Comment on "Separability of quantum states and the violation of Bell-type inequalities"

The statement of E.R. Loubenets, Phys. Rev. A 69, 042102 (2004), that separable states can violate classical probabilistic constraints is based on a misleading definition of classicality, which is much narrower than Bell's concept of local hidden variables. In a Bell type setting the notion of classicality used by Loubenets corresponds to the assumption of perfect correlations if the same observable is measured on both sides. While it is obvious that most separable states do not satisfy this assumption, this does not constitute "non-classical" behaviour in any usual sense of the word.Comment: 1 page, accepted by Phys. Rev.

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

Monogamy of Bell's inequality violations in non-signaling theories

We derive monogamy relations (tradeoffs) between strengths of violations of Bell's inequalities from the non-signaling condition. Our result applies to general Bell inequalities with an arbitrary large number of partners, outcomes and measurement settings. The method is simple, efficient and does not require linear programming. The results are used to derive optimal fidelity for asymmetric cloning in nonsignaling theories.Comment: 4 pages, 2 figures, published versio

Quantum interference and non-locality of independent photons from disparate sources

We quantitatively investigate the non-classicality and non-locality of a whole new class of mixed disparate quantum and semiquantum photon sources at the quantum-classical boundary. The latter include photon added thermal and photon added coherent sources, experimentally investigated recently by Zavatta et al. [Phys. Rev. Lett. 103, 140406 (2009)]. The key quantity in our investigations is the visibility of the corresponding photon-photon correlation function. We present explicit results on the violations of the Cauchy-Schwarz inequality - which is a measure of nonclassicality - as well as of Bell-type inequalities.Comment: 9 pages, 3 figure

Loophole-free test of quantum non-locality using high-efficiency homodyne detectors

We provide a detailed analysis of the recently proposed setup for a loophole-free test of Bell inequality using conditionally generated non-Gaussian states of light and balanced homodyning. In the proposed scheme, a two-mode squeezed vacuum state is de-gaussified by subtracting a single photon from each mode with the use of an unbalanced beam splitter and a standard low-efficiency single-photon detector. We thoroughly discuss the dependence of the achievable Bell violation on the various relevant experimental parameters such as the detector efficiencies, the electronic noise and the mixedness of the initial Gaussian state. We also consider several alternative schemes involving squeezed states, linear optical elements, conditional photon subtraction and homodyne detection.Comment: 13 pages, 14 figures, RevTeX

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

Maximal violation of Bell inequality for any given two-qubit pure state

In the case of bipartite two qubits systems, we derive the analytical expression of bound of Bell operator for any given pure state. Our result not only manifest some properties of Bell inequality, for example which may be violated by any pure entangled state and only be maximally violated for a maximally entangled state, but also give the explicit values of maximal violation for any pure state. Finally we point out that for two qubits systems there is no mixed state which can produce maximal violation of Bell inequality.Comment: 3 pages, 1 figure

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

No purification for two copies of a noisy entangled state

We consider whether two copies of a noisy entangled state can be transformed into a single copy of greater purity using local operations and classical communication. We show that it is never possible to achieve such a purification with certainty when the family of noisy states is twirlable (i.e. when there exists a local transformation that maps all states into the family, yet leaves the family itself invariant). This implies that two copies of a Werner state cannot be deterministically purified. Furthermore, due to the construction of the proof, it will hold not only in quantum theory, but in any generalised probabilistic theory. We use this to show that two copies of a noisy PR-box (a hypothetical device more non-local than is allowed by quantum theory) cannot be purified.Comment: 4 pages, 2 figure