Tamás Vértesi

Closing the Detection Loophole in Bell Experiments Using Qudits

We show that the detection efficiencies required for closing the detection loophole in Bell tests can be significantly lowered using quantum systems of dimension larger than two. We introduce a series of asymmetric Bell tests for which an efficiency arbitrarily close to 1/N can be tolerated using N-dimensional systems, and a symmetric Bell test for which the efficiency can be lowered down to 61.8% using four-dimensional systems. Experimental perspectives for our schemes look promising considering recent progress in atom-photon entanglement and in photon hyperentanglement.

One-way Einstein-Podolsky-Rosen steering

Einstein-Podolsky-Rosen steering is a form of quantum nonlocality exhibiting an inherent asymmetry between the observers, Alice and Bob. A natural question is then whether there exist entangled states which are one-way steerable, that is, Alice can steer Bob’s state, but it is impossible for Bob to steer the state of Alice. So far, such a phenomenon has been demonstrated for continuous variable systems, but with a strong restriction on allowed measurements, namely, considering only Gaussian measurements. Here we present a simple class of entangled two-qubit states which are one-way steerable, considering arbitrary projective measurements. This shows that the nonlocal properties of entangled states can be fundamentally asymmetrical.

Joint measurability, Einstein-Podolsky-Rosen steering, and bell nonlocality

We investigate the relation between the incompatibility of quantum measurements and quantum nonlocality. We show that a set of measurements is not jointly measurable (i.e., incompatible) if and only if it can be used for demonstrating Einstein-Podolsky-Rosen steering, a form of quantum nonlocality. Moreover, we discuss the connection between Bell nonlocality and joint measurability, and give evidence that both notions are inequivalent. Specifically, we exhibit a set of incompatible quantum measurements and show that it does not violate a large class of Bell inequalities. This suggests the existence of incompatible quantum measurements which are Bell local, similarly to certain entangled states which admit a local hidden variable model.

Inequivalence of entanglement, steering, and Bell nonlocality for general measurements

Einstein-Podolsky-Rosen steering is a form of inseparability in quantum theory commonly acknowledged to be intermediate between entanglement and Bell nonlocality. However, this statement has so far only been proven for a restricted class of measurements, namely, projective measurements. Here we prove that entanglement, one-way steering, two-way steering, and nonlocality are genuinely different considering general measurements, i.e., single round positive-operator-valued measures. Finally, we show that the use of sequences of measurements is relevant for steering tests, as they can be used to reveal “hidden steering.”

Maximal violation of a bipartite three-setting, two-outcome Bell inequality using infinite-dimensional quantum systems

The I3322 inequality is the simplest bipartite two-outcome Bell inequality beyond the ClauserHorne-Shimony-Holt (CHSH) inequality, consisting of three two-outcome measurements per party. In case of the CHSH inequality the maximal quantum violation can already be attained with local two-dimensional quantum systems, however, there is no such evidence for the I3322 inequality. In this paper a family of measurement operators and states is given which enables us to attain the largest possible quantum value in an infinite dimensional Hilbert space. Further, it is conjectured that our construction is optimal in the sense that measuring finite dimensional quantum systems is not enough to achieve the true quantum maximum. We also describe an efficient iterative algorithm for computing quantum maximum of an arbitrary two-outcome Bell inequality in any given Hilbert space dimension. This algorithm played a key role to obtain our results for the I3322 inequality, and we also applied it to improve on our previous results concerning the maximum quantum violation of several bipartite two-outcome Bell inequalities with up to five settings per party.

Disproving the Peres conjecture by showing Bell nonlocality from bound entanglement

Quantum entanglement has a central role in many areas of physics. To grasp the essence of this phenomenon, it is fundamental to understand how different manifestations of entanglement relate to each other. In 1999, Peres conjectured that Bell nonlocality is equivalent to distillability of entanglement. The intuition of Peres was that the non-classicality of an entangled state, as witnessed via Bell inequality violation, implies that pure entanglement can be distilled from this state, hence making it useful for quantum information protocols. Subsequently, the Peres conjecture was shown to hold true in several specific cases, and became a central open question in quantum information theory. Here we disprove the Peres conjecture by showing that an undistillable bipartite entangled state--a bound entangled state--can violate a Bell inequality. Hence Bell nonlocality implies neither entanglement distillability, nor non-positivity under partial transposition. This clarifies the relation between three fundamental aspects of entanglement.

Closed sets of nonlocal correlations

We present a fundamental concept - closed sets of correlations - for studying nonlocal correlations. We argue that sets of correlations corresponding to information-theoretic principles, or more generally to consistent physical theories, must be closed under a natural set of operations. Hence, studying the closure of sets of correlations gives insight into which information-theoretic principles are genuinely different, and which are ultimately equivalent. This concept also has implications for understanding why quantum nonlocality is limited, and for finding constraints on physical theories beyond quantum mechanics.

Detecting nonlocality in many-body quantum states

Testing nonlocality for many particles Distant parts of a quantum-mechanical system can be correlated in ways that cannot be described classically—a concept known as nonlocality. Tura et al. propose a simple test for nonlocality in systems with multiple particles. The test involves quantities that should readily be measurable in, for example, cold atom experiments. This is an improvement over currently available tests, which are difficult to implement experimentally. Science, this issue p. 1256 A simplified, experimentally accessible form of Bell inequalities is derived for systems with many particles. Intensive studies of entanglement properties have proven essential for our understanding of quantum many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems because the available multipartite Bell inequalities involve correlations among many particles, which are difficult to access experimentally. We constructed multipartite Bell inequalities that involve only two-body correlations and show how they reveal the nonlocality in many-body systems relevant for nuclear and atomic physics. Our inequalities are violated by any number of parties and can be tested by measuring total spin components, opening the way to the experimental detection of many-body nonlocality, for instance with atomic ensembles.Bell inequalities define experimentally observable quantities to detect non-locality. In general, they involve correlation functions of all the parties. Unfortunately, these measurements are hard to implement for systems consisting of many constituents, where only few-body correlation functions are accessible. Here we demonstrate that higher-order correlation functions are not necessary to certify nonlocality in multipartite quantum states by constructing Bell inequalities from one- and two-body correlation functions for an arbitrary number of parties. The obtained inequalities are violated by some of the Dicke states, which arise naturally in many-body physics as the ground states of the two-body Lipkin-Meshkov-Glick Hamiltonian.

All quantum states useful for teleportation are nonlocal resources

Understanding the relation between the different forms of inseparability in quantum mechanics is a longstanding problem in the foundations of quantum theory and has implications for quantum information processing. Here we make progress in this direction by establishing a direct link between quantum teleportation and Bell nonlocality. In particular, we show that all entangled states which are useful for teleportation are nonlocal resources, i.e., lead to deterministic violation of Bells inequality. Our result also extends the phenomenon of superactivation of quantum nonlocality, recently proven by C. Palazuelos [Phys. Rev. Lett. 109, 190401 (2012)], and suggests that the latter might in fact be more general than initially thought.

Quantum Nonlocality Does Not Imply Entanglement Distillability

Entanglement and nonlocality are both fundamental aspects of quantum theory, and play a prominent role in quantum information science. The exact relation between entanglement and nonlocality is, however, still poorly understood. Here we make progress in this direction by showing that, contrary to what previous work suggested, quantum nonlocality does not imply entanglement distillability. Specifically, we present analytically a 3-qubit entangled state that is separable along any bipartition. This implies that no bipartite entanglement can be distilled from this state, which is thus fully bound entangled. Then we show that this state nevertheless violates a Bell inequality. Our result also disproves the multipartite version of a long-standing conjecture made by Peres.