Joint measurability, steering and entropic uncertainty

The notion of incompatibility of measurements in quantum theory is in stark contrast with the corresponding classical perspective, where all physical observables are jointly measurable. It is of interest to examine if the results of two or more measurements in the quantum scenario can be perceived from a classical point of view or they still exhibit non-classical features. Clearly, commuting observables can be measured jointly using projective measurements and their statistical outcomes can be discerned classically. However, such simple minded association of compatibility of measurements with commutativity turns out to be limited in an extended framework, where the usual notion of sharp projective valued measurements of self adjoint observables gets broadened to include unsharp measurements of generalized observables constituting positive operator valued measures (POVM). There is a surge of research activity recently towards gaining new physical insights on the emergence of classical behavior via joint measurability of unsharp observables. Here, we explore the entropic uncertainty relation for a pair of discrete observables (of Alice's system) when an entangled quantum memory of Bob is restricted to record outcomes of jointly measurable POVMs only. Within the joint measurability regime, the sum of entropies associated with Alice's measurement outcomes - conditioned by the results registered at Bob's end - are constrained to obey an entropic steering inequality. In this case, Bob's non-steerability reflects itself as his inability in predicting the outcomes of Alice's pair of non-commuting observables with better precision, even when they share an entangled state. As a further consequence, the quantum advantage envisaged for the construction of security proofs in key distribution is lost, when Bob's measurements are restricted to the joint measurability regime.Comment: 5 pages, RevTeX, 1 pdf figure, Comments welcom

Joint Measurability and Temporal Steering

Quintino et. al. (Phys. Rev. Lett. 113, 160402 (2014)) and Uola et. al. (Phys. Rev. Lett. 113, 160403 (2014)) have recently established an intrinsic relation between non-joint measurability and Einstein-Podolsky- Rosen steering. They showed that a set of measurements is incompatible (i.e., not jointly measurable) if and only if it can be used for the demonstration of steering. In this paper, we prove the temporal analog of this result viz., a set of measurements are incompatible if and only if it exhibits temporal steering.Comment: 6 pages,no figures, typos corrected, improved presentation; To appear in JOSA B feature issue "80 years of Steering and the Einstein-Podolsky-Rosen Paradox

Controlled Population of Floquet-Bloch States via Coupling to Bose and Fermi Baths

External driving is emerging as a promising tool for exploring new phases in quantum systems. The intrinsically non-equilibrium states that result, however, are challenging to describe and control. We study the steady states of a periodically driven one-dimensional electronic system, including the effects of radiative recombination, electron-phonon interactions, and the coupling to an external fermionic reservoir. Using a kinetic equation for the populations of the Floquet eigenstates, we show that the steady-state distribution can be controlled using the momentum and energy relaxation pathways provided by the coupling to phonon and Fermi reservoirs. In order to utilize the latter, we propose to couple the system and reservoir via an energy filter which suppresses photon-assisted tunneling. Importantly, coupling to these reservoirs yields a steady state resembling a band insulator in the Floquet basis. The system exhibits incompressible behavior, while hosting a small density of excitations. We discuss transport signatures, and describe the regimes where insulating behavior is obtained. Our results give promise for realizing Floquet topological insulators.Comment: 24 pages, 7 figures; with appendice

Inversion of moments to retrieve joint probabilities in quantum sequential measurements

A sequence of moments encode the corresponding probability distribution. Probing if quantum joint probability distribution can be retrieved from the associated set of moments -- realized in the sequential measurement of a dichotomic observable at different time intervals -- reveals a negative answer i.e., the joint probabilities of sequential measurements do not agree with the ones obtained by inverting the moments. This is indeed a reflection of the non-existence of a bonafide grand joint probability distribution, consistent with all the physical marginal probability distributions. Here we explicitly demonstrate that given the set of moments, it is not possible to retrieve the three-time quantum joint probability distribution resulting from quantum sequential measurement of a single qubit dichotomic observable at three different times. Experimental results using a nuclear magnetic resonance (NMR) system are reported here to corroborate these theoretical observations viz., the incompatibility of the three-time joint probabilties with those extracted from the moment sequence.Comment: 7 pages, 5 figures, RevTe

