It is emphasized that quantum entanglement determined in terms of the von Neumann entropy operator is a stochastic quantity and, therefore, can fluctuate. The rms fluctuations of the entanglement entropy of two-qubit systems in both pure and mixed states have been obtained. It has been found that entanglement fluctuations in the maximally entangled states are absent. Regions where the entanglement fluctuations are larger than the entanglement itself (strong fluctuation regions) have been revealed. It has been found that the magnitude of the relative entanglement fluctuations is divergent at the points of the transition of systems from an entangled state to a separable state. It has been shown that entanglement fluctuations vanish in the separable states.
We show that due to entanglement, quantum fluctuations may differ significantly from statistical fluctuations. We calculate quantum fluctuations of the particle number and of the energy in a sub-volume of a system of bosons in a pure state, and briefly discuss the possibility of measuring them. We find that energy fluctuations have a non-extensive nature.
We discuss maximum entangled states of quantum systems in terms of quantum fluctuations of all essential measurements responsible for manifestation of entanglement. Namely, we consider maximum entanglement as a property of states, for which quantum fluctuations come to their extreme.
A general theory of thermal magnetic fluctuations near conductive materials is developed; such fluctuations are the magnetic analog of Johnson noise. For realistic experiments in quantum computing and magnetic resonance force microscopy, the predicted relaxation can be rapid enough that substantial experimental care should be taken to minimize it. The same Hamiltonian matrix elements that govern fluctuation and dissipation are shown to also govern entanglement and renormalization, and a specific example of a fluctuation-dissipation-entanglement theorem is constructed.
In one dimension very general results from conformal field theory and exact calculations for certain quantum spin systems have established universal scaling properties of the entanglement entropy between two parts of a critical system. Using both analytical and numerical methods, we show that if particle number or spin is conserved, fluctuations in a subsystem obey identical scaling as a function of subsystem size, suggesting that fluctuations are a useful quantity for determining the scaling of entanglement, especially in higher dimensions. We investigate the effects of boundaries and sublead…
A system of two coupled cavities is studied in the context of bipartite, continuous variable entanglement. One of the cavities is pumped by an external classical source that is coupled quadratically, to the cavity field. Dynamics of entanglement, quantified by covariance measure [Dodonov {\it et al}, Phys. Lett A {\bf 296}, (2002) 73], in the presence of cavity-cavity coupling and external pumping is investigated. The importance of tailoring the coupling between the cavities is brought out by studying the effects of pump fluctuations on the entanglement.
We study the dynamics of a pair of molecular ensembles trapped inside a superconducting resonator through which they are strongly coupled via a microwave field mode. We find that entanglement can be generated via "vacuum fluctuations" even when the molecules and cavity field are initially prepared in their ground state. This entanglement is created in a relatively short time and without the need for further manipulation of the system. It does, therefore, provide a convenient scheme to entangle two mesoscopic systems, and may well be useful quantum information processing.
A detailed study of the effects of phase fluctuation and dephasing on the dynamics of the entanglement generated from a coherently pumped correlated emission laser is presented. It is found that the time evolution of the entanglement is significantly reliant on the phase fluctuation and dephasing, particularly, at early stages of the lasing process. In the absence of external driving radiation, the degree of entanglement and intensity turns out to attain a maximum value just before starting to exhibit oscillation which dies at longer time scale. However, in case the driving mechanism is on, th…
We report on the dissipative dynamics of an entangled, bipartite interacting system. We show how to induce and control the so-called early stage disentanglement (and the delayed entanglement generation) dynamics by means of a driving laser field. We demonstrate that some of the features currently associated with pure non-Markovian effects in such entanglement behavior can actually take place in Markovian environments if background noise QED fluctuations are considered. We illustrate this for the case of a dimer interacting molecular system for which emission rates, interaction strength, and ra…
Pure state entanglement transformations have been thought of as irreversible, with reversible transformations generally only possible in the limit of many copies. Here, we show that reversible entanglement transformations do not require processing on the many copy level, but can instead be undertaken on individual systems, provided the amount of entanglement which is produced or consumed is allowed to fluctuate. We derive necessary and sufficient conditions for entanglement manipulations in this case. As a corollary, we derive an equation which quantifies the fluctuations of entanglement, whic…
