A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model

Recently, it has been shown that the quantum Fisher information via local observables and via local measurements (i.e., local quantum Fisher information (LQFI)) is a central concept in quantum estimation and quantum metrology and captures the quantumness of correlations in multi-component quantum system (Kim et al. (2018) [28]). This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In the present study, we have revealed that LQU is bounded by LQFI in the phase estimation protocol. Also, a comparative study between these two quantum correlations quantifiers is addressed for the quantum Heisenberg XY model. Two distinct situations are considered. The first one concerns the anisotropic XY model and the second situation concerns isotropic XY model submitted to an external magnetic field. Our results confirm that LQFI reveals more quantum correlations than LQU.     

Tests of quantum mechanics with single atoms in high Q cavities

A Rydberg atom coupled to a single field mode in a high Q superconducting cavity is an ideal tool to perform experiments testing the most puzzling aspects of the quantum theory. The coupling between the atom and the field is either resonant or dispersive. In the resonant case, quantum Rabi oscillations in the vacuum or in a small coherent field injected in the cavity are observed. The analysis of these signals reveals in a striking way the quantization of the field. Quantum Rabi oscillations are also used to produce entanglement between successive atoms crossing the cavity. Dispersive atom-field coupling is used to prepare coherent superpositions of field states with different phases (Schrödinger cat states). The progressive decoherence of these states is studied by measuring correlations between the energies of pairs of atoms sent through the cavity with a variable delay between them. These experiments provide fundamental tests of quantum theory and shed light on the transition from quantum to classical in mesoscopic systems.     

Quantum parameter estimation in the Unruh–DeWitt detector model

Relativistic effects on the precision of quantum metrology for particle detectors, such as two-level atoms are studied. The quantum Fisher information is used to estimate the phase sensitivity of atoms in non-inertial motions or in gravitational fields. The Unruh–DeWitt model is applicable to the investigation of the dynamics of a uniformly accelerated atom weakly coupled to a massless scalar vacuum field. When a measuring device is in the same relativistic motion as the atom, the dynamical behavior of quantum Fisher information as a function of Rindler proper time is obtained. It is found out that monotonic decrease in phase sensitivity is characteristic of dynamics of relativistic quantum estimation. The origin of the decay of quantum Fisher information is the thermal bath that the accelerated detector finds itself in due to the Unruh effect. To improve relativistic quantum metrology, we reasonably take into account two reflecting plane boundaries perpendicular to each other. The presence of the reflecting boundary can shield the detector from the thermal bath in some sense.     

Correlations in atomic systems: diagnosing coherent superpositions

While investigating quantum correlations in atomic systems, we note that single measurements contain information about these correlations. Using a simple model of measurement-analogous to the one used in quantum optics-we show how to extract higher-order correlation functions from individual "photographs" of the atomic sample. As a possible application, we apply the method to detect a subtle phase coherence in mesoscopic superpositions.     

Hidden Vacuum Rabi Oscillations:Dynamical Quantum Superpositions of On/Off Interaction between a Single Quantum Dot and a Microcavity

We show that it is possible to realize quantum superpositions of switched-on and-off strong light-matter interaction in a single quantum dot-semiconductor microcavity system.Such superpositions enable the observation of counterintuitive quantum conditional dynamics effects.Situations are possible where cavity photons as well as the emitter luminescence display exponential decay but their joint detection probability exhibits vacuum Rabi oscillations.Remarkably,these quantum correlations are also present in the nonequilibrium steady state spectra of such coherently driven dissipative quantum systems.     

Dynamics of a Moving Two-Level Atom Under the Influence of Intrinsic Decoherence

We present a general and fascinating problem of quantum entanglement (QE) that is calculated with the help of quantum Fisher information (QFI) and von Neumann entropy (VNE) for moving two-level atomic systems. We calculate numerically the temporal evolution of the state vector of the entire system under the influence of intrinsic decoherence for a moving two-level atom. We demonstrate that the phase shifts of an estimator parameter, intrinsic decoherence, and the atomic motion play an important and prominent role during the time evolution of the atomic system. We observe that there is a monotonic relation between the atomic quantum Fisher information (QFI) and quantum entanglement (QE) in the absence of atomic motion. We also show that at the revival time the local maximum values of QFI decreases gradually. A periodic behavior of QFI is observed in the presence of atomic motion, which becomes more important and remarkable for two-level atomic systems. Moreover, the atomic quantum Fisher information and entanglement demonstrate an opposite response during the time evolution in the presence of atomic motion. We show that the evolution of entanglement is more susceptible to the intrinsic decoherence; a considerable change occurs in the degree of entanglement when the intrinsic decoherence parameter increases. Intrinsic decoherence in the atom–field interaction represses the nonclassical effects of the atomic systems. Both the entanglement and the quantum Fisher information saturate to their lower levels for longer time scales in the presence of intrinsic decoherence. For larger values of intrinsic decoherence, the sudden death of entanglement is observed.     

