Entanglement and the process of measuring the position of a quantum particle

We explore the entanglement-related features exhibited by the dynamics of a composite quantum system consisting of a particle and an apparatus (here referred to as the “pointer”) that measures the position of the particle. We consider measurements of finite duration, and also the limit case of instantaneous measurements. We investigate the time evolution of the quantum entanglement between the particle and the pointer, with special emphasis on the final entanglement associated with the limit case of an impulsive interaction. We consider entanglement indicators based on the expectation values of an appropriate family of observables, and also an entanglement measure computed on particular exact analytical solutions of the particle–pointer Schrödinger equation. The general behavior exhibited by the entanglement indicators is consistent with that shown by the entanglement measure evaluated on particular analytical solutions of the Schrödinger equation. In the limit of instantaneous measurements the system’s entanglement dynamics corresponds to that of an ideal quantum measurement process. On the contrary, we show that the entanglement evolution corresponding to measurements of finite duration departs in important ways from the behavior associated with ideal measurements. In particular, highly localized initial states of the particle lead to highly entangled final states of the particle–pointer system. This indicates that the above mentioned initial states, in spite of having an arbitrarily small position uncertainty, are not left unchanged by a finite-duration position measurement process.     

Logical reformulation of quantum mechanics. II. Interferences and the Einstein-Podolsky-Rosen experiment

The consistent quantum interpretations of logic that were introduced in a previous paper are applied to four experiments: (1) ordinary interferences, (2) the Badurek-Rauch-Tuppinger neutron interferometry experiment, (3) the Einstein-Podolsky-Rosen experiment, and (4) the detection far away of the origin of a nonrelativistic particle initially near the origin. In the first two cases, the proposition calculus excludes the possibility of observing interferences and of asserting together through which path the particles went. It is used to provide a somewhat complete discussion of the Badurek-Rauch-Tuppinger experiment. The possibility of using logical implication allows a rather complete discussion of the EPR experiment, including the question of causality, although the lack of a relativistic version of the theory does not allow a complete discussion of causality. The last experiment leads to the following result: Detecting the position of a particle at timet sometimes allows one to determine with a finite uncertainty what its momentum was just before the position measurement, even when it is infinitely precise.     

Decoherence in generalized measurement and the quantum Zeno paradox

In the development of quantum mechanics, the evolution of a quantum system was a controversial item. The duality of unitary evolution and state reduction as proposed by John von Neumann was widely felt unsatisfactory. Among the various attempts to reconcile the two incompatible modes of dynamics, the model of decoherence has turned out rather convincing.     

Nonclassical joint distributions and Bell measurements

Derivation and experimental violation of Bell-like inequalities involve the measurement of incompatible observables. Simple complementarity forbids the existence of such joint probability distribution. Moreover, the measurement of incompatible observables requires different experimental procedures, which no necessarily must share a common joint statistics. In this work, we avoid these difficulties by proposing a joint simultaneous measurement. We can obtain the exact individual statistics of all the observables involved in the Bell inequalities after a suitable data inversion. A lack of positivity or any other pathology of the so retrieved joint distribution is then a signature of nonclassical behavior.     

Spectral-statistics properties of the experimental and theoretical light meson spectra

We present a robust analysis of the spectral fluctuations exhibited by the light meson spectrum. This analysis provides information about the degree of chaos in light mesons and may be useful to get some insight on the underlying interactions. Our analysis unveils that the statistical properties of the light meson spectrum are close, but not exactly equal, to those of chaotic systems. In addition, we have analyzed several theoretical spectra including the latest lattice QCD calculation. With a single exception, their statistical properties are close to those of a generic integrable system, and thus incompatible with the experimental spectrum.     

Physical Propositions and Quantum Languages

The word proposition is used in physics with different meanings, which must be distinguished to avoid interpretational problems. We construct two languages ℒ ^* (x) and ℒ(x) with classical set-theoretical semantics which allow us to illustrate those meanings and to show that the non-Boolean lattice of propositions of quantum logic (QL) can be obtained by selecting a subset of p-testable propositions within the Boolean lattice of all propositions associated with sentences of ℒ(x). Yet, the aforesaid semantics is incompatible with the standard interpretation of quantum mechanics (QM) because of known no-go theorems. But if one accepts our criticism of these theorems and the ensuing SR (semantic realism) interpretation of QM, the incompatibility disappears, and the classical and quantum notions of truth can coexist, since they refer to different metalinguistic concepts (truth and verifiability according to QM, respectively). Moreover one can construct a quantum language ℒ _TQ (x) whose Lindenbaum–Tarski algebra is isomorphic to QL, the sentences of which state (testable) properties of individual samples of physical systems, while standard QL does not bear this interpretation.     

