507 research outputs found
Preferred Measurements: Optimality and Stability in Quantum Parameter Estimation
We explore precision in a measurement process incorporating pure probe
states, unitary dynamics and complete measurements via a simple formalism. The
concept of `information complement' is introduced. It undermines measurement
precision and its minimization reveals the system properties at an optimal
point. Maximally precise measurements can exhibit independence from the true
value of the estimated parameter, but demanding this severely restricts the
type of viable probe and dynamics, including the requirement that the
Hamiltonian be block-diagonal in a basis of preferred measurements. The
curvature of the information complement near a globally optimal point provides
a new quantification of measurement stability.Comment: 4 pages, 2 figures, in submission. Substantial Extension and
replacement of arXiv:0902.3260v1 in response to Referees' remark
Analysis of a convenient information bound for general quantum channels
Open questions from Sarovar and Milburn (2006 J.Phys. A: Math. Gen. 39 8487)
are answered. Sarovar and Milburn derived a convenient upper bound for the
Fisher information of a one-parameter quantum channel. They showed that for
quasi-classical models their bound is achievable and they gave a necessary and
sufficient condition for positive operator-valued measures (POVMs) attaining
this bound. They asked (i) whether their bound is attainable more generally,
(ii) whether explicit expressions for optimal POVMs can be derived from the
attainability condition. We show that the symmetric logarithmic derivative
(SLD) quantum information is less than or equal to the SM bound, i.e.\
and we find conditions for equality. As
the Fisher information is less than or equal to the SLD quantum information,
i.e. , we can deduce when equality holds in
. Equality does not hold for all
channels. As a consequence, the attainability condition cannot be used to test
for optimal POVMs for all channels. These results are extended to
multi-parameter channels.Comment: 16 pages. Published version. Some of the lemmas have been corrected.
New resuts have been added. Proofs are more rigorou
Measuring Polynomial Invariants of Multi-Party Quantum States
We present networks for directly estimating the polynomial invariants of
multi-party quantum states under local transformations. The structure of these
networks is closely related to the structure of the invariants themselves and
this lends a physical interpretation to these otherwise abstract mathematical
quantities. Specifically, our networks estimate the invariants under local
unitary (LU) transformations and under stochastic local operations and
classical communication (SLOCC). Our networks can estimate the LU invariants
for multi-party states, where each party can have a Hilbert space of arbitrary
dimension and the SLOCC invariants for multi-qubit states. We analyze the
statistical efficiency of our networks compared to methods based on estimating
the state coefficients and calculating the invariants.Comment: 8 pages, 4 figures, RevTex4, v2 references update
Optimal estimation of one parameter quantum channels
We explore the task of optimal quantum channel identification, and in
particular the estimation of a general one parameter quantum process. We derive
new characterizations of optimality and apply the results to several examples
including the qubit depolarizing channel and the harmonic oscillator damping
channel. We also discuss the geometry of the problem and illustrate the
usefulness of using entanglement in process estimation.Comment: 23 pages, 4 figures. Published versio
Entropy Distance: New Quantum Phenomena
We study a curve of Gibbsian families of complex 3x3-matrices and point out
new features, absent in commutative finite-dimensional algebras: a
discontinuous maximum-entropy inference, a discontinuous entropy distance and
non-exposed faces of the mean value set. We analyze these problems from various
aspects including convex geometry, topology and information geometry. This
research is motivated by a theory of info-max principles, where we contribute
by computing first order optimality conditions of the entropy distance.Comment: 34 pages, 5 figure
Mixtures in non stable Levy processes
We analyze the Levy processes produced by means of two interconnected classes
of non stable, infinitely divisible distribution: the Variance Gamma and the
Student laws. While the Variance Gamma family is closed under convolution, the
Student one is not: this makes its time evolution more complicated. We prove
that -- at least for one particular type of Student processes suggested by
recent empirical results, and for integral times -- the distribution of the
process is a mixture of other types of Student distributions, randomized by
means of a new probability distribution. The mixture is such that along the
time the asymptotic behavior of the probability density functions always
coincide with that of the generating Student law. We put forward the conjecture
that this can be a general feature of the Student processes. We finally analyze
the Ornstein--Uhlenbeck process driven by our Levy noises and show a few
simulation of it.Comment: 28 pages, 3 figures, to be published in J. Phys. A: Math. Ge
Non elliptic SPDEs and ambit fields: existence of densities
Relying on the method developed in [debusscheromito2014], we prove the
existence of a density for two different examples of random fields indexed by
(t,x)\in(0,T]\times \Rd. The first example consists of SPDEs with Lipschitz
continuous coefficients driven by a Gaussian noise white in time and with a
stationary spatial covariance, in the setting of [dalang1999]. The density
exists on the set where the nonlinearity of the noise does not vanish.
This complements the results in [sanzsuess2015] where is assumed to be
bounded away from zero. The second example is an ambit field with a stochastic
integral term having as integrator a L\'evy basis of pure-jump, stable-like
type.Comment: 23 page
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