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 $\simeq N^{-\gamma}$ 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