Entanglement detection by local orthogonal observables

We propose a family of entanglement witnesses and corresponding positive maps that are not completely positive based on local orthogonal observables. As applications the entanglement witness of a 3x3 bound entangled state [P. Horodecki, Phys. Lett. A 232, 333 (1997)] is explicitly constructed and a family of dxd bound entangled states is introduced, whose entanglement can be detected by permuting local orthogonal observables. The proposed criterion of separability can be physically realized by measuring a Hermitian correlation matrix of local orthogonal observables.     

Uncertainty measures and uncertainty relations for angle observables

Uncertainty measures must not depend on the choice of origin of the measurement scale; it is therefore argued that quantum-mechanical uncertainty relations, too, should remain invariant under changes of origin. These points have often been neglected in dealing with angle observables. Known measures of location and uncertainty for angles are surveyed. The angle variance angv {ø} is defined and discussed. It is particularly suited to the needs of quantum theory, because of its affinity to the Hilbert space metric, and its use of the basic sine and cosine operators. Corresponding uncertainty relations involving azimuthal or phase angles are indicated, and their relevance to study and definition of coherent states is briefly reviewed.     

On some groups of automorphisms of physical observables

Given a weakly continuous one-parameter group of automorphisms of aC*-algebra of operators on a Hilbert space we show that it is implementable by a strongly continuous one-parameter group of unitary operators belonging to the weak closure of , provided that a certain condition — akin to the boundedness from below of the spectrum of the generators — is satisfied.On leave from the Istituto di Fisica Teorica, Universitá di Napoli.     

Quantitative complementarity relations in bipartite systems: Entanglement as a physical reality

We introduce a complete set of complementary quantities in bipartite, two-dimensional systems. Complementarity then relates the quantitative entanglement measure concurrence which is a bipartite property to the single-particle quantum properties predictability and visibility, for the most general quantum state of two qubits. Consequently, from an interferometric point of view, the usual wave-particle duality relation must be extended to a “triality” relation containing, in addition, the quantitative entanglement measure concurrence, which has no classical counterpart and manifests a genuine quantum aspect of bipartite systems. A generalized duality relation, that also governs possible violations of the Bell’s inequality, arises between single- and bipartite properties.     

Extreme value laws in dynamical systems under physical observables

Extreme value theory for chaotic deterministic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory studies the limit probabilistic laws obeyed by large values attained by the observable along orbits of the system. Based on this theory, the so-called block maximum method is often used in applications for statistical prediction of large value occurrences. In this method, one performs statistical inference for the parameters of the Generalised Extreme Value (GEV) distribution, using maxima over blocks of regularly sampled observable values along an orbit of the system. The observables studied so far in the theory are expressed as functions of the distance with respect to a point, which is assumed to be a density point of the system’s invariant measure. However, at least with respect to the ambient (usually Euclidean) metric, this is not the structure of the observables typically encountered in physical applications, such as windspeed or vorticity in atmospheric models. In this paper we consider extreme value limit laws for observables which are not expressed as functions of the distance (in the ambient metric) from a density point of the dynamical system. In such cases, the limit laws are no longer determined by the functional form of the observable and the dimension of the invariant measure: they also depend on the specific geometry of the underlying attractor and of the observable’s level sets. We present a collection of analytical and numerical results, starting with a toral hyperbolic automorphism as a simple template to illustrate the main ideas. We then formulate our main results for a uniformly hyperbolic system, the solenoid map. We also discuss non-uniformly hyperbolic examples of maps (Hénon and Lozi maps) and of flows (the Lorenz63 and Lorenz84 models). Our purpose is to outline the main ideas and to highlight several serious problems found in the numerical estimation of the limit laws.     

Quantum logics,physical space,position observables and symmetry

The concepts of physical space, localizability, position and symmetry are incorporated in the quantum logic approach to axiomatic quantum mechanics. The corresponding structure then reduces to the usual von Neumann Hilbert space model for quantum mechanics.     

