Amplitude control of quantum interference

Usually, the oscillations of interference effects are controlled by relative phases. We show that varying the amplitudes of quantum waves, for instance by changing the reflectivity of beam splitters, can also lead to quantum oscillations and even to Bell violations of local realism. We first study theoretically a generalization of the Hong-Ou-Mandel experiment to arbitrary source numbers and beam splitter transmittivity. We then consider a Bell type experiment with two independent sources, and find strong violations of local realism for arbitrarily large source number $N$; for small $N$, one operator measures essentially the relative phase of the sources and the other their intensities. Since, experimentally, one can measure the parity of the number of atoms in an optical lattice more easily than the number itself, we assume that the detectors measure parity.Comment: 4 pages; 4 figure

Class of bipartite quantum states satisfying the original Bell inequality

In a general setting, we introduce a new bipartite state property sufficient for the validity of the perfect correlation form of the original Bell inequality for any three bounded quantum observables. A bipartite quantum state with this property does not necessarily exhibit perfect correlations. The class of bipartite states specified by this property includes both separable and nonseparable states. We prove analytically that, for any dimension d>2, every Werner state, separable or nonseparable, belongs to this class.Comment: 6 pages, v.2: one reference added, the statement on Werner states essentially extended; v.3: details of proofs inserte

Bell's theorem as a signature of nonlocality: a classical counterexample

For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local probabilistic interaction in the measurement process can lead to a violation of the Bell inequalities. We first introduce two-particle phase-space distributions in classical mechanics constructed to be the analogs of quantum mechanical angular momentum eigenstates. These distributions are then employed in four schemes characterized by different types of detectors measuring the angular momenta. When the model includes an interaction between the detector and the measured particle leading to ensemble dependencies, the relevant Bell inequalities are violated if total angular momentum is required to be conserved. The violation is explained by identifying assumptions made in the derivation of Bell's theorem that are not fulfilled by the model. These assumptions will be argued to be too restrictive to see in the violation of the Bell inequalities a faithful signature of nonlocality.Comment: Extended manuscript. Significant change

Threshold bounds for noisy bipartite states

For a nonseparable bipartite quantum state violating the Clauser-Horne-Shimony-Holt (CHSH) inequality, we evaluate amounts of noise breaking the quantum character of its statistical correlations under any generalized quantum measurements of Alice and Bob. Expressed in terms of the reduced states, these new threshold bounds can be easily calculated for any concrete bipartite state. A noisy bipartite state, satisfying the extended CHSH inequality and the perfect correlation form of the original Bell inequality for any quantum observables, neither necessarily admits a local hidden variable model nor exhibits the perfect correlation of outcomes whenever the same quantum observable is measured on both "sides".Comment: 9 pages; v.2: minor editing corrections; to appear in J. Phys. A: Math. Ge

Causal Quantum Theory and the Collapse Locality Loophole

Causal quantum theory is an umbrella term for ordinary quantum theory modified by two hypotheses: state vector reduction is a well-defined process, and strict local causality applies. The first of these holds in some versions of Copenhagen quantum theory and need not necessarily imply practically testable deviations from ordinary quantum theory. The second implies that measurement events which are spacelike separated have no non-local correlations. To test this prediction, which sharply differs from standard quantum theory, requires a precise theory of state vector reduction. Formally speaking, any precise version of causal quantum theory defines a local hidden variable theory. However, causal quantum theory is most naturally seen as a variant of standard quantum theory. For that reason it seems a more serious rival to standard quantum theory than local hidden variable models relying on the locality or detector efficiency loopholes. Some plausible versions of causal quantum theory are not refuted by any Bell experiments to date, nor is it obvious that they are inconsistent with other experiments. They evade refutation via a neglected loophole in Bell experiments -- the {\it collapse locality loophole} -- which exists because of the possible time lag between a particle entering a measuring device and a collapse taking place. Fairly definitive tests of causal versus standard quantum theory could be made by observing entangled particles separated by $\approx 0.1$ light seconds.Comment: Discussion expanded; typos corrected; references adde

Quantum Preferred Frame: Does It Really Exist?