Quantum Fisher Information of Driven Multi-particle Systems in Structured Bosonic Reservoirs

We investigate the dynamics of the precision of the parameter estimation in many driven atoms, each of which interacts with a local structured bosonic reservoir respectively. The evolution of quantum states for single driven atom is described by the time local quantum master equation. The dynamics of the quantum Fisher information for many entangled atoms is obtained by means of the supreoperator mapping. The estimation limit is superior to the standard quantum limit during a characteristic interval. At a given time, the precision of parameter estimation can be improved to a maximal value if the number of entangled atoms is chosen to be an optimal value. The optimal number of entangled atoms is determined by the dynamical property. The decay of quantum Fisher information is accelerated with the increase of the number of entangled atoms.     

Fisher Information of Wavefunctions： Classical and Quantum

A parametric quantum mechanical wavefunction naturally induces parametric probability distributions by taking absolute square, and we can consider its classical Fisher information. On the other hand, it also induces parametric rank-one projections which may be viewed as density operators, and we can talk about its quantum Fisher information. Among many versions of quantum Fisher information, there are two prominent ones. The first, defined via a quantum score function, was introduced by Helstrom in 1967 and is well known. The second, defined via the square root of the density operator, has its origin in the skew information introduced by Wigner and Yanase in 1963 and remains relatively unnoticed. This study is devoted to investigating the relationships between the classical Fisher information and these two versions of quantum Fisher information for wavefunctions. It is shown that the two versions of quantum Fisher information differ by a factor 2 and that they dominate the classical Fisher information. The non-coincidence of these two versions of quantum Fisher information may be interpreted as a manifestation of quantum discord. We further calculate the difference between the Helstrom quantum Fisher information and the classical Fisher information, and show that it is precisely the instantaneous phase fluctuation of the wavefunctions.     

Environmental parameter estimation with the two-level atom probes

A novel scheme is proposed to estimate three environmental parameters, the detuning, the temperature and the squeezing strength with one-qubit or two-qubit probes. Quantum Fisher information and the fidelity of the atom probes are calculated. When the detuning between the frequency of cavity field and the atomic transition frequency is estimated, the dynamics of quantum Fisher information shows oscillatory and rising behaviors. To estimate the temperature of the thermal reservoir, the one-qubit probe with the superposition initial state is more favorable than the two-qubit probe with the entangled initial state. When the squeezing strength of the squeezed vacuum reservoir is estimated, we find that the estimation precision is significantly improved by utilizing the two-qubit probe with the maximal entangled initial state. Our work provides a potential application in the open quantum system and quantum information processing.     

Transmission of Quantum Fisher Information through Fluctuating Quantum Fields

Transmission of quantum Fisher information (QFI) of initially disentangled parties is studied and the results show that the indirect correlations generated by the environment, which is considered as a bath of fluctuating quantum fields, will help transmit the quantum information. Specifically, using N initially disentangled atoms—one in an excited state carried by one party (the sender, Alice) and the other in the ground state carried by the other parties (the receivers: Bob1, Bob2,…, Bob(N?1)), the phase factor of the state of another atom held by Alice can be transmitted from Alice to Bob with proper time. The transmitted QFI of the phase factor for each receiver has been calculated as a function of the transmitted distance as well as the measurement time and is found to be in relation with the concurrence of the pair of atoms that the sender and the receiver carry. For each transmitted distance, there exists an optimal measurement time to obtain the maximal transmitted QFI, which is in relation with the total number of receivers.     

Quantum state engineering by superpositions of coherent states along a straight line with a single atomic state measurement

A new scheme is proposed for preparation of a type of nonclassical state in cavity QED. In the scheme, an atom either flying through or trapped within a cavity, is controlled by the classical Stark effect; this makes it interact alternately with a (resonant) classical field and with the (dispersive) cavity field. The cavity field, which allows an arbitrary displacement operation during the process, after the detection on the atom, finally collapses to the specific superpositions of coherent states, with their weighting factors controllable. The scheme is also applied for preparation of superpositions of motional coherent states for a trapped ion. The scheme is in contrast to all the previous ones, and thus provides a new perspective for quantum state engineering.     

Control of Correlation Using Confinement in Case of Quantum System

This article investigates the behavior of a Moshinsky atom in a 1D harmonic trap. Focus is given on the theoretical foundations of confinement and its impact on the correlation between particles in the Moshinsky atom. The investigation begins by illustrating the (de)localization of the probability density function using Shannon entropy. The basics of correlation and interpretation of correlation using tools such as mutual information and statistical correlation coefficients and how these can be quantified are discussed. Then the concept of confinement is explored. The impact of interaction strength and confinement on Shannon entropy, statistical correlation coefficients, and mutual information is investigated. How interaction strength and confinement can be used to induce correlations between previously uncorrelated particles, as well as how they can be used to suppress correlations between previously correlated particles is discussed. Their implications for quantum information processing and quantum simulation are discussed. In conclusion, confinement is a powerful tool for controlling correlations in quantum systems, and its impact on correlation can be understood through theoretical models. The importance of experimental studies in this field, which provide insights into the behavior of quantum systems under confinement and pave the way for future applications in quantum technology is also emphasized.     