The algebra of physical observables in non-linearly realized gauge theories

We classify the physical observables in spontaneously broken non-linearly realized gauge theories in the recently proposed loopwise expansion governed by the Weak Power-Counting (WPC) and the Local Functional Equation. The latter controls the non-trivial quantum deformation of the classical non-linearly realized gauge symmetry, to all orders in the loop expansion. The Batalin–Vilkovisky (BV) formalism is used. We show that the dependence of the vertex functional on the Goldstone fields is obtained via a canonical transformation w.r.t. the BV bracket associated with the BRST symmetry of the model. We also compare the WPC with strict power-counting renormalizability in linearly realized gauge theories. In the case of the electroweak group we find that the tree-level Weinberg relation still holds if power-counting renormalizability is weakened to the WPC condition.     

Entanglement as a Semantic Resource

The characteristic holistic features of the quantum theoretic formalism and the intriguing notion of entanglement can be applied to a field that is far from microphysics: logical semantics. Quantum computational logics are new forms of quantum logic that have been suggested by the theory of quantum logical gates in quantum computation. In the standard semantics of these logics, sentences denote quantum information quantities: systems of qubits (quregisters) or, more generally, mixtures of quregisters (qumixes), while logical connectives are interpreted as special quantum logical gates (which have a characteristic reversible and dynamic behavior). In this framework, states of knowledge may be entangled, in such a way that our information about the whole determines our information about the parts; and the procedure cannot be, generally, inverted. In spite of its appealing properties, the standard version of the quantum computational semantics is strongly “Hilbert-space dependent”. This certainly represents a shortcoming for all applications, where real and complex numbers do not generally play any significant role (as happens, for instance, in the case of natural and of artistic languages). We propose an abstract version of quantum computational semantics, where abstract qumixes, quregisters and registers are identified with some special objects (not necessarily living in a Hilbert space), while gates are reversible functions that transform qumixes into qumixes. In this framework, one can give an abstract definition of the notions of superposition and of entangled pieces of information, quite independently of any numerical values. We investigate three different forms of abstract holistic quantum computational logic.     

Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems

We develop a level set method for the computation of multi-valued physical observables (density, velocity, energy, etc.) for the high frequency limit of symmetric hyperbolic systems in any number of space dimensions. We take two approaches to derive the method.The first one starts with a weakly coupled system of an eikonal equation for phase S and a transport equation for density ρ:

The main idea is to evolve the density near the n-dimensional bi-characteristic manifold of the eikonal (Hamiltonian–Jacobi) equation, which is identified as the common zeros of n level set functions in phase space . These level set functions are generated from solving the Liouville equation with initial data chosen to embed the phase gradient. Simultaneously, we track a new quantity f = ρ(t,x,k)|det(_k)| by solving again the Liouville equation near the obtained zero level set = 0 but with initial density as initial data. The multi-valued density and higher moments are thus resolved by integrating f along the bi-characteristic manifold in the phase directions.The second one uses the high frequency limit of symmetric hyperbolic systems derived by the Wigner transform. This gives rise to Liouville equations in the phase space with measure-valued solution in its initial data. Due to the linearity of the Liouville equation we can decompose the density distribution into products of function, each of which solves the Liouville equation with L^∞ initial data on any bounded domain. It yields higher order moments such as energy and energy flux.The main advantages of these new approaches, in contrast to the standard kinetic equation approach using the Liouville equation with a Dirac measure initial data, include: (1) the Liouville equations are solved with L^∞ initial data, and a singular integral involving the Dirac-δ function is evaluated only in the post-processing step, thus avoiding oscillations and excessive numerical smearing; (2) a local level set method can be utilized to significantly reduce the computation in the phase space. These methods can be used to compute all physical observables for multi-dimensional problems.Our method applies to the wave fields corresponding to simple eigenvalues of the dispersion matrix. One such example is the wave equation, which will be studied numerically in this paper.     

Entanglement Fidelity as a Measure of Preservation of Entanglement in Local Noisy Process

A new formula of entanglement fidelity has been introduced, which can serve as a measure of the preservation of entanglement between two initially entangled subsystems exposed to local noisy environments. For a simple model we derive analytic expressions of concurrence and entanglement fidelity and draw the relationship between them. We find that such entanglement fidelity exhibits the behavior similar to that of the concurrence in quantum evolutions.     

