifies a
degree of belief for a single trial, without any a priori connection to
limiting frequencies. In this paper we show that, despite being prescribed by a
fundamental law, probabilities for individual quantum systems can be understood
within the Bayesian approach. We argue that the distinction between classical
and quantum probabilities lies not in their definition, but in the nature of
the information they encode. In the classical world, maximal information about
a physical system is complete in the sense of providing definite answers for
all possible questions that can be asked of the system. In the quantum world,
maximal information is not complete and cannot be completed. Using this
distinction, we show that any Bayesian probability assignment in quantum
mechanics must have the form of the quantum probability rule, that maximal
information about a quantum system leads to a unique quantum-state assignment,
and that quantum theory provides a stronger connection between probability and
measured frequency than can be justified classically. Finally we give a
Bayesian formulation of quantum-state tomography.Comment: 6 pages, Latex, final versio
Chaos for Liouville probability densities
Using the method of symbolic dynamics, we show that a large class of
classical chaotic maps exhibit exponential hypersensitivity to perturbation,
i.e., a rapid increase with time of the information needed to describe the
perturbed time evolution of the Liouville density, the information attaining
values that are exponentially larger than the entropy increase that results
from averaging over the perturbation. The exponential rate of growth of the
ratio of information to entropy is given by the Kolmogorov-Sinai entropy of the
map. These findings generalize and extend results obtained for the baker's map
[R. Schack and C. M. Caves, Phys. Rev. Lett. 69, 3413 (1992)].Comment: 26 pages in REVTEX, no figures, submitted to Phys. Rev.
Hypersensitivity to Perturbations in the Quantum Baker's Map
We analyze a randomly perturbed quantum version of the baker's
transformation, a prototype of an area-conserving chaotic map. By numerically
simulating the perturbed evolution, we estimate the information needed to
follow a perturbed Hilbert-space vector in time. We find that the Landauer
erasure cost associated with this information grows very rapidly and becomes
much larger than the maximum statistical entropy given by the logarithm of the
dimension of Hilbert space. The quantum baker's map thus displays a
hypersensitivity to perturbations that is analogous to behavior found earlier
in the classical case. This hypersensitivity characterizes ``quantum chaos'' in
a way that is directly relevant to statistical physics.Comment: 8 pages, LATEX, 3 Postscript figures appended as uuencoded fil
Quantum Mechanics and Linearized Gravitational Waves
The interaction of classical gravitational waves (GW) with matter is studied
within a quantum mechanical framework. The classical equations of motion in the
long wave-length limit is quantized and a Schroedinger equation for the
interaction of GW with matter is proposed. Due to its quadrapole nature, the GW
interacts with matter by producing squeezed quantum states. The resultant
hamiltonian is quite different from one would expect from general principles,
however. The interaction of GW with the free particle, the harmonic oscillator
and the hydrogen atom is then studied using this hamiltonian.Comment: 24 pages, written in REVTE
Chaos and quantum-nondemolition measurements
The problem of chaotic behavior in quantum mechanics is investigated against the background of the theory of quantum-nondemolition (QND) measurements. The analysis is based on two relevant features: The outcomes of a sequence of QND measurements are unambiguously predictable, and these measurements actually can be performed on one single system without perturbing its time evolution. Consequently, QND measurements represent an appropriate framework to analyze the conditions for the occurrence of ‘‘deterministic randomness’’ in quantum systems. The general arguments are illustrated by a discussion of a quantum system with a time evolution that possesses nonvanishing algorithmic complexity
Reduction of quantum noise in optical interferometers using squeezed light
We study the photon counting noise in optical interferometers used for
gravitational wave detection. In order to reduce quantum noise a squeezed
vacuum state is injected into the usually unused input port. Here, we
specifically investigate the so called `dark port case', when the beam splitter
is oriented close to 90{\deg} to the incoming laser beam, such that nearly all
photons go to one output port of the interferometer, and only a small fraction
of photons is seen in the other port (`dark port'). For this case it had been
suggested that signal amplification is possible without concurrent noise
amplification [R.Barak and Y.Ben-Aryeh, J.Opt.Soc.Am.B25(361)2008]. We show
that by injection of a squeezed vacuum state into the second input port,
counting noise is reduced for large values of the squeezing factor, however the
signal is not amplified. Signal strength only depends on the intensity of the
laser beam.Comment: 8 pages, 1 figur
Coherent Quantum-Noise Cancellation for Optomechanical Sensors
Using a flowchart representation of quantum optomechanical dynamics, we
design coherent quantum-noise-cancellation schemes that can eliminate the
back-action noise induced by radiation pressure at all frequencies and thus
overcome the standard quantum limit of force sensing. The proposed schemes can
be regarded as novel examples of coherent feedforward quantum control.Comment: 4 pages, 5 figures, v2: accepted by Physical Review Letter
Optimal Monitoring of Position in Nonlinear Quantum Systems
We discuss a model of repeated measurements of position in a quantum system
which is monitored for a finite amount of time with a finite instrumental
error. In this framework we recover the optimum monitoring of a harmonic
oscillator proposed in the case of an instantaneous collapse of the
wavefunction into an infinite-accuracy measurement result. We also establish
numerically the existence of an optimal measurement strategy in the case of a
nonlinear system. This optimal strategy is completely defined by the spectral
properties of the nonlinear system.Comment: 4 pages, REVTeX 3.0, 4 PostScript figure
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