Quantum Fisher Information in the Generalized One-axis Twisting Model

We investigate the quantum Fisher information (QFI) of symmetric states for spin-s particles. We derive the maximal QFI, and find that quantum spin correlations are essential ingredients of the maximal QFI. We make applications to the generalized one-axis twisting model. The results show that the redistributions of uncertainties on the basis of the quantum correlations in the multiqubit system are useful for sub-shot-noise phase sensitivity. Furthermore, for high-spin (s>1/2) composite systems, we find a sufficient criterion for entanglement.     

Two-Qubit Local Fisher Information Correlation beyond Entanglement in a Nonlinear Generalized Cavity with an Intrinsic Decoherence

In this paper, we study a Hamiltonian system constituted by two coupled two-level atoms (qubits) interacting with a nonlinear generalized cavity field. The nonclassical two-qubit correlation dynamics are investigated using Bures distance entanglement and local quantum Fisher information under the influences of intrinsic decoherence and qubit–qubit interaction. The effects of the superposition of two identical generalized coherent states and the initial coherent field intensity on the generated two-qubit correlations are investigated. Entanglement of sudden death and sudden birth of the Bures distance entanglement as well as the sudden changes in local Fisher information are observed. We show that the robustness, against decoherence, of the generated two-qubit correlations can be controlled by qubit–qubit coupling and the initial coherent cavity states.     

Spin Squeezing and Quantum Fisher Information in Generalized Two-Axis Twisting Model

We investigated spin squeezing and quantum Fisher information in generalized two-axis twisting model; which generalizes the two-axis twisting model including a linear interaction controlled by an external field. In particular, we are interested in the dependence of spin squeezing and quantum Fisher information on the external field. By adopting frozen-spin approximation, we derive the theoretical and numerical results for spin squeezing and quantum Fisher information. Except certain special conditions, the stronger external field induces to stronger squeezing. Spin squeezing parameter and the reciprocal of the mean quantum Fisher information per particle are periodic function; but the external field has not important effect on the period.     

Chaos and quantum Fisher information in the quantum kicked top

Quantum Fisher information is related to the problem of parameter estimation.Recently,a criterion has been proposed for entanglement in multipartite systems based on quantum Fisher information.This paper studies the behaviours of quantum Fisher information in the quantum kicked top model,whose classical correspondence can be chaotic.It finds that,first,detected by quantum Fisher information,the quantum kicked top is entangled whether the system is in chaotic or in regular case.Secondly,the quantum Fisher information is larger in chaotic case than that in regular case,which means,the system is more sensitive in the chaotic case.     

Vortex phase qubit: generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams

We propose a scheme for the generation of arbitrary coherent superpositions of vortex states in Bose-Einstein condensates (BEC) using the orbital-angular-momentum states of light. We devise a scheme to generate coherent superpositions of two such counterrotating states of light using well-known experimental techniques. We show that a specially designed Raman scheme allows for transfer of the optical vortex-superposition state onto an initially nonrotating BEC. This creates an arbitrary and coherent superposition of a vortex and antivortex pair in the BEC. The ideas presented here could be extended to generate entangled vortex states, design memories for the orbital-angular-momentum states of light, and perform other quantum information tasks. Applications to inertial sensing are also discussed.     

On the Analytical Derivation of Quantum Fisher Information and Skew Information for two Qubit X States

The quantum Fisher information defined via the symmetric logarithmic derivative and the skew information are two different aspects describing the information contents of quantum mechanical density operators. They are considered as natural generalizations of the classical Fisher information and constitute key ingredients in the emerging field of quantum metrology. In this paper, we give the analytical expression of quantum Fisher information and skew information for two-qubit system prepared in a two-qubit state of X type.

     

The Paraconsistent Logic of Quantum Superpositions

Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by ‘superposition’ in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the literature regarding superpositions in quantum mechanics. We argue that all these interpretations have something in common: they all attempt to avoid ‘contradiction’. We argue in this paper, in favor of the importance of developing a new interpretation of superpositions which takes into account contradiction, as a key element of the formal structure of the theory, “right from the start”. In order to show the feasibility of our interpretational project we present an outline of a paraconsistent approach to quantum superpositions which attempts to account for the contradictory properties present in general within quantum superpositions. This approach must not be understood as a closed formal and conceptual scheme but rather as a first step towards a different type of understanding regarding quantum superpositions.     

Quantum Fisher Information and the Heisenberg Limit in Superpositions of Two W States and Symmetric State

We investigate the quantum Fisher information and the Heisenberg limit in superposition of a four-qubit symmetric state and two W states. Numerical and analytical calculations for quantum Fisher information and the Heisenberg limit of the four-qubit state are driven. It is shown that quantum Fisher information of the four-qubit state depends on the superposition coefficients and the relative phase. It is also shown that under certain conditions, the maximal quantum Fisher information occurred; which leads to the estimation sensitivity beats the Heisenberg limit.