13,089 research outputs found
A Theory of Errors in Quantum Measurement
It is common to model random errors in a classical measurement by the normal
(Gaussian) distribution, because of the central limit theorem. In the quantum
theory, the analogous hypothesis is that the matrix elements of the error in an
observable are distributed normally. We obtain the probability distribution
this implies for the outcome of a measurement, exactly for the case of 2x2
matrices and in the steepest descent approximation in general. Due to the
phenomenon of `level repulsion', the probability distributions obtained are
quite different from the Gaussian.Comment: Based on talk at "Spacetime and Fundamental Interactions: Quantum
Aspects" A conference to honor A. P. Balachandran's 65th Birthda
Passage-time distributions from a spin-boson detector model
The passage-time distribution for a spread-out quantum particle to traverse a
specific region is calculated using a detailed quantum model for the detector
involved. That model, developed and investigated in earlier works, is based on
the detected particle's enhancement of the coupling between a collection of
spins (in a metastable state) and their environment. We treat the continuum
limit of the model, under the assumption of the Markov property, and calculate
the particle state immediately after the first detection. An explicit example
with 15 boson modes shows excellent agreement between the discrete model and
the continuum limit. Analytical expressions for the passage-time distribution
as well as numerical examples are presented. The precision of the measurement
scheme is estimated and its optimization discussed. For slow particles, the
precision goes like , which improves previous estimates,
obtained with a quantum clock model.Comment: 11 pages, 6 figures; minor changes, references corrected; accepted
for publication in Phys. Rev.
Probing of the Kondo peak by the impurity charge measurement
We consider the real-time dynamics of the Kondo system after the local probe
of the charge state of the magnetic impurity. Using the exactly solvable
infinite-degeneracy Anderson model we find explicitly the evolution of the
impurity charge after the measurement.Comment: 4 pages, 1 eps figure, revte
Weak Measurements with Arbitrary Pointer States
The exact conditions on valid pointer states for weak measurements are
derived. It is demonstrated that weak measurements can be performed with any
pointer state with vanishing probability current density. This condition is
found both for weak measurements of noncommuting observables and for -number
observables. In addition, the interaction between pointer and object must be
sufficiently weak. There is no restriction on the purity of the pointer state.
For example, a thermal pointer state is fully valid.Comment: 4 page
Classical, quantum and total correlations
We discuss the problem of separating consistently the total correlations in a
bipartite quantum state into a quantum and a purely classical part. A measure
of classical correlations is proposed and its properties are explored.Comment: 10 pages, 3 figure
Relative momentum for identical particles
Possible definitions for the relative momentum of identical particles are
considered
Nonclassicality of Thermal Radiation
It is demonstrated that thermal radiation of small occupation number is
strongly nonclassical. This includes most forms of naturally occurring
radiation. Nonclassicality can be observed as a negative weak value of a
positive observable. It is related to negative values of the Margenau-Hill
quasi-probability distribution.Comment: 3 pages, 3 figure
Quantum strategies
We consider game theory from the perspective of quantum algorithms.
Strategies in classical game theory are either pure (deterministic) or mixed
(probabilistic). We introduce these basic ideas in the context of a simple
example, closely related to the traditional Matching Pennies game. While not
every two-person zero-sum finite game has an equilibrium in the set of pure
strategies, von Neumann showed that there is always an equilibrium at which
each player follows a mixed strategy. A mixed strategy deviating from the
equilibrium strategy cannot increase a player's expected payoff. We show,
however, that in our example a player who implements a quantum strategy can
increase his expected payoff, and explain the relation to efficient quantum
algorithms. We prove that in general a quantum strategy is always at least as
good as a classical one, and furthermore that when both players use quantum
strategies there need not be any equilibrium, but if both are allowed mixed
quantum strategies there must be.Comment: 8 pages, plain TeX, 1 figur
Investigation of a quantum mechanical detector model for moving, spread-out particles
We investigate a fully quantum mechanical spin model for the detection of a moving particle. This model, developed in earlier work, is based on a collection of spins at fixed locations and in a metastable state, with the particle locally enhancing the coupling of the spins to an environment of bosons. Appearance of bosons from particular spins signals the presence of the particle at the spin location, and the first boson indicates its arrival. The original model used discrete boson modes. Here we treat the continuum limit, under the assumption of the Markov property, and calculate the arrival-time distribution for a particle to reach a specific region
- âŠ