Nonseparable States Research Articles

Diffraction of entangled particles by light gratings

We analyze the diffraction regime of the Kapitza–Dirac effect for particles entangled in momentum. The detection patterns show two-particle interferences. In the single-mode case we identify a discontinuity in the set of joint detection probabilities, associated with the disconnected character of the space of non-separable states. For Gaussian multi-mode states we derive the diffraction patterns, providing an example of the dependence of the light–matter interaction on entanglement. When the particles are identical, we can explore the relation between exchange and entanglement effects. We find a complementary behavior between overlapping and Schmidt’s number. In particular, symmetric entanglement can cancel the exchange effects.

Entanglement in Classical Optics

The emerging field of entanglement or nonseparability in classical optics is reviewed, and its similarities with and differences from quantum entanglement clearly pointed out through a recapitulation of Hilbert spaces in general, the special restrictions on Hilbert spaces imposed in quantum mechanics and the role of Hilbert spaces in classical polarization optics. The production of Bell-like states in classical polarization optics is discussed, and new theorems are proved to discriminate between separable and nonseparable states in classical wave optics where no discreteness is involved. The influence of the Pancharatnam phase on a classical Bell-like state is deived. Finally, to what extent classical polarization optics can be used to simulate quantum information processing tasks is also discussed. This should be of great practical importance because coherence and entanglement are robust in classical optics but not in quantum systems.

Entanglement in fermion systems and quantum metrology

Entanglement in fermion many-body systems is studied using a generalized definition of separability based on partitions of the set of observables, rather than on particle tensor products. In this way, the characterizing properties of non-separable fermion states can be explicitly analyzed, allowing a precise description of the geometric structure of the corresponding state space. These results have direct applications in fermion quantum metrology: sub-shot noise accuracy in parameter estimation can be obtained without the need of a preliminary state entangling operation.

Novel States of Classical Light and Noncontextuality

A new criterion, based on noncontextuality, is derived to discriminate between separable and nonseparable states in classical wave optics where no discreteness is involved. An experiment is proposed to test the violation of noncontextuality by a nonseparable state. Such states have only recently begun to be explored. The significance of their nonseparability or entanglement as well as their similarities with and differences from entangled quantum states are discussed.

Dissipative fields in de Sitter and black hole spacetimes: Quantum entanglement due to pair production and dissipation

For free fields, pair creation in expanding universes is associated with the building up of correlations that lead to nonseparable states, i.e., quantum mechanically entangled ones. For dissipative fields, i.e., fields coupled to an environment, there is a competition between the squeezing of the state and the coupling to the external bath. We compute the final coherence level for dissipative fields that propagate in a two-dimensional de Sitter space, and we characterize the domain in parameter space where the state remains nonseparable. We then apply our analysis to (analogue) Hawking radiation by exploiting the close relationship between Lorentz violating theories propagating in de Sitter and black hole metrics. We establish the robustness of the spectrum and find that the entanglement among Hawking pairs is generally much stronger than that among pairs of quanta with opposite momenta.

Measure of multipartite entanglement with computable lower bounds

In this paper, we present a measure of multipartite entanglement ($k$-nonseparable), $k$-ME concurrence $C_{k-\mathrm{ME}}(\rho)$ that unambiguously detects all $k$-nonseparable states in arbitrary dimensions, where the special case, 2-ME concurrence $C_{2-\mathrm{ME}}(\rho)$, is a measure of genuine multipartite entanglement. The new measure $k$-ME concurrence satisfies important characteristics of an entanglement measure including entanglement monotone, vanishing on $k$-separable states, convexity, subadditivity and strictly greater than zero for all $k$-nonseparable states. Two powerful lower bounds on this measure are given. These lower bounds are experimentally implementable without quantum state tomography and are easily computable as no optimization or eigenvalue evaluation is needed. We illustrate detailed examples in which the given bounds perform better than other known detection criteria.

