13,704 research outputs found
Retrodiction of Generalised Measurement Outcomes
If a generalised measurement is performed on a quantum system and we do not
know the outcome, are we able to retrodict it with a second measurement? We
obtain a necessary and sufficient condition for perfect retrodiction of the
outcome of a known generalised measurement, given the final state, for an
arbitrary initial state. From this, we deduce that, when the input and output
Hilbert spaces have equal (finite) dimension, it is impossible to perfectly
retrodict the outcome of any fine-grained measurement (where each POVM element
corresponds to a single Kraus operator) for all initial states unless the
measurement is unitarily equivalent to a projective measurement. It also
enables us to show that every POVM can be realised in such a way that perfect
outcome retrodiction is possible for an arbitrary initial state when the number
of outcomes does not exceed the output Hilbert space dimension. We then
consider the situation where the initial state is not arbitrary, though it may
be entangled, and describe the conditions under which unambiguous outcome
retrodiction is possible for a fine-grained generalised measurement. We find
that this is possible for some state if the Kraus operators are linearly
independent. This condition is also necessary when the Kraus operators are
non-singular. From this, we deduce that every trace-preserving quantum
operation is associated with a generalised measurement whose outcome is
unambiguously retrodictable for some initial state, and also that a set of
unitary operators can be unambiguously discriminated iff they are linearly
independent. We then examine the issue of unambiguous outcome retrodiction
without entanglement. This has important connections with the theory of locally
linearly dependent and locally linearly independent operators.Comment: To appear in Physical Review
Retrodiction with two-level atoms: atomic previvals
In the Jaynes-Cummings model a two-level atom interacts with a single-mode
electromagnetic field. Quantum mechanics predicts collapses and revivals in the
probability that a measurement will show the atom to be excited at various
times after the initial preparation of the atom and field. In retrodictive
quantum mechanics we seek the probability that the atom was prepared in a
particular state given the initial state of the field and the outcome of a
later measurement on the atom. Although this is not simply the time reverse of
the usual predictive problem, we demonstrate in this paper that retrodictive
collapses and revivals also exist. We highlight the differences between
predictive and retrodictive evolutions and describe an interesting situation
where the prepared state is essentially unretrodictable.Comment: 15 pages, 3 (5) figure
Thermalization of Squeezed States
Starting with a thermal squeezed state defined as a conventional thermal
state based on an appropriate hamiltonian, we show how an important physical
property, the signal-to-noise ratio, is degraded, and propose a simple model of
thermalization (Kraus thermalization).Comment: 7 pages, 1 table, 1 figure. Presented at ICSSUR 2005, Besancon,
Franc
Weak Values and Continuous-Variable Entanglement Concentration
We demonstrate a general weak measurement model which allows Gaussian
preserving entanglement concentration of the two mode squeezed vacuum. The
power of this simple and elegant protocol is through the constraints it places
on possible ancilla states and measurement strategies that will allow
entanglement concentration. In particular, it is shown how previously
discovered protocols of this kind emerge as special examples of the general
model described here. Finally, as evidence of its utility, we use it to provide
another novel example of such a protocol.Comment: 4 pages, 1 figure, Final version to appear in Phys. Rev.
