Experimentally testing Bell’s theorem based on Hardy’s nonlocal ladder proofs

Bell's theorem argues the existence of quantum nonlocality which goes basically against the hidden variable theory(HVT). Many experiments have been done via testing the violations of Bell's inequalities to statistically verify the Bell's theorem. Alternatively,by testing the Hardy's ladder proofs we experimentally demonstrate the deterministic violation of HVT and thus confirm the quantum nonlocality. Our tests are implemented with non-maximal entangled photon pairs generated by spontaneous parametric down conversions(SPDCs). We show that the degree freedom of photon entanglement could be significantly enhanced by using interference filters. As a consequence, the Hardy's ladder proofs could be tested and Bell's theorem is verified robustly. The probability of violating the locality reach to 41.9%, which is close to the expectably ideal value 46.4% for the photon pairs with degree of entanglement ε = 0.93. The higher violating probability is possible by further optimizing the experimental parameters.     

Generalization of Bell's theorem

A concise proof of Bell's theorem on the necessary nonlocality of any theory which models individual measurements in correlated quantum mechanical systems is presented. A family of inequalities is derived which may be applied to a broad class of correlated systems to test the assumption of locality.     

Two proofs of Fine's theorem

Fine's theorem concerns the question of determining the conditions under which a certain set of probabilities for pairs of four bivalent quantities may be taken to be the marginals of an underlying probability distribution. The eight CHSH inequalities are well-known to be necessary conditions, but Fine's theorem is the striking result that they are also sufficient conditions. Here two transparent and self-contained proofs of Fine's theorem are presented. The first is a physically motivated proof using an explicit local hidden variables model. The second is an algebraic proof which uses a representation of the probabilities in terms of correlation functions.     

Signatures of quantum behavior in single-qubit weak measurements

With the recent surge of interest in quantum computation, it has become very important to develop clear experimental tests for "quantum behavior" in a system. This issue has been addressed in the past in the form of the inequalities due to Bell and those due to Leggett and Garg. These inequalities concern the results of ideal projective measurements, however, which are experimentally difficult to perform in many proposed qubit designs, especially in many solid-state qubit systems. Here, we show that weak continuous measurements, which are often practical to implement experimentally, can yield particularly clear signatures of quantum coherence, both in the measured correlation functions and in the measured power spectrum.     

Bell's theorem and backwards-in-time causality

Bell has shown that quantum mechanics is incompatible with the notion of locality. The present paper begins by considering the possibility of invoking backwards-in-time causality to explain this violation of locality. This then leads to an examination of the possible relevance of backwards-in-time causality to measurement outcomes in general. It is found that the situations in which it could be involved are limited owing to causality paradoxes.     

Bell's theorem for general N-qubit states

We derive a single general Bell inequality which is a sufficient and necessary condition for the correlation function for N particles to be describable in a local and realistic picture, for the case in which measurements on each particle can be chosen between two arbitrary dichotomic observables. We also derive a necessary and sufficient condition for an arbitrary N-qubit mixed state to violate this inequality. This condition is a generalization and reformulation of the Horodecki family condition for two qubits.     

Bell's theorem and the nature of reality

We rediscuss the Einstein-Podolsky-Rosen paradox in Bohm's spin version and oppose to it Bohr's controversial point of view. Then we explain Bell's theorem, Bell inequalities, and its consequences. We describe the experiment of Aspect, Dalibard, and Roger in detail. Finally we draw attention to the nonlocal structure of the underlying theory.Dedicated to J. S. Bell on his 60th birthday.     

On the real meaning of Bell's theorem

In the last couple of years many important results have been derived showing that Bell's inequalities are nothing else but the indicator of whether certain events and their probabilities can be represented within a Kolmogorovian probabilistic model. It has become evident that one can derive Bell's inequalities without mentioning locality, causality, hidden variables, etc. Many authors jumped to the conclusion that the original content of Bell's theorem had lost its meaning. I reconsider the original problem posed by Bell and I show that Bell's theorem is still valid.On leave from the Institute for Theoretical Physics, Eötvös University, Budapest, Hungary.     

On the real meaning of Bell's theorem

In the last couple of years many important results have been derived showing that Bell's inequalities are nothing else but the indicator whether certain events and their probabilities can be represented or not within a Kolmogorovian probabilistic model. It has become evident that one can derive the Bell's inequalities without mentioning locality, causality hidden variable, etc. Many authors jumped to conclusion that the original content of the Bell's theorem had lost its meaning. I reconsider original problem posed by Bell and I show that the Bell's theorem is still valid.1. On leave from the Institute for Theoretical Physics, Eötvös University, Budapest.     