The Ising chains in a transverse magnetic field of constant strength (h=1) and with the spin interaction value λare considered. In the case of infinitely long chain, exact analytical expressions are found for the second central moment (dispersion) of the entropy operator S^\hat=-lnρwith reduced density matrix ρwhich corresponds to a semi-infinite part of the model in the ground state. It is shown that in the vicinity of a critical point λ_c=1, the entanglement entropy fluctuation ΔS (square root of dispersion) diverges as \Delts S\sim[ln(1/|1-λ|)]^{1/2}. Taking into account the known behavior …
We identify subsystem fluctuations (variances) that measure entanglement in an arbitrary bipartite pure state. These fluctuations are of observables that generalize the notion of polarization to an arbitrary N-level subsystem. We express this polarization fluctuation in terms of subsystem purity and other entanglement measures. The derived fluctuation-entanglement relation is evaluated for the ground states of a one-dimensional free fermion gas and the Affleck-Kennedy-Lieb-Tasaki spin chain. Our results provide a framework for experimentally measuring entanglement using Stern-Gerlach-type stat…
We derive experimentally measurable lower bounds for the two-site entanglement of the spin-degrees of freedom of many-body systems with local particle-number fluctuations. Our method aims at enabling the spatially resolved detection of spin-entanglement in Hubbard systems using high-resolution imaging in optical lattices. A possible application is the observation of entanglement generation and spreading during spin impurity dynamics, for which we provide numerical simulations. More generally, the scheme can simplify the entanglement detection in ion chains, Rydberg atoms, or similar atomic sys…
Quantum communications require efficient implementations of quantum state transportation with high fidelity. Here, we consider the transport of entanglement along a chain of qubits. A series of SWAP operations involving successive pairs of qubits can transport entanglement along the chain. We report that the fidelity of the abovementioned gate has a maximum value corresponding to an optimum value of the drive amplitude in the presence of drive-induced decoherence. To incorporate environmental effect, we use a previously reported fluctuation-regulated quantum master equation [A. Chakrabarti and…
Discussed in the study are gravitational noise and the nature of entanglement states. Their role in forming of entangled states. Nonlocal nature of entangled states can be brought about by Polarization Variables. Polarization Variables consists of sum a background of random classical gravitational fields and waves, random electromagnets fields and so on known or unknown, distributed average isotropically in the space. This background is capable of correlating phases the oscillations of microobjects. From this follow, that entanglement polarizations states is the functions of Polarization Varia…
Twisted photons carrying orbital angular momentum (OAM) are competent candidates for future interstellar communications. However, the gravitational fluctuations are ubiquitous in spacetime. Thus a fundamental question arises naturally as to how the gravitational fluctuations affect the coherence and the degree of high-dimensional OAM entanglement when twisted photons travel across the textures of curved spacetime. Here, we consider the covariant scalar Helmholtz equations and the Minkowski metric with fluctuations of Gaussian distribution and formulate analytically the equations describing the…
Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this paper, we study the entanglement entropy of topological phases in two-spaces from a new perspective---the perspective of quasiparticle fluctuations. In this picture, the entanglement spectrum of a topologically ordered system is identified with the spectrum of quasiparticle fluctuations of the system, and the entanglement entropy measures the maximal quasiparticle fluctuations on the EB. As a consequence, entanglement entropy corresponds to the thermal entropy of the quasipa…
We report distinct nonanalytic signatures in the spin-orbit entanglement of a 2D electron gas with Rashba interactions at integer values of the filling factor and at certain level crossings. The accompanying sharp changes in the bulk spin-orbit entanglement entropy can be probed by measuring the fluctuation in the transverse spin polarization of the electron gas.
Quantum fluctuations of local quantities can be a direct signature of entanglement in an extended quantum many-body system. Hence they may serve as a theoretical (as well as an experimental) tool to detect the spatial properties of the entanglement entropy of a subsystem. In the ground state of quantum many-body systems, its scaling is typically linear in the boundary of the subsystem (area law). Here we propose a microscopic insight into the spatial structure of entanglement and fluctuations using the concept of \emph{contour}, recently introduced to decompose the bipartite entanglement entro…
We apply the Wigner formalism of quantum optics to study the role of the zeropoint field fluctuations in entanglement swapping produced via parametric down conversion. It is shown that the generation of mode entanglement between two initially non interacting photons is related to the quadruple correlation properties of the electromagnetic field, through the stochastic properties of the vacuum. The relationship between the process of transferring entanglement and the different zeropoint inputs at the nonlinear crystal and the Bell-state analyser is emphasized.
