486 research outputs found
Information gain versus state disturbance for a single qubit
The trade-off between the information gain and the state disturbance is
derived for quantum operations on a single qubit prepared in a uniformly
distributed pure state. The derivation is valid for a class of measures
quantifying the state disturbance and the information gain which satisfy
certain invariance conditions. This class includes in particular the Shannon
entropy versus the operation fidelity. The central role in the derivation is
played by efficient quantum operations, which leave the system in a pure output
state for any measurement outcome. It is pointed out that the optimality of
efficient quantum operations among those inducing a given operator-valued
measure is related to Davies' characterization of convex invariant functions on
hermitian operators.Comment: 17 pages, LaTeX, osid.sty. Substantially expanded and generalize
Transition probabilities between quasifree states
We obtain a general formula for the transition probabilities between any
state of the algebra of the canonical commutation relations (CCR-algebra) and a
squeezed quasifree state. Applications of this formula are made for the case of
multimode thermal squeezed states of quantum optics using a general canonical
decomposition of the correlation matrix valid for any quasifree state. In the
particular case of a one mode CCR-algebra we show that the transition
probability between two quasifree squeezed states is a decreasing function of
the geodesic distance between the points of the upper half plane representing
these states. In the special case of the purification map it is shown that the
transition probability between the state of the enlarged system and the product
state of real and fictitious subsystems can be a measure for the entanglement.Comment: 13 pages, REVTeX, no figure
Lower and upper bounds on the fidelity susceptibility
We derive upper and lower bounds on the fidelity susceptibility in terms of
macroscopic thermodynamical quantities, like susceptibilities and thermal
average values. The quality of the bounds is checked by the exact expressions
for a single spin in an external magnetic field. Their usefulness is
illustrated by two examples of many-particle models which are exactly solved in
the thermodynamic limit: the Dicke superradiance model and the single impurity
Kondo model. It is shown that as far as divergent behavior is considered, the
fidelity susceptibility and the thermodynamic susceptibility are equivalent for
a large class of models exhibiting critical behavior.Comment: 19 page
New measure of electron correlation
We propose to quantify the "correlation" inherent in a many-electron (or
many-fermion) wavefunction by comparing it to the unique uncorrelated state
that has the same single-particle density operator as it does.Comment: Final version to appear in PR
SHRINKAGE IN TERNARY MIXES OF CONTAINER MEDIA
Based on functional relationships established for binary mixes of container media, a mathematical model is proposed for ternary component mixtures. Shrinkage values are generated for three-component mixtures based on mathematical equations. Empirically observed shrinkage values for corresponding three-component mixtures are determined and used as the basis for assessing the reliability of the proposed mathematical model for characterizing shrinkage in mixtures of container media. . Regression equations were developed and compared for both theoretical and empirical results
Berry phase and fidelity susceptibility of the three-qubit Lipkin-Meshkov-Glick ground state
Berry phases and quantum fidelities for interacting spins have attracted
considerable attention, in particular in relation to entanglement properties of
spin systems and quantum phase transitions. These efforts mainly focus either
on spin pairs or the thermodynamic infinite spin limit, while studies of the
multipartite case of a finite number of spins are rare. Here, we analyze Berry
phases and quantum fidelities of the energetic ground state of a
Lipkin-Meshkov-Glick (LMG) model consisting of three spin-1/2 particles
(qubits). We find explicit expressions for the Berry phase and fidelity
susceptibility of the full system as well as the mixed state Berry phase and
partial-state fidelity susceptibility of its one- and two-qubit subsystems. We
demonstrate a realization of a nontrivial magnetic monopole structure
associated with local, coordinated rotations of the three-qubit system around
the external magnetic field.Comment: The title of the paper has been changed in this versio
Locating Overlap Information in Quantum Systems
When discussing the black hole information problem the term ``information
flow'' is frequently used in a rather loose fashion. In this article I attempt
to make this notion more concrete. I consider a Hilbert space which is
constructed as a tensor product of two subspaces (representing for example
inside and outside the black hole). I discuss how the system has the capacity
to contain information which is in NEITHER of the subspaces. I attempt to
quantify the amount of information located in each of the two subspaces, and
elsewhere, and analyze the extent to which unitary evolution can correspond to
``information flow''. I define the notion of ``overlap information'' which
appears to be well suited to the problem.Comment: 25 pages plain LaTeX, no figures. Imperial/TP/93-94/2
Generating random density matrices
We study various methods to generate ensembles of random density matrices of
a fixed size N, obtained by partial trace of pure states on composite systems.
Structured ensembles of random pure states, invariant with respect to local
unitary transformations are introduced. To analyze statistical properties of
quantum entanglement in bi-partite systems we analyze the distribution of
Schmidt coefficients of random pure states. Such a distribution is derived in
the case of a superposition of k random maximally entangled states. For another
ensemble, obtained by performing selective measurements in a maximally
entangled basis on a multi--partite system, we show that this distribution is
given by the Fuss-Catalan law and find the average entanglement entropy. A more
general class of structured ensembles proposed, containing also the case of
Bures, forms an extension of the standard ensemble of structureless random pure
states, described asymptotically, as N \to \infty, by the Marchenko-Pastur
distribution.Comment: 13 pages in latex with 8 figures include
Statistical distinguishability between unitary operations
The problem of distinguishing two unitary transformations, or quantum gates,
is analyzed and a function reflecting their statistical distinguishability is
found. Given two unitary operations, and , it is proved that there
always exists a finite number such that and are perfectly distinguishable, although they were not in the single-copy
case. This result can be extended to any finite set of unitary transformations.
Finally, a fidelity for one-qubit gates, which satisfies many useful properties
from the point of view of quantum information theory, is presented.Comment: 6 pages, REVTEX. The perfect distinguishability result is extended to
any finite set of gate
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