6,796 research outputs found
Coexistence of qubit effects
Two quantum events, represented by positive operators (effects), are coexistent if they can occur as possible outcomes in a single measurement scheme. Equivalently, the corresponding effects are coexistent if and only if they are contained in the ranges of a single (joint) observable. Here we give several equivalent characterizations of coexistent pairs of qubit effects. We also establish the equivalence between our results and those obtained independently by other authors. Our approach makes explicit use of the Minkowski space geometry inherent in the four-dimensional real vector space of selfadjoint operators in a two-dimensional complex Hilbert space
Quantum reservoirs with ion chains
Ion chains are promising platforms for studying and simulating quantum
reservoirs. One interesting feature is that their vibrational modes can mediate
entanglement between two objects which are coupled through the vibrational
modes of the chain. In this work we analyse entanglement between the transverse
vibrations of two heavy impurity defects embedded in an ion chain, which is
generated by the coupling with the chain vibrations. We verify general scaling
properties of the defects dynamics and demonstrate that entanglement between
the defects can be a stationary feature of these dynamics. We then analyse
entanglement in chains composed of tens of ions and propose a measurement
scheme which allows one to verify the existence of the predicted entangled
state.Comment: 14 pages, 12 figure
The norm-1-property of a quantum observable
A normalized positive operator measure has the
norm-1-property if \no{E(X)}=1 whenever . This property reflects
the fact that the measurement outcome probabilities for the values of such
observables can be made arbitrary close to one with suitable state
preparations. Some general implications of the norm-1-property are
investigated. As case studies, localization observables, phase observables, and
phase space observables are considered.Comment: 14 page
The Medical Treatment of Depression, 1991-1996: Productive Inefficiency, Expected Outcome Variations, and Price Indexes
We examine the price of treating episodes of acute phase major depression over the 1991-1996 time period. We combine data from a large retrospective medical claims data base (MarketScanTM, from the MedStat Group) with clinical literature and expert clinical opinion elicited from a two-state Delphi procedure. This enables us to construct a variety of treatment price indexes that include variations over time in the proportion of off-frontier' production, as well as the corresponding variations in expected treatment outcomes. We also incorporate the fact that the no treatment option ( waiting list') frequently results in spontaneous remission of depressive symptoms. We find that in general the incremental cost of successfully treating an episode of acute phase major depression has generally fallen over the 1991-96 time period. Based on hedonic regression equations that account for the effects of changing patient mix, we find price reductions that range from about -1.66% to -2.13% per year. An implication of this is that, since expenditures on depression are thought to be increasing since at least 1991, the source of the spending increases is volume (quantity) increases, and not price increases.
A dilemma in representing observables in quantum mechanics
There are self-adjoint operators which determine both spectral and
semispectral measures. These measures have very different commutativity and
covariance properties. This fact poses a serious question on the physical
meaning of such a self-adjoint operator and its associated operator measures.Comment: 10 page
Optical detection of a BCS transition of Lithium-6 in harmonic traps
We study the detection of a BCS transition within a sample of Lithium--6
atoms confined in a harmonic trap. Using the local density approximation we
calculate the pair correlation function in the normal and superfluid state at
zero temperature. We show that the softening of the Fermi hole associated with
a BCS transition leads to an observable increase in the intensity of
off--resonant light scattered from the atomic cloud at small angles.Comment: 7 pages, 3 figures, submitted to Europhysics Letter
A complete characterization of phase space measurements
We characterize all the phase space measurements for a non-relativistic
particle.Comment: 11 pages, latex, no figures, iopart styl
A new model for the double well potential
A new model for the double well potential is presented in the paper. In the
new potential, the exchanging rate could be easily calculated by the
perturbation method in supersymmetric quantum mechanics. It gives good results
whether the barrier is high or sallow. The new model have many merits and may
be used in the double well problem.Comment: 3pages, 3figure
Coherent States on Hilbert Modules
We generalize the concept of coherent states, traditionally defined as
special families of vectors on Hilbert spaces, to Hilbert modules. We show that
Hilbert modules over -algebras are the natural settings for a
generalization of coherent states defined on Hilbert spaces. We consider those
Hilbert -modules which have a natural left action from another
-algebra say, . The coherent states are well defined in this
case and they behave well with respect to the left action by .
Certain classical objects like the Cuntz algebra are related to specific
examples of coherent states. Finally we show that coherent states on modules
give rise to a completely positive kernel between two -algebras, in
complete analogy to the Hilbert space situation. Related to this there is a
dilation result for positive operator valued measures, in the sense of Naimark.
A number of examples are worked out to illustrate the theory
Bottleneck Routing Games with Low Price of Anarchy
We study {\em bottleneck routing games} where the social cost is determined
by the worst congestion on any edge in the network. In the literature,
bottleneck games assume player utility costs determined by the worst congested
edge in their paths. However, the Nash equilibria of such games are inefficient
since the price of anarchy can be very high and proportional to the size of the
network. In order to obtain smaller price of anarchy we introduce {\em
exponential bottleneck games} where the utility costs of the players are
exponential functions of their congestions. We find that exponential bottleneck
games are very efficient and give a poly-log bound on the price of anarchy:
, where is the largest path length in the
players' strategy sets and is the set of edges in the graph. By adjusting
the exponential utility costs with a logarithm we obtain games whose player
costs are almost identical to those in regular bottleneck games, and at the
same time have the good price of anarchy of exponential games.Comment: 12 page
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