We study entanglement between the spin components of the Bardeen-Cooper-Schrieffer (BCS) ground state by calculating the full entanglement spectrum and the corresponding von Neumann entanglement entropy. The entanglement spectrum is effectively modeled by a generalized Gibbs ensemble (GGE) of non-interacting electrons, which may be approximated by a canonical ensemble at the BCS critical temperature. We further demonstrate that the entanglement entropy is jointly proportional to the pairing energy and to the number of electrons about the Fermi surface (an area law). Furthermore, the entangleme…
We derive exact relations between the Renyi entanglement entropies and the particle number fluctuations of spatial connected regions in systems of N noninteracting fermions in arbitrary dimension. We prove that the asymptotic large-N behavior of the entanglement entropies is proportional to the variance of the particle number. We also consider 1D Fermi gases with a localized impurity, where all particle cumulants contribute to the asymptotic large-N behavior of the entanglement entropies. The particle cumulant expansion turns out to be convergent for all integer-order Renyi entropies (except f…
Entanglement harvesting from the quantum field is a well-known fact that, in recent times, is being rigorously investigated further in flat and different curved backgrounds. The usually understood formulation studies the possibility of two uncorrelated Unruh-DeWitt detectors getting entangled over time due to the effects of quantum vacuum fluctuations. Our current work presents a thorough formulation to realize the entanglement harvesting from non-vacuum background fluctuations. In particular, we further consider single excitation field states and a pair of inertial detectors, respectively, in…
We consider two non-interacting infinite quantum spin chains immersed in a common thermal environment and undergoing a local dissipative dynamics of Lindblad type. We study the time evolution of collective mesoscopic quantum spin fluctuations that, unlike macroscopic mean-field observables, retain a quantum character in the thermodynamical limit. We show that the microscopic dissipative dynamics is able to entangle these mesoscopic degrees of freedom, through a purely mixing mechanism. Further, the behaviour of the dissipatively generated quantum correlations between the two chains is studied …
We investigate entanglement dynamics for two atoms coupling with fluctuating electromagnetic field in the cosmic string spacetime. We calculate the entanglement for different conditions. It is found that the entanglement behaviors are dependent on vacuum fluctuation, spacetime topology, two-atom separation and atomic polarization orientation. After a long time of evolution, entanglement would vanish, which means entanglement affected by electromagnetic fluctuation can not maintain for a long time. For different spacetime topologies, entanglement presents different behaviors dependent on variou…
We present a fully quantum mechanical treatment of the nondegenerate optical parametric oscillator both below and near threshold. This is a non-equilibrium quantum system with a critical point phase-transition, that is also known to exhibit strong yet easily observed squeezing and quantum entanglement. Our treatment makes use of the positive P-representation and goes beyond the usual linearized theory. We compare our analytical results with numerical simulations and find excellent agreement. We also carry out a detailed comparison of our results with those obtained from stochastic electrodynam…
Recent theoretical and experiments have explored the use of entangled photons as a spectroscopic probe of material systems. We develop here a theoretical description for entropy production in the scattering of an entangled biphoton state within an optical cavity. We develop this using perturbation theory by expanding the biphoton scattering matrix in terms of single-photon terms in which we introduce the photon-photon interaction via a complex coupling constant, $ξ$. We show that the von Neumann entropy provides a succinct measure of this interaction. We then develop a microscopic model and sh…
Sympathetic laser cooling of a single mode graphene membrane coupled to an atomic cloud interacting via Casimir-Polder forces has been recently proposed. Here, we extend this study to the effect of secondary graphene membrane whose frequency may be far or close to resonance. We show that if the two mechanical modes are close together, it is possible to simultaneously cool both modes. Conversely, if the two frequencies are set far apart, the secondary mode does not affect the cooling of the first one. We also study the entanglement properties of the steady-state using the logarithmic negativity…
Quantum entanglement as the one of the most general quantum resources, can be quantified by von Neumann entropy. However, as we know, the von Neumann entropy is only statistical quantity or operator, it therefore has fluctuation. The quantum fluctuation of entanglement (QFE) between Unruh-Dewitt detector modeled by a two-level atom is investigated in a relativistic setting. The Unruh radiation and quantum fluctuation effects affect the precise measurement of quantum entanglement. Inspired by this we present how the relativistic motion effects QFE for two entangled Unruh-Dewitt detectors when o…
