QUANTUM: The Exhibition - the wy and the process

Robert Seiringer

It was recently shown by Hansen that the Wigner-Yanase entropy is, for general states of quantum systems, not subadditive with respect to decomposition into two subsystems, although this property is known to hold for pure states. We investigate the question whether the weaker property of subadditivity for pure states with respect to decomposition into more than two subsystems holds. This property would have interesting applications in quantum chemistry. We show, however, that it does not hold in general, and provide a counterexample. In 1963, Wigner and Yanase [4] introduced the entropy-like quantity S WY (ρ, K) = 1 2 Tr[ρ1/2, K] 2 = Trρ 1/2 Kρ 1/2 K − TrρK 2 for density matrices ρ of quantum systems, with K some fixed self-adjoint operator. They showed that S WY is concave in ρ [4, 5] and, for pure states, subadditive with respect to decomposition of the quantum system into two subsystems.

Martin Laforest, Angela Olano, Tobi Day-Hamilton

Anindita Banerjee, Kishore Thapliyal, Chitra Shukla +1 more

Diego Paiva Pires, Eduardo Ribeiro DeAzevedo, Diogo O. Soares-Pinto +2 more

Abstract The quantum speed limit (QSL) is a fundamental lower bound on the evolution time for quantum systems, and its tightness has been observed to be dependent on the properties of the physical process. However, experimental studies exploring the QSL in open quantum systems are still missing. Here, we studied geometric quantum speed limits of a qubit subject to decoherence in an ensemble of chloroform molecules in a Nuclear Magnetic Resonance experiment. We controlled the system-reservoir interaction and the spin relaxation rates by adding a paramagnetic salt, allowing the observation of both Markovian and non-Markovian open system dynamics for the qubit. We used two distinguishability measures of quantum states to assess the speed of the qubit evolution: the quantum Fisher information (QFI) and Wigner-Yanase skew information (WY). For non-Markovianity and low salt concentrations, we found crossovers between QSLs related to those metrics. The WY metric sets the tighter QSL for high concentrations and Markovian dynamics. We also show that QSLs are sensitive even to small fluctuations in spin magnetization.

Bernard Zygelman

We present results of a numerical experiment in which a neutral spin-1/2 particle subjected to a static magnetic vortex field passes through a double slit barrier. We demonstrate that the resulting interference pattern on a detection screen exhibits fringes reminiscent of Aharonov-Bohm scattering by a magnetic flux tube. To gain better understanding of the observed behavior, we provide analytic solutions for a neutral spin-1/2 rigid planar rotor in the aforementioned magnetic field. We demonstrate how that system exhibits a generalized Aharonov-Bohm effect [Wu and Yang, Phys. Rev. D 12, 3845 (1975)], due to the emergence of an effective SU(2) Wu-Yang (WY) flux tube. We study the behavior of the gauge invariant partition function and demonstrate a topological phase transition for the spin-1/2 planar rotor. We provide an expression for the partition function in which its dependence on the Wilson loop integral of the WY gauge potential is explicit. We generalize to a spin-1 system in order to explore the Wilczek-Zee (WZ) mechanism in a full quantum setting. We show how degeneracy is lifted by higher-order gauge corrections that alter the semiclassical WZ phase. Models that allow analytic description provide a foil to objections that question the fidelity of predictions based on the generalized Born-Oppenheimer approximation in atomic and molecular systems. Though the primary focus of this paper concerns the emergence of gauge structure in neutral systems, the theory is also applicable to systems that possess electric charge. In that case, we explore interference between fundamental gauge fields (i.e., electromagnetism) with effective gauge potentials. We propose a possible laboratory demonstration for the latter in an ion trap setting. We illustrate how effective gauge potentials influence wave-packet revivals in the said ion trap.

Carol Anne Fischer