The joint action of a magnetic field and of interactions is crucial for the appearance of exotic quantum phenomena, such as the quantum Hall effect. Owing to their rich nuclear structure, equivalent to an additional synthetic dimension, one-dimensional alkaline-earth(-like) fermionic gases with synthetic gauge potential and atomic contact repulsion may display similar related properties. Here w...

The standard formalism of quantum theory treats space and time in fundamentally different ways. In particular, a composite system at a given time is represented by a joint state, but the formalism does not prescribe a joint state for a composite of systems at different times. If there were a way of defining such a joint state, this would potentially permit a more even-handed treatment of space ...

Tsirelson showed that 2 √ 2 is the maximum value that CHSH expression can take for quantumcorrelations [B. S. Tsirelson Lett. Math. Phys. 4, (1980) 93]. This bound simply follows from the algebra of observables. Recently by exploiting the physical structure of quantum mechanics like unitarity and linearity, Buhrman and Massar [H. Buhrman and S. Massar Phys. Rev. A 72, (2005) 052103] have establ...

A quantum version of Bochner’s theorem characterising Fourier transforms of probability measures on locally compact Abelian groups gives a characterisation of the Fourier transforms of Wigner quasi-joint distributions of position and momentum. An analogous quantum Bochner theorem characterises quasi-joint distributions of components of spin. In both cases quantum states in which a true distribu...

This paper takes up a suggestion that the reason we cannot find hidden variable theories for quantum mechanics, as in Bell’s Theorem, is that we require them to assign joint probability distributions on incompatible observables; these joint distributions are empirically meaningless on one standard interpretation of quantum mechanics. Some have proposed to get around this problem by using genera...

The creation of a quantum network requires the distribution of coherent information across macroscopic distances. We demonstrate the entanglement of two superconducting qubits, separated by more than a meter of coaxial cable, by designing a joint measurement that probabilistically projects onto an entangled state. By using a continuous measurement scheme, we are further able to observe single q...

The spinless Salpeter equation is the combination of relativistic kinematics with some static interaction potential. The nonlocal nature of the Hamiltonian resulting from this approximation renders difficult to obtain rigorous analytic statements on resulting solutions. In view of this unsatisfactory state of affairs, we calculate analytic upper bounds on the involved energy levels, and, for th...

We derive “Bell inequalities” in four dimensional phase space and prove the following “three marginal theorem” for phase space densities ρ(−→q ,−→p ), thus settling a long standing conjecture : “there exist quantum states for which more than three of the quantum probability distributions for (q1, q2), (p1, p2), (q1, p2) and (p1, q2) cannot be reproduced as marginals of a positive ρ(−→q ,−→p )”....