A theoretical model for quantum nanostructures electronic wave functions, magnetic field effects

Analytical solutions of electronic wave functions in symmetric quantum ring (QR), quantum wire (QWR) and quantum dots (QD) structures are given using a parabolic coordinates system. The solutions for low-energy states are combinations of Bessel functions. The density of states of perfect 1D QR and QWR are shown to be equivalent. The continuous evolution from a 0D QD to a perfect 1D QR can be precisely described. The sharp variation of electronic properties, related to the build up of a potential energy barrier at the early stage of the QR formation, is studied analytically. Paramagnetic and diamagnetic couplings to a magnetic field are computed for QR and QD. It is shown theoretically that magnetic field induces an oscillation of the magnetization in QR.     

Quantum inspired evolutionary algorithm for community detection in complex networks

Community structure is indispensable to discover the potential property of complex network systems. In this paper we propose two algorithms (QIEA-net and iQIEA-net) to discover communities in social networks by optimizing modularity. Unlike many existing methods, the proposed algorithms adopt quantum inspired evolutionary algorithm (QIEA) to optimize a population of solutions and do not need to give the number of community beforehand, which is determined by optimizing the value of modularity function and needs no human intervention. In order to accelerate the convergence speed, in iQIEA-net, we apply the result of classical partitioning algorithm as a guiding quantum individual, which can instruct other quantum individuals' evolution. We demonstrate the potential of two algorithms on five real social networks. The results of comparison with other community detection algorithms prove our approaches have very competitive performance.     

Particle detection and non-detection in a quantum time of arrival measurement

The standard time-of-arrival distribution cannot reproduce both the temporal and the spatial profile of the modulus squared of the time-evolved wave function for an arbitrary initial state. In particular, the time-of-arrival distribution gives a non-vanishing probability even if the wave function is zero at a given point for all values of time. This poses a problem in the standard formulation of quantum mechanics where one quantizes a classical observable and uses its spectral resolution to calculate the corresponding distribution. In this work, we show that the modulus squared of the time-evolved wave function is in fact contained in one of the degenerate eigenfunctions of the quantized time-of-arrival operator. This generalizes our understanding of quantum arrival phenomenon where particle detection is not a necessary requirement, thereby providing a direct link between time-of-arrival quantization and the outcomes of the two-slit experiment.     

Detection of mid-IR radiation by sum frequency generation for free space optical communication

We present an experiment where mid-infrared radiation is detected indirectly via the second-order non-linear process of sum frequency generation. The mid-infrared sources used for the experiment are quantum cascade lasers, and we use a pump wavelength that yields an up-converted wavelength within the detection window of Silicon avalanche photo diodes. Compared with direct detection using state-of-the-art mid-infrared semiconductor detectors, the detection scheme we propose in this paper has the advantages of greater bandwidth and lower noise equivalent power.     

On the measurability of quantum correlation functions

The concept of correlation function is widely used in classical statistical mechanics to characterize how two or more variables depend on each other. In quantum mechanics, on the other hand, there are observables that cannot be measured at the same time; the so-called incompatible observables. This prospect imposes a limitation on the definition of a quantum analog for the correlation function in terms of a sequence of measurements. Here, based on the notion of sequential weak measurements, we circumvent this limitation by introducing a framework to measure general quantum correlation functions, in principle, independently of the state of the system and the operators involved. To illustrate, we propose an experimental configuration to obtain explicitly the quantum correlation function between two Pauli operators, in which the input state is an arbitrary mixed qubit state encoded on the polarization of photons.     

Simultaneous Elements of Reality for Incompatible Properties by Exploiting Locality

We propose an ideal experiment enabling the simultaneous assignment of the objective values, 0 or 1, of two incompatible properties of a system made up of two separated, non-interacting spin particles when a strict interpretation of the criterion of reality of Einstein, Podolsky and Rosen is adopted. We compare this experiment with the physical situation involving two-value observables of a system of two correlated spin-1/2 particles envisaged by Bohm; in particular, we show its inadequacy in the dual assignment at issue. Finally, we discuss a number of questions of interpretation of the consistent quantum theory highlighted by our experiment.     

