Dynamical quantum non-locality

Jeff Tollaksen, Andrei Yu. Khrennikov, Gregg S. Jaeger +2 more

Jeff Tollaksen

Abdel‐Baset A. Mohamed, Atta Ur Rahman, Hichem Eleuch

The engineering properties of trapped ions and their capacity to engender numerous quantum information resources determine many aspects of quantum information processing. We devise a setup of coherent and even coherent fields acting on two trapped ions to generate quantum memory, non-locality, and entanglement. Various effects, such as intrinsic decoherence, Lamb–Dicke regime, and dipole–dipole interaction are investigated. The inter-coupling of trapped ions, as well as the generation and dynamics of correlations between them, are analyzed. Using quantum memory assisted entropic uncertainty, trace-norm measurement induced non-locality, and concurrence, we find that the coherent and even coherent fields successfully generate non-local correlations in trapped-ions, with the latter being more resourceful for the dynamics and preservation of the non-local correlations. Furthermore, we observe that the entropic uncertainty and the trace norm induced non-locality present symmetrical dynamics. The dipole–dipole interaction improves correlation’s generation, robustness, and entropic uncertainty suppression.

Shi-Liang Zhu, Zheng‐Yuan Xue, Dan-Wei Zhang +1 more

Quantum non-locality based on the well-known Bell inequality is of kinematic nature. A different type of quantum non-locality, the non-locality of the quantum equation of motion, is recently put forward with connection to the Aharonov-Bohm effect (Popescu S., Nat. Phys. , 6 (2010) 151 ). Evolution of the displacement operator provides an example to manifest such dynamic quantum non-locality. We propose an experiment using single-atom interferometry to test such dynamic quantum non-locality. We show how to measure evolution of the displacement operator with cold atoms in a spin-dependent optical lattice potential and discuss signature to identify dynamic quantum non-locality under a realistic experimental setting.

Stefano Pironio

Cesar E. Pachon, Leonardo A. Pachón

Non-locality is one of the hallmarks of quantum mechanics and is responsible for paradigmatic features such as entanglement and the Aharonov-Bohm effect. Non-locality comes in two flavours: a \emph{kinematic} non-locality -- arising from the structure of the Hilbert space -- and a \emph{dynamical} non-locality -- arising from the quantum equations of motion. Recently, the origin of kinematic non-locality was traced to the uncertainty principle; here we rigorously trace the origin of dynamical non-locality to the superposition principle. We prove, via deformation quantization and Marinov's phase-space path integrals, that the exact Wigner propagator reduces to the classical Liouville propagator if and only if the Hamiltonian has at-most-quadratic Weyl symbol. This unified theorem covers both continuous-variable and finite-dimensional Hilbert spaces, aligning the Gaussian (CV) and Clifford (finite-$d$) boundaries of classical simulability into a single algebraic criterion. We introduce a macroscopic, experimentally accessible measure of dynamical non-locality -- the signed divergence $\mathcal{D}(t)$ -- and show that it governs five phenomena: (i) the dynamical penalty incurred by quantum non-local games under post-measurement evolution; (ii) the quantum corrections to out-of-time-order correlators; (iii) the metrological gain beyond the shot-noise limit; (iv) the generation of non-Gaussian entanglement from product states; and (v) the non-Clifford / magic-state content of finite-dimensional dynamics. A concrete experimental protocol in circuit QED is proposed and complemented by a three-qubit CCZ protocol accessible on current qubit platforms.