Entanglement-enhanced fluctuation-free daemonic ergotropy with random measurements
TCG CREST；Seoul National University（首尔大学）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute（哈里斯-钱德拉研究所，霍米·巴巴国立学院成员机构）；Slovak Academy of Sciences（斯洛伐克科学院）
The block entanglement entropy and fluctuations are investigated in one dimension in finite size correlated electron systems using the Gutzwiller wave function as a prototype correlated electron state. Entanglement entropy shows logarithmic divergence for all values of the correlation projection parameter $g$, as predicted by conformal field theories for critical systems, but the central charge requires finite size corrections. There is an infinite correlation length corresponding to correlation between same kinds of spins, for all values of $g$. A scaling form for the block entropy, as a func…
Pairs of pseudoscalar neutral mesons from decays of vector resonances are studied as bipartite systems in the framework of density operator. Time-dependent quantum entanglement is quantified in terms of the entanglement entropy and these dependences are demonstrated on data on correlated pairs of K and B mesons, as measured by the KLOE and Belle experiments . Another interesting characteristics of such bipartite systems are moments of the CP distributions. These moments are directly measurable and they appear to be very sensitive to the initial degree of entanglement of a pair.
I revisit Jordan's derivation of Einstein's formula for energy fluctuations in the black body in thermal equilibrium. This formula is usually taken to represent the unification of the wave and the particle aspects of the electromagnetic field since the fluctuations can be shown to be the sum of wave-like and particle-like contributions. However, in Jordan's treatment there is no mention of the Planck distribution and all averages are performed with respect to pure number states of radiation (mixed states had not yet been discovered!). The chief reason why Jordan does reproduce Einstein's resul…
We investigate quantum entanglement of a scalar field in the inflationary universe. By introducing a bipartite system using a lattice model of scalar field, we apply the separability criterion based on the partial transpose operation and numerically calculate the bipartite entanglement between separate spatial regions. We find that the initial entangled state becomes separable or dis-entangled when the size of the spatial regions exceed the Hubble horizon. This is necessary condition for the appearance of classicality of the quantum fluctuation. We further investigate the condition for the app…
We investigate, in the framework of open quantum systems, the entanglement dynamics of two circularly accelerated two-level atoms with the same centripetal acceleration interacting with a bath of fluctuating electromagnetic fields in the Minkowski vacuum. We assume that the two atoms rotate synchronically with their separation perpendicular to the rotating plane, and study the entanglement degradation, creation, revival, and enhancement by solving the Markovian master equation. In contrast to the scalar-field case, the entanglement dynamics is crucially dependent on the atomic polarizations in…
The measurement of quantum entanglement in many-body systems remains challenging. One experimentally relevant fact about quantum entanglement is that in systems whose degrees of freedom map to free fermions with conserved total particle number, exact relations hold relating the Full Counting Statistics associated with the bipartite charge fluctuations and the sequence of R\' enyi entropies. We draw a correspondence between the bipartite charge fluctuations and the entanglement spectrum, mediated by the R\' enyi entropies. In the case of the integer quantum Hall effect, we show that it is possi…
The aim of this work is to study the entanglement harvesting between two graphene layers inside a planar microcavity. Applying time-dependent perturbation theory it is shown that nonclassical correlations between electrons in different layers are obtained through the exchange of virtual photons. Considering different initial states of the electrons and the vacuum state of the electromagnetic field, the negativity measure that quantifies the entanglement is computed through the photon propagator for time scales smaller than the light-crossing time of the double layer. The results are compared w…
We analyze the possible quantum correlations between two coupled dimer systems in the presence of independent losses and driven by a fluctuating field. For the case of the interaction being of a Heisenberg exchange type, we first analytically show the possibility for robust stationary entanglement for realistic values of the dissipation rates and then analyze its robustness as a function of the noise to signal ratio of the pump. We find that for a common fluctuating driving field, a stochastic resonance effect appears as function of the ratio between field strength and noise strength. The effe…