Elementary Excitations of a Bose-Einstein Condensate in an Effective Magnetic Field
We calculate the low energy elementary excitations of a Bose-Einstein
Condensate in an effective magnetic field. The field is created by the
interplay between light beams carrying orbital angular momentum and the trapped
atoms. We examine the role of the homogeneous magnetic field, familiar from
studies of rotating condensates, and also investigate spectra for vector
potentials with a more general radial dependence. We discuss the instabilities
which arise and how these may be manifested.Comment: 8 pages, 4 figure
Quasicondensation reexamined
We study in detail the effect of quasicondensation. We show that this effect
is strictly related to dimensionality of the system. It is present in one
dimensional systems independently of interactions - exists in repulsive,
attractive or in non-interacting Bose gas in some range of temperatures below
characteristic temperature of the quantum degeneracy. Based on this observation
we analyze the quasicondensation in terms of a ratio of the two largest
eigenvalues of the single particle density matrix for the ideal gas. We show
that in the thermodynamic limit in higher dimensions the second largest
eigenvalue vanishes (as compared to the first one) with total number of
particles as whereas goes to zero only logarithmically in
one dimension. We also study the effect of quasicondensation for various
geometries of the system: from quasi-1D elongated one, through spherically
symmetric 3D case to quasi-2D pancake-like geometry
Stress analysis of compression of aluminium with rotating tools
Compression tests carried out on aluminium specimens showed that when the die was rotated the compression load dropped. A slab method is employed to examine this process. The load reduction is explained by the deviation of friction vector due to the relative circumferential movement between the die and the material. This mechanism is incorporated into a theoretical model and an expression is derived for compression pressure. Analytical solutions established compare favourably with experimental results. It is also shown that there is a limitation to the load reduction: the compressive load can never be lower than 70 percent of the yield limit.<br /
Weak Values, Quantum Trajectories, and the Stony-Brook Cavity QED experiment
Weak values as introduced by Aharonov, Albert and Vaidman (AAV) are ensemble
average values for the results of weak measurements. They are interesting when
the ensemble is preselected on a particular initial state and postselected on a
particular final measurement result. I show that weak values arise naturally in
quantum optics, as weak measurements occur whenever an open system is monitored
(as by a photodetector). I use quantum trajectory theory to derive a
generalization of AAV's formula to include (a) mixed initial conditions, (b)
nonunitary evolution, (c) a generalized (non-projective) final measurement, and
(d) a non-back-action-evading weak measurement. I apply this theory to the
recent Stony-Brook cavity QED experiment demonstrating wave-particle duality
[G.T. Foster, L.A. Orozco, H.M. Castro-Beltran, and H.J. Carmichael, Phys. Rev.
Lett. {85}, 3149 (2000)]. I show that the ``fractional'' correlation function
measured in that experiment can be recast as a weak value in a form as simple
as that introduced by AAV.Comment: 6 pages, no figures. To be published in Phys. Rev.
Experiences and Responses to Microaggressions on Historically White Campuses: A Qualitative Interpretive Meta-Synthesis
According to the U.S. Department of Education (2011), only 59% of students who sought bachelors’ degrees from four-year postsecondary institutions in 2006 completed the degree within six years, and among African American/Black students, only 40% finished college within six years. Despite efforts to quantify factors that contribute to low retention rates among African American students, less is known about the qualitative experiences of students who remain on campuses across the United States. This qualitative interpretive meta-synthesis examines the microaggressive encounters experienced by African American undergraduate college students (ages 17-22) at historically White, fouryear colleges and universities to better understand how African American students experience, make sense of, and resist microaggressions occurring at the intersection of race and gender
The simplest demonstrations of quantum nonlocality
We investigate the complexity cost of demonstrating the key types of nonclassical correlations-Bell inequality violation, Einstein, Podolsky, Rosen (EPR)-steering, and entanglement-with independent agents, theoretically and in a photonic experiment. We show that the complexity cost exhibits a hierarchy among these three tasks, mirroring the recently discovered hierarchy for how robust they are to noise. For Bell inequality violations, the simplest test is the well-known Clauser-Horne-Shimony-Holt test, but for EPR-steering and entanglement the tests that involve the fewest number of detection patterns require nonprojective measurements. The simplest EPR-steering test requires a choice of projective measurement for one agent and a single nonprojective measurement for the other, while the simplest entanglement test uses just a single nonprojective measurement for each agent. In both of these cases, we derive our inequalities using the concept of circular two-designs. This leads to the interesting feature that in our photonic demonstrations, the correlation of interest is independent of the angle between the linear polarizers used by the two parties, which thus require no alignment
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