Entanglement measures of a new type pseudo-pure state in accelerated frames

In this work we analyze the characteristics of quantum entanglement of the Dirac field in noninertial reference frames in the context of a new type pseudo-pure state, which is composed of the Bell states. This will help us to understand the relationship between the relativity and quantum information theory. Some states will be changed from entangled states into separable ones around the critical value F = 1/4, but there is no such a critical value for the variable y related to acceleration a. We find that the negativity N_ABI (ρ^TA_ABI) increases with F but decreases with the variable y, while the variation of the negativity N_BIBII(ρ^TA_ABI) is opposite to that of the negativity N_ABI (ρ^TA_ABI). We also study the von Neumann entropies S(ρ_ABI) and S(ρ_BIBII). We find that the S(ρ_ABI) increases with variable y but S(ρ_BIBII) is independent of it. However, both S(ρ_ABI) and S(ρ_BIBII) first decreases with F and then increases with it. The concurrences C(ρ_ABI) and C(ρ_BIBII) are also discussed. We find that the former decreases with y while the latter increases with y but both of them first increase with F and then decrease with it.     

Uncertainty of parton distribution functions due to physical observables in a global analysis

The recent measurement of the differential γ + c-jet cross section, performed at the Tevatron collider in Run II by the D0 collaboration, is studied in a next-to-leading order(NLO) global QCD analysis to assess its impact on the proton parton distribution functions(PDFs). We show that these data lead to a significant change in the gluon and charm quark distributions. We demonstrate also that there is an inconsistency between the new high precision HERA I+II combined data and Tevatron measurement. Moreover, in this study we investigate the impact of older EMC measurements of charm structure function F_c~2 on the PDFs and compare the results with those from the analysis of Tevatron data. We show that both of them have the same impact on the PDFs, and thus can be recognized as the same evidence for the inefficiency of perturbative QCD in dealing with charm production in some kinematic regions.     

Energy and momentum as observables in quantum field theory

The spectrum condition implies that energy and momentum are limits of local observables.     

Entanglement measures with asymptotic weak-monotonicity as lower (upper) bound for the entanglement of cost (distillation)

We propose entanglement measures with asymptotic weak-monotonicity. We show that a normalized form of entanglement measures with the asymptotic weak-monotonicity are lower (upper) bound for the entanglement of cost (distillation).     

Correlated Emission Laser as an Entanglement Amplifier

We consider a two-photon correlated emission laser as a source of an entangled radiation with a large number of photons in each mode. The system consists of three-level atomic schemes inside a doubly resonant cavity. We study the dynamics of this system in the presence of cavity losses, concluding that the creation of entangled states with photon numbers up to tens of thousands seems achievable.     

Negativity as Entanglement Degree of a Non-Hermitian Model

We investigate non-Hermitian Hamiltonian which governs system includes two-level atoms and electromagnetical field. Using the notion of negativity, we study the degree of entanglement of a two- level atom interacting with a quantized electromagnetical field, described by the non-Hermitian Hamiltonian (Saaidi in Phys. Scr. 77:0065002, 2008). With the help of numerical calculation for the case that the system state is pure, we show that the measurement of negativity of this system is nonzero and has a different functional with respect to negativity of the Jaynes-Cumming model (JCM).     

Entanglement without dissipation: A touchstone for an exact comparison of entanglement measures

Entanglement, which is an essential characteristic of quantum mechanics, is the key element in potential practical quantum information and quantum communication systems. However, there are many open and fundamental questions (relating to entanglement measures, sudden death, etc.) that require a deeper understanding. Thus, we are motivated to investigate a simple but non-trivial correlated two-body continuous variable system in the absence of a heat bath, which facilitates an exact measure of the entanglement at all times. In particular, we find that the results obtained from all well-known existing entanglement measures agree with each other but that, in practice, some are more straightforward to use than others.     

A Geometrical Representation of Entanglement as Internal Constraint

We study a system of two entangled spin 1/2, were the spin's are represented by a sphere model developed within the hidden measurement approach which is a generalization of the Bloch sphere representation, such that also the measurements are represented. We show how an arbitrary tensor product state can be described in a complete way by a specific internal constraint between the ray or density states of the two spin 1/2. We derive a geometrical view of entanglement as a “rotation” and “stretching” of the sphere representing the states of the second particle as measurements are performed on the first particle. In the case of the singlet state entanglement can be represented by a real physical constraint, namely by means of a rigid rod.