The Dynamics of Two Spherical Particles in a Confined Rotating Flow: Pedalling Motion

We have numerically investigated the interaction dynamics between two rigid spherical particles moving in a fluid-filled cylinder that is rotating at a constant speed. The cylinder rotation is about a horizontal axis. The particle densities are less than that of the fluid. The numerical procedure employed to solve the mathematical formulation is based on a three-dimensional arbitrary Larangian–Eulerian (ALE), moving mesh finite-element technique, described in a frame of reference rotating with the cylinder. Results are obtained in the ranges of particle Reynolds number, 1\u3cRep≤60, and shear Reynolds number, 1≤Res \u3c10. Two identical particles, depending on initial conditions at release, approach each other (‘drafting’ and ‘kissing’), tumble in the axial direction, and axially migrate towards opposing transverse planes on which they ‘settle’ (settling planes). Under some other initial conditions, the particles migrate directly onto their settling planes. For two identical particles, the settling planes are equidistant from the mid-transverse plane of the cylinder and the locations of the planes are determined by particle–particle and particle–wall force balances. Furthermore, for identical particles and given values of Rep and Res, the locations of such settling planes remain the same, independent of the initial conditions at release. While located on these settling planes, as viewed in an inertial frame, the particles may attain three possible distinct states depending on the values of the Reynolds numbers. In one state (low Rep, high Res ), the particles attain and remain at fixed equilibrium points on their settling planes. In the second (all Rep, low Res ), they execute spiralling motions about fixed points on their respective settling planes. These fixed points coincide with the locations of the equilibrium point which would occur on the mid-axial plane in the case of a single particle. In the third state (low Rep, moderate Res or high Rep, moderate to high Res ), they execute near-circular orbital motion on their respective settling planes, again about fixed points. These fixed points also coincide with the locations of the equilibrium points corresponding to single-particle dynamics. Both the spiral and near-circular motions of the particles occur in an out-of-phase manner with regard to their radial positions about the fixed point; the near-circular out-of-phase motion resembles bicycle pedalling. Also, in the second and third states, the particles simultaneously experience very weak axial oscillations about their settling planes, the frequency of such oscillations coinciding with the frequency of rotation of the circular cylinder. The behaviours of two non-identical particles (same density but different sizes, or same size but different densities) are different from those of identical particles. For example, non-identical particles may both end up settling on the mid-axial plane. This occurs when the locations of their corresponding single-particle equilibrium points are far apart. When such points are not far apart, particles may settle on planes that may not be symmetrical about the mid-axial plane. While located on their settling planes, their equilibrium states may not be similar. For example, for particles of the same density but of different sizes, the smaller of the two may execute a spiralling motion while the larger is in near-circular orbital motion. With particles of the same size but of different densities, while the lighter of the two approaches its equilibrium point on the mid-axial plane, the heavier one experiences a circular motion on the same plane about its equilibrium point. A major reason for the eventual attainment of these various states is noted to be the interplay between the particle–particle and particle–wall forces

Macrorealism from entropic Leggett-Garg inequalities

We formulate entropic Leggett-Garg inequalities, which place constraints on the statistical outcomes of temporal correlations of observables. The information theoretic inequalities are satisfied if macrorealism holds. We show that the quantum statistics underlying correlations between time-separated spin component of a quantum rotor mimics that of spin correlations in two spatially separated spin-$s$ particles sharing a state of zero total spin. This brings forth the violation of the entropic Leggett-Garg inequality by a rotating quantum spin-$s$ system in similar manner as does the entropic Bell inequality (Phys. Rev. Lett. 61, 662 (1988)) by a pair of spin-$s$ particles forming a composite spin singlet state.Comment: 5 pages, RevTeX, 2 eps figures, Accepted for publication in Phys. Rev.