Generation of quantum correlations for two qubits through a common reservoir

Recently, besides entanglement, an entropy-based measurement called quantum discord has been used to describe the quantum correlations in separable and non-separable states. Here we compare the dynamics of entanglement with that of quantum discord, in the case of two qubits in a common thermal or squeezed reservoir. We focus on the generation of quantum correlations, starting from an uncorrelated system.

Entanglement beyond tensor product structure: algebraic aspects of quantum non-separability

An algebraic approach to quantum non-separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not exploited. Even in this simple case, such a general formulation has some advantages. Using algebraic formalism, we can explicitly show the relativity of the notion of entanglement to the observables measured in the system and characterize separable and non-separable pure states. As a universal measure of non-separability of pure states, we propose to take the so-called total correlation. This quantity depends on the state as well as on the algebraic partition. Its numerical value is given by the norm of the corresponding correlation matrix.

Detection of genuinely entangled and nonseparablen-partite quantum states

We investigate the detection of entanglement in $n$-partite quantum states. We obtain practical separability criteria to identify genuinely entangled and non-separable mixed quantum states. No numerical optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. We provide examples in which our criteria perform better than all known separability criteria. Specifically, we are able to detect genuine $n$-partite entanglement which has previously not been identified. In addition, our criteria can be used in today's experiment.

Generic local distinguishability and completely entangled subspaces

A subspace of a multipartite Hilbert space is completely entangled if it contains no product states. Such subspaces can be large with a known maximum size, smax, approaching the full dimension of the system, D. We show that almost all subspaces with dimension s ⩽ smax are completely entangled and then use this fact to prove that n random pure quantum states are unambiguously locally distinguishable if and only if n ⩽ D − smax. This condition holds for almost all sets of states of all multipartite systems and reveals something surprising. The criterion is identical for separable and nonseparable states: entanglement makes no difference.

Quantum key distribution without a shared reference frame

We report a simple quantum-key-distribution experiment in which Alice and Bob do not need to share a common polarization direction in order to send information. Logical qubits are encoded into nonseparable states of polarization and first-order transverse spatial modes of the same photon.

Useful entanglement can be extracted from all nonseparable states

We consider entanglement distillation from a single copy of multipartite quantum states, and instead of rates we analyze the “quality” of the distilled entanglement. This quality is quantified by the fidelity with the gigahertz state. We show that each not fully separable state σ can increase the quality of the entanglement distilled from other states, no matter how weakly entangled is σ. We also generalize this to the case where the goal is distilling states different from the gigahertz. These results provide new insights on the geometry of the set of separable states and its dual (the set of entanglement witnesses).

Nonseparability of continuously measured quantum systems in the classical limit

We analyze the question of separability in a continuously measured quantum system as it approaches the classical limit. We show that the record of position measurements can approach the classical limit even when the system is described by highly nonseparable states. In particular, in systems with a chaotic classical limit, chaos can work to enhance the entanglement in the system in the classical regime. This coexistence of nonclassical states and classical dynamics can be understood by analyzing the conditioned evolution of the measured system and the conditions for the quantum-to-classical transition. PACS Nos.: 03.65.Ta, 03.65.Ud, 03.67.Mn, 05.45.Mt, 03.67.–a

Bell inequality with an arbitrary number of settings and its applications

Based on a geometrical argument introduced by \ifmmode \dot{Z}\else \.{Z}\fi{}ukowski, a new multisetting Bell inequality is derived, for the scenario in which many parties make measurements on two-level systems. This generalizes and unifies some previous results. Moreover, a necessary and sufficient condition for the violation of this inequality is presented. It turns out that the class of nonseparable states which do not admit local realistic description is extended when compared to the two-setting inequalities. However, supporting the conjecture of Peres, quantum states with positive partial transposes with respect to all subsystems do not violate the inequality. Additionally, we follow a general link between Bell inequalities and communication complexity problems, and present a quantum protocol linked with the inequality, which outperforms the best classical protocol.

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.