Event‐by‐event simulation of quantum phenomena

A discrete‐event simulation approach is reviewed that does not require the knowledge of the solution of the wave equation of the whole system, yet reproduces the statistical distributions of wave theory by generating detection events one‐by‐one. The simulation approach is illustrated by applications to a two‐beam interference experiment and two Bell test experiments, an Einstein‐Podolsky‐Rosen‐Bohm experiment with single photons employing post‐selection for pair identification and a single‐neutron Bell test interferometry experiment with nearly 100 % detection efficiency.     

Quantum diffraction of position-momentum entangled photons from a sharp edge

In this paper, an experiment of quantum diffraction of position-momentum entangled photons from a straight sharp edge is presented. Path of a single photon of an entangled pair is partially blocked by a sharp edge whereas the other photon is detected at a stationary location without revealing the which-path information of the other photon. Quantum diffraction pattern of the sharp edge is revealed only in the correlated conditional detection of spatially separated photons and no diffraction pattern is formed in local detections of individual photons. Theoretical analysis of the quantum diffraction of position-momentum entangled photons from a sharp edge is also presented in this paper. Experimental measurements of the quantum diffraction pattern are compared with theoretically calculated quantum diffraction pattern of position-momentum entangled photons.     

On the standard quantum Brownian equation and an associated class of non-autonomous master equations

It is shown that the standard quantum Brownian equation (QBE) can violate positivity not only past the thermal correlation time, but at arbitrarily long times at high system frequencies. In an effort to improve the standard QBE, exact operator solutions are provided for a class of non-autonomous master equations. These exact solutions are used to derive sufficient positivity conditions for the coefficients of the master equations.     

Cyclic groups and quantum logic gates

We present a formula for an infinite number of universal quantum logic gates, which are 4$4$ by 4$4$ unitary solutions to the Yang–Baxter (Y–B) equation. We obtain this family from a certain representation of the cyclic group of order n$n$. We then show that this discrete   family, parametrized by integers n$n$, is in fact, a small sub-class of a larger continuous   family, parametrized by real numbers θ$\theta$, of universal quantum gates. We discuss the corresponding Yang-Baxterization and related symmetries in the concomitant Hamiltonian.     

Cosmological Acceleration from Virtual Gravitons

Intrinsic properties of the space itself and quantum fluctuations of its geometry are sufficient to provide a mechanism for the acceleration of cosmological expansion (dark energy effect). Applying Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy approach to self-consistent equations of one-loop quantum gravity, we found exact solutions that yield acceleration. The permanent creation and annihilation of virtual gravitons is not in exact balance because of the expansion of the Universe. The excess energy comes from the spontaneous process of graviton creation and is trapped by the background. It provides the macroscopic quantum effect of cosmic acceleration.     

Double detected spin-dependent quantum dot

We study the dynamics of a spin-dependent quantum dot system, where an unsharp and a sharp detection scenario is introduced. The back-action of the unsharp detection related to the magnetization, proposed in terms of the continuous quantum measurement theory, is observed via the von Neumann measurement (sharp detection) of the electric charge current. The behavior of the average electron charge current is studied as a function of the unsharp detection strength γ$\gamma$, and features of measurement back-action are discussed. The achieved equations reproduce the quantum Zeno effect. Considering magnetic leads, we demonstrate that the measurement process may freeze the system in its initial state. We show that the continuous observation may enhance the transition between spin states, in contradiction with rapidly repeated projective observations, when it slows down. Experimental issue, such as the accuracy of the electric current measurement, is analyzed.     

Generalized uncertainty principle and self-adjoint operators

In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Neumann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are self-adjoint or not, or they have self-adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the self-adjoint extensions of the specific Hamiltonian operator are obtained.     

On the stochastic measurement of incompatible spin components

Working in stochastic spin space and using POV measures as in the Davies and Lewis measurement scheme, we construct a formalism to describe the simultaneous measurement of incompatible spin components. The methods are illustrated with a new analysis of the Stern-Gerlach experiment, and with a discussion of spin dynamics in stochastic spin space. We also present a new short proof of a theorem on representations of spin-1/2 systems, find a joint spectral family for (noncommuting) spin components, and indicate the connection of our result with the Riesz extension theorem.