We study a (1+1)-dimensional quantum circuit consisting of Haar-random unitary gates and projective measurements that conserve a total $U(1)$ charge and thus have $U(1)$ symmetry. In addition to a measurement-induced entanglement transition between a volume-law and an area-law entangled phase, we find a phase transition between two phases characterized by bipartite charge fluctuation growing with the subsystem size or staying constant. At this charge-fluctuation transition, steady-state quantities obtained by evolving an initial state with a definitive total charge exhibit critical scaling beh…
The radiation pressure induced coupling between an optical cavity field and a mechanical oscillator can create entanglement between them. In previous works this entanglement was treated as that of the quantum fluctuations of the cavity and mechanical modes around their classical mean values. Here we provide a fully quantum approach to optomechanical entanglement, which goes beyond the approximation of classical mean motion plus quantum fluctuation, and applies to arbitrary cavity drive. We illustrate the real-time evolution of optomechanical entanglement under drive of arbitrary detuning to sh…
We investigate the entanglement dynamics of two uniformly accelerated atoms with the same acceleration perpendicular to their separation. The two-atom system is treated as an open system coupled with fluctuating electromagnetic fields in the Minkowski vacuum, and in the Born-Markov approximation the master equation that describes the completely positive time evolution of the two-atom system is derived. In particular, we investigate the phenomena of entanglement degradation, generation, revival and enhancement. As opposed to the scalar-field case, the entanglement dynamics is crucially dependen…
The intrinsic fluctuations of the underlying, immutable quantum fields that fill all space and time can support the element of reality of a wave function in quantum mechanics. The mysterious non-locality of quantum entanglement may also be understood in terms of these inherent quantum fluctuations, ever-present at the most fundamental level of the universe.
We consider the ground state of simple quantum systems coupled to an environment. In general the system is entangled with its environment. As a consequence, even at zero temperature, the energy of the system is not sharp: a projective measurement can find the system in an excited state. We show that energy fluctuation measurements at zero temperature provide entanglement information. For two-state systems which exhibit a persistent current in the ground state, energy fluctuations and persistent current fluctuations are closely related. The harmonic oscillator serves to illustrate energy fluctu…
We investigate in detail the behavior of the bipartite fluctuations of particle number $\hat{N}$ and spin $\hat{S}^z$ in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and Full Counting Statistics have been used in mesoscopic transport and cold atomic gases. For systems that can be mapped to a problem of non-in…
A completely quantum description of Raman process is used to investigate the nonclassical properties of the modes in the stimulated, spontaneous and partially spontaneous Raman process. Both coherent scattering (where all the initial modes are coherent) and chaotic scattering (where initial phonon mode is chaotic and all the other modes are coherent) are studied. Nonclassical character of Raman process is observed by means of intermodal entanglement, single mode and intermodal squeezing of vacuum fluctuations, sub-shot noise and wave variances. Joint photon-phonon number and integrated-intensi…
The effects of an intracavity photonic crystal in a multimode optical parametric oscillator are studied, with a special focus on quantum fluctuations. The capability to either stimulate or inhibit the spatial instability, lowering or increasing the parametric threshold, allows to control the intensity fluctuations and correlations. A significative quantum noise reduction and an increase of the range of squeezed quadratures are found above threshold where spatial Einstein-Podolsky-Rosen entanglement and inseparability are found.
The flavor evolution of neutrinos in environments with large neutrino number densities is an open problem at the nexus of astrophysics and neutrino flavor physics. Among the many unanswered questions pertaining to this problem, it remains to be determined whether neutrino-neutrino coherent scattering can give rise to nontrivial quantum entanglement among neutrinos, and whether this can affect the flavor evolution in a meaningful way. To gain further insight into this question, here we study a simple system of two interacting neutrino beams, and obtain the exact phase-space explored by this sys…
There should be quantum vacuum fluctuations of spacetime itself, if we accept that the basic quantum principles we are already familiar with apply as well to a quantum theory of gravity. In this paper, we study, in linearized quantum gravity, the quantum entanglement generation at the neighborhood of the initial time between two independent gravitationally polarizable two-level subsystems caused by fluctuating quantum vacuum gravitational fields in the framework of open quantum systems. A bath of fluctuating quantum vacuum gravitational fields serves as an environment that provides indirect in…