Separability of two-party Gaussian states

We investigate the separability properties of quantum two-party Gaussian states in the framework of the operator formalism for the density operator. Such states arise as natural generalizations of the entangled state originally introduced by Einstein, Podolsky, and Rosen. We present explicit forms of separable and nonseparable Gaussian states.

Channel estimation with noisy entanglement

We analyze the Pauli-channel estimation with mixed nonseparable states. It turns out that within a specific range entanglement can serve as a nonclassical resource. However, this range is rather small, that is entanglement is not very robust for this application. We further show that Werner states yield the best result of all Bell diagonal states with the same amount of entanglement.

Nonlocal correlations are generic in infinite-dimensional bipartite systems

It was recently shown that the nonseparable density operators for a bipartite system are trace norm dense if either factor space has infinite dimension. We show here that non-local states -- i.e., states whose correlations cannot be reproduced by any local hidden variable model -- are also dense. Our constructions distinguish between the cases where both factor spaces are infinite-dimensional, where we show that states violating the CHSH inequality are dense, and the case where only one factor space is infinite-dimensional, where we identify open neighborhoods of nonseparable states that do not violate the CHSH inequality but show that states with a subtler form of non-locality (often called "hidden" non-locality) remain dense.

La objetividad del azar en un mundo determinista

This paper deals with the notion of objective randomness in classical deterministic theories. After the introduction, section 2 establishes an important distinction between a strictly metaphysical thesis of determinism (as characterized in the Montague-Earman definition, for example), and the doctrine of determinism, which can be roughly characterized as a methodological set of principles. The doctrine of determinism is associated with the idea that probability assignments can only reflect our ignorance of facts, and it also grounds the (ontological) thesis of separability: A system or process can be characterized completely in terms of the properties that a system has when in a given state, independently of the properties of other systems, The key notions of "completeness" and "independence" are only briefly discussed, as they are examined more in depth elsewhere.
 Section three examines attempts to characterize a notion of objective randomness in ergodic theory. The characterization can be seen to be equivalent to the formulation of a notion of a "physically impossible process". One way of expressing this idea is grounded on the thesis of the "coarse graining" of our measuring instruments. This leads to the problem of distinguishing "objective" from "apparent" randomness. The problem seems to be intrinsic to any attempt of characterizing the required notion of physical impossibility (and thus of objective randomness) in terms of an ideal observer. The alternative of trying to characterize physical impossibility in terms of a theory of algorithms suffers from the difficulty that it is not clear what would be the required notion of (non-epistemic) computability.
 The "coarse graining" approach, as well as the alternative in terms of a theory of algorithms seem to share the usual confusion between a strictly metaphysical thesis of determinism and the (methodological) doctrine of determinism. In section four an alternative approach is suggested. It is noticed that a denial of the thesis of separability is compatible with a strict deterministic theory, and thus that at least some classical systems (the "statistical" ones) can be described in terms of non-separable states. We do not have to think that the impossibility of preparing a classical state is too only possible explanation for physical (objective) randomness in deterministic theories. This proposal is an elaboration of an idea of Blatt (1959), although Blatt was still trying to understand objective randomness within an ideal-observer framework.[S.M.]

Nonseparable Baroclinic Instability. Part I: Quasi-geostroPhic Dynamics

Abstract We address the problem of the stability of nonseparable baroclinic mean states against small-amplitude quasi-geostrophic perturbations. A general numerical methodology is developed that allows us to construct solutions to such problems without requiring any simplifying assumptions. A previous investigation of frontal stability (Moore and Peltier) which was based upon the use of the primitive equations, demonstrated that frontal zones are unstable to a cyclone-scale mode of baroclinic instability. This mode had not been detected in any previous stability analysis. No evidence of this new mode is found in the results for the quasi-geostrophic problems reported here. In fact, it is shown that the dynamical constraints implied by the quasi-geostrophic approximation forbid the existence of such modes. We also show that recently reported quasi-geostrophic stability analyses that make simplifying assumptions regarding the meridional structure of the basic state have a markedly limited validity. The pres...