The Kochen-Specker theorem and Bell's theorem: An algebraic approach

In this paper we present a systematic formulation of some recent results concerning the algebraic demonstration of the two major no-hidden-variables theorems for N spin-1/2 particles. We derive explicitly the GHZ states involved and their associated eigenvalues. These eigenvalues turn out to be undefined for N=, this fact providing a new proof showing that the nonlocality argument breaks down in the limit of a truly infinite number of particles.     

Bell's theorem without inequalities and without alignments

A proof of Bell's theorem without inequalities is presented which exhibits three remarkable properties: (a). reduced local states are immune to collective decoherence; (b). distant local setups do not need to be aligned, since the required perfect correlations are achieved for any local rotation of the local setups; (c). local measurements require only individual measurements on the qubits. Indeed, it is shown that this proof is essentially the only one which fulfills (a). (b). and (c).     

Interpretation of the quantum formalism and Bell's theorem

It is argued that quantum mechanics must be interpreted according to the Copenhagen interpretation. Consequently the formalism must be used in a purely operational way. The relation between realism, hidden variables, and the Bell inequalities is discussed. The proof of impossibility of local hidden-variables theories (Bell's theorem) is criticized on the basis that the quantum mechanical states violating local realism are not physically realizable states.Einstein had great difficulty in reaching a sharp formulation of Bohr's meaning. What hope then for the rest of us.—John S. Bell (Ref. 1, p. 189).     

Robust QKD-based private database queries based on alternative sequences of single-qubit measurements

Quantum channel noise may cause the user to obtain a wrong answer and thus misunderstand the database holder for existing QKD-based quantum private query (QPQ) protocols. In addition, an outside attacker may conceal his attack by exploiting the channel noise. We propose a new, robust QPQ protocol based on four-qubit decoherence-free (DF) states. In contrast to existing QPQ protocols against channel noise, only an alternative fixed sequence of single-qubit measurements is needed by the user (Alice) to measure the received DF states. This property makes it easy to implement the proposed protocol by exploiting current technologies. Moreover, to retain the advantage of flexible database queries, we reconstruct Alice’s measurement operators so that Alice needs only conditioned sequences of single-qubit measurements.     

EPR and Bell's theorem: A critical review

The argument of Einstein, Podolsky, and Rosen is reviewed with attention to logical structure and character of assumptions. Bohr's reply is discussed. Bell's contribution is formulated without use of hidden variables, and efforts to equate hidden variables to realism are critically examined. An alternative derivation of nonlocality that makes no use of hidden variables, microrealism, counterfactual definiteness, or any other assumption alien to orthodox quantum thinking is described in detail, with particular attention to the quartet or broken-square question.     

Hidden variables and Bell's theorem in quantum mechanics

In the present paper we give a precise definition of a hidden-variable theory for quantum mechanics, whereby we adopt the weakest possible definition of a hidden-variable theory, which is compatible with the assumption that the bounded observables of a quantum mechanical system are represented by the elements of the real part A_r of a W^*-algebra A (of the most general type) and the states are represented by the normal states (in the mathematical sense) of A. We then go on to show that an example put forward by Bell in 1966 satisfies our definition (Sec. 2). Finally we make use of Bell's famous theorem to show that for a sufficiently non-commutative W^*-algebra A no hidden-variable theory in our sense exists (Theorem 3.3 and its corollaries).     

From Bell's theorem to secure quantum key distribution

The first step in any quantum key distribution (QKD) protocol consists of sequences of measurements that produce correlated classical data. We show that these correlation data must violate some Bell inequality in order to contain distillable secrecy, if not they could be produced by quantum measurements performed on a separable state of larger dimension. We introduce a new QKD protocol and prove its security against any individual attack by an adversary only limited by the no-signaling condition.     

Bell's theorem,inference, and quantum transactions

Bell's theorem is expounded as an analysis in Bayesian inference. Assuming the result of a spin measurement on a particle is governed by a causal variable internal (hidden, local) to the particle, one learns about it by making a spin measurement; thence about the internal variable of a second particle correlated with the first; and from there predicts the probabilistic result of spin measurements on the second particle. Such predictions are violated by experiment: locality/causality fails. The statistical nature of the observations rules out signalling; acausal, superluminal, or otherwise. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of experiment imply that it has a nonlocal/acausal interpretation. Cramer's newtransactional interpretation, which incorporates this feature by adapting the Wheeler-Feynman idea of advanced and retarded processes to the quantum laws, is advocated. It leads to an invaluable way of envisaging quantum processes. The usual paradoxes melt before this, and one, the delayed choice experiment, is chosen for detailed inspection. Nonlocality implies practical difficulties in influencing hidden variables, which provides a very plausible explanation for why they have not yet been found; from this standpoint, Bell's theoremreinforces arguments in favor of hidden variables.