The idea of the preferred frame as a remedy for difficulties of the relativistic quantum mechanics in description of the non-local quantum phenomena was undertaken by such physicists as J. S. Bell and D. Bohm. The possibility of the existence of preferred frame was also seriously treated by P. A. M. Dirac. In this paper, we propose an Einstein-Podolsky-Rosen-type experiment for testing the possible existence of a quantum preferred frame. Our analysis suggests that to verify whether a preferred frame of reference in the quantum world exists it is enough to perform an EPR type experiment with pair of observers staying in the same inertial frame and with use of the massive EPR pair of spin one-half or spin one particles.Comment: 5 pp., 6 fig

Unified criteria for multipartite quantum nonlocality

Wiseman and co-workers (Phys. Rev. Lett. 98, 140402, 2007) proposed a distinction between the nonlocality classes of Bell's nonlocality, steering and entanglement based on whether or not an overseer trusts each party in a bipartite scenario where they are asked to demonstrate entanglement. Here we extend that concept to the multipartite case and derive inequalities that progressively test for those classes of nonlocality, with different thresholds for each level. This framework includes the three classes of nonlocality above in special cases and introduces a family of others.Comment: V2: corrected image display; V3: substantial changes including new proofs, arguments, and result

Criteria for generalized macroscopic and mesoscopic quantum coherence

We consider macroscopic, mesoscopic and "S-scopic" quantum superpositions of eigenstates of an observable, and develop some signatures for their existence. We define the extent, or size $S$ of a superposition, with respect to an observable \hat{x}, as being the range of outcomes of \hat{x} predicted by that superposition. Such superpositions are referred to as generalized $S$-scopic superpositions to distinguish them from the extreme superpositions that superpose only the two states that have a difference $S$ in their prediction for the observable. We also consider generalized $S$-scopic superpositions of coherent states. We explore the constraints that are placed on the statistics if we suppose a system to be described by mixtures of superpositions that are restricted in size. In this way we arrive at experimental criteria that are sufficient to deduce the existence of a generalized $S$-scopic superposition. The signatures developed are useful where one is able to demonstrate a degree of squeezing. We also discuss how the signatures enable a new type of Einstein-Podolsky-Rosen gedanken experiment.Comment: 15 pages, accepted for publication in Phys. Rev.

Fine-grained uncertainty relation and nonlocality of tripartite systems

The upper bound of the fine-grained uncertainty relation is different for classical physics, quantum physics and no-signaling theories with maximal nonlocality (supper quantum correlation), as was shown in the case of bipartite systems [J. Oppenheim and S. Wehner, Science 330, 1072 (2010)]. Here, we extend the fine-grained uncertainty relation to the case of tripartite systems. We show that the fine-grained uncertainty relation determines the nonlocality of tripartite systems as manifested by the Svetlichny inequality, discriminating between classical physics, quantum physics and super quantum correlations.Comment: 4 page

Quantum Equilibrium and the Origin of Absolute Uncertainty

The quantum formalism is a ``measurement'' formalism--a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schr\"odinger's equation for a system of particles when we merely insist that ``particles'' means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. We find that a Bohmian universe, though deterministic, evolves in such a manner that an {\it appearance} of randomness emerges, precisely as described by the quantum formalism and given, for example, by ``\rho=|\psis|^2.'' A crucial ingredient in our analysis of the origin of this randomness is the notion of the effective wave function of a subsystem, a notion of interest in its own right and of relevance to any discussion of quantum theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with (nonrelativistic) quantum theory simply evaporate.Comment: 75 pages. This paper was published a long time ago, but was never archived. We do so now because it is basic for our recent article quant-ph/0308038, which can in fact be regarded as an appendix of the earlier on