8,251 research outputs found
Quantum Mechanics as a Framework for Dealing with Uncertainty
Quantum uncertainty is described here in two guises: indeterminacy with its
concomitant indeterminism of measurement outcomes, and fuzziness, or
unsharpness. Both features were long seen as obstructions of experimental
possibilities that were available in the realm of classical physics. The birth
of quantum information science was due to the realization that such
obstructions can be turned into powerful resources. Here we review how the
utilization of quantum fuzziness makes room for a notion of approximate joint
measurement of noncommuting observables. We also show how from a classical
perspective quantum uncertainty is due to a limitation of measurability
reflected in a fuzzy event structure -- all quantum events are fundamentally
unsharp.Comment: Plenary Lecture, Central European Workshop on Quantum Optics, Turku
2009
Non-disturbing quantum measurements
We consider pairs of quantum observables (POVMs) and analyze the relation
between the notions of non-disturbance, joint measurability and commutativity.
We specify conditions under which these properties coincide or
differ---depending for instance on the interplay between the number of outcomes
and the Hilbert space dimension or on algebraic properties of the effect
operators. We also show that (non-)disturbance is in general not a symmetric
relation and that it can be decided and quantified by means of a semidefinite
program.Comment: Minor corrections in v
Characterization of the Sequential Product on Quantum Effects
We present a characterization of the standard sequential product of quantum
effects. The characterization is in term of algebraic, continuity and duality
conditions that can be physically motivated.Comment: 11 pages. Accepted for publication in the Journal of Mathematical
Physic
The Standard Model of Quantum Measurement Theory: History and Applications
The standard model of the quantum theory of measurement is based on an
interaction Hamiltonian in which the observable-to-be-measured is multiplied
with some observable of a probe system. This simple Ansatz has proved extremely
fruitful in the development of the foundations of quantum mechanics. While the
ensuing type of models has often been argued to be rather artificial, recent
advances in quantum optics have demonstrated their prinicpal and practical
feasibility. A brief historical review of the standard model together with an
outline of its virtues and limitations are presented as an illustration of the
mutual inspiration that has always taken place between foundational and
experimental research in quantum physics.Comment: 22 pages, to appear in Found. Phys. 199
New spin squeezing and other entanglement tests for two mode systems of identical bosons
For any quantum state representing a physical system of identical particles, the density operator must satisfy the symmetrization principle (SP) and conform to super-selection rules (SSR) that prohibit coherences between differing total particle numbers. Here we consider bi-partitite states for massive bosons, where both the system and sub-systems are modes (or sets of modes) and particle numbers for quantum states are determined from the mode occupancies. Defining non-entangled or separable states as those prepared via local operations (on the sub-systems) and classical communication processes, the sub-system density operators are also required to satisfy the SP and conform to the SSR, in contrast to some other approaches. Whilst in the presence of this additional constraint the previously obtained sufficiency criteria for entanglement, such as the sum of the ˆSx and ˆSy variances for the Schwinger spin components being less than half the mean boson number, and the strong correlation test of |haˆm (bˆ†)ni|2 being greater than h(aˆ†)maˆm (bˆ†)nbˆni(m, n = 1, 2, . . .) are still valid, new tests are obtained in our work. We show that the presence of spin squeezing in at least one of the spin components ˆSx , ˆSy and ˆSz is a sufficient criterion for the presence of entanglement and a simple correlation test can be constructed of |haˆm (bˆ†)ni|2 merely being greater than zero.We show that for the case of relative phase eigenstates, the new spin squeezing test for entanglement is satisfied (for the principle spin operators), whilst the test involving the sum of the ˆSx and ˆSy variances is not. However, another spin squeezing entanglement test for Bose–Einstein condensates involving the variance in ˆSz being less than the sum of the squared mean values for ˆSx and ˆSy divided by the boson number was based on a concept of entanglement inconsistent with the SP, and here we present a revised treatment which again leads to spin squeezing as an entanglement test
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