An isolated spin system that is in internal thermodynamic equilibrium and that has an upper limit to its allowed energy states can possess a negative temperature. We calculate the thermodynamic characteristics and the concurrence in this system over the entire range of positive and negative temperatures. Our calculation was performed for different real structures, which can be used in experiments. It is found that the temperature dependence of the concurrence is substantially asymmetrical similarly other thermodynamic characteristics. At a negative temperature the maximum concurrence and the absolute temperature of the entanglement appearance are sufficiently larger than those at a positive temperature. The concurrence can be characterized by two dimensionless parameters: by the ratio between the Zeeman and dipolar energies and by the ratio of the thermal and dipolar energies. It was shown that for all considered structures the dimensionless temperatures of the transition between entanglement and separability of the first and second spins are independent of spin structure and number of spins.
We define a negative entanglement measure for separable states which shows that how much entanglement one should compensate the unentangled state at least for changing it into an entangled state. For two-qubit systems and some special classes of states in higher-dimensional systems, the explicit formula and the lower bounds for the negative entanglement measure have been presented, and it always vanishes for bipartite separable pure states. The negative entanglement measure can be used as a useful quantity to describe the entanglement dynamics and the quantum phase transition. In the transvers…
In this paper, we extract from concurrence its variable part, denoted $Λ$, and use $Λ$ as a time-dependent measure of "distance", either postive or negative, from the separability boundary. We use it to investigate entanglement dynamics of two isolated but initially entangled qubits, each coupled to its own environment.
Bound entanglement with a nonpositive partial transposition (NPT) does not exist. For any NPT entangled state a distillation procedure can be based on a certain number of copies. This number is the minimal Schmidt rank of a pure state needed to witness the NPT entanglement under study.
A dipolar coupled spin system can achieve internal thermodynamic equilibrium states at negative absolute temperature. We study analytically and numerically the temperature dependence of the concurrence in a dipolar coupled spin-1/2 system in both non-zero and zero fields and show that, at negative temperatures, entangled states can exist even in zero magnetic field.
In this Letter, we show that the fulfillment of uncertainty relations is a sufficient criterion for a quantum-mechanically permissible state. We specifically construct two pseudo-spin observables for an arbitrary non-positive Hermitian matrix whose uncertainty relation is violated. This method enables us to systematically derive separability conditions for all negative partial-transpose states in experimentally accessible forms. In particular, generalized entanglement criteria are derived from the Schrodinger-Robertson inequalities for bipartite continuous-variable states.
The generation of entangled states that display negative values of the Wigner function in the quantum phase space is a challenging task, particularly elusive for massive, and possibly macroscopic, systems such as mechanical resonators. In this work, we propose two schemes based on reservoir engineering for generating Wigner-negative entangled states unconditionally. We consider two non-interacting mechanical resonators that are radiation-pressure coupled to either one or two common cavity fields; the optomechanical coupling with the field(s) features both a linear and quadratic part in the mec…
Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one may reconstruct such quasi-propabilities from experimental data. Because of ambiguity, the quasi-probabilities obtained by the bare reconstruction are insufficient to identify entanglement. An optimization procedure is introduced to derive quasi-probabilities with a minimal amount of negativity. Negativities of optimized quasi-probabilities unambiguously pr…
We review the geometric features of negative conditional entropy and the properties of the conditional amplitude operator proposed by Cerf and Adami for two qubit states in comparison with entanglement and nonlocality of the states. We identify the region of negative conditional entropy in the tetrahedron of locally maximally mixed two-qubit states. Within this set of states, negative conditional entropy implies nonlocality and entanglement, but not vice versa, and we show that the Cerf-Adami conditional amplitude operator provides an entanglement witness equivalent to the Peres-Horodecki crit…
We establish a characterization of multi-qubit entanglement constraints in terms of non-negative power of entanglement measures based on unified-$(q,s)$ entropy. Using the Hamming weight of the binary vector related with the distribution of subsystems, we establish a class of tight monogamy inequalities of multi-qubit entanglement based on the $α$th-power of unified-$(q,s)$ entanglement for $α\geq 1$. For $0 \leq β\leq 1$, we establish a class of tight polygamy inequalities of multi-qubit entanglement in terms of the $β$th-power of unified-$(q,s)$ entanglement of assistance. Thus our results c…
Detecting bipartite entanglement with PnCP maps and non-negative polynomials
Sorbonne Université（索邦大学）；ICFO-Institut de Ciencies Fotoniques（光子科学研究所）；Thales SIX GTS France（泰雷兹 SIX GTS 法国）；CRAN,Université de Lorraine, CNRS（洛林大学、南锡国立高等理工学院）
We investigate the nonclassicality of photon-added coherent states in the photon loss channel by exploring the entanglement potential and negative Wigner distribution. The total negative probability defined by the absolute value of the integral of the Wigner function over the negative distribution region reduces with the increase of decay time. The total negative probability and the entanglement potential of pure photon-added coherent states exhibit the similar dependence on the beam intensity. The reduce of the total negative probability is consistent with the behavior of entanglement potenti…
We propose experimental methods to engineer reservoirs at arbitrary temperature which are feasible with current technology. Our results generalize to mixed states the possibility of quantum state engineering through controlled decoherence. Finite temperature engineered reservoirs can lead to the experimental observation of thermal entanglement --the appearance and increase of entanglement with temperature-- to the study of the dependence of finite time disentanglement and revival with temperature, quantum thermodynamical effects, among many other applications, enlarging the comprehension of te…
Spin collective phenomena including superradiance are even today being intensively investigated with experimental tests performed based on state-of-the-art quantum technologies. Such attempts are not only for the simple experimental verification of predictions from the last century but also as a motivation to explore new applications of spin collective phenomena and the coherent control of the coupling between spin ensembles and reservoirs. In this paper, we investigate the open quantum dynamics of two spin ensembles (double spin domains) coupled to a common bosonic reservoir. We analyze in de…
We develop a thermodynamical theory to describe the behavior of the entanglement between a single two-level atom with a single mode of the electromagnetic field. The resonant Jaynes-Cummings model is used to study both the entanglement thermodynamics, in particular the entanglement temperature, and its connection with the average number of photons in the optical cavity. We find that this entanglement temperature has a strong dependence with the initial conditions of the atom. We show that the entanglement temperature between the photons and the atom defined in this work is the same temperature…
We present arguments to the effect that time and temperature can be viewed as a form of quantum entanglement. Furthermore, if temperature is thought of as arising from the quantum mechanical tunneling probability this then offers us a way of dynamically "converting" time into temperature based on the entanglement between the transmitted and reflected modes. We then show how similar entanglement-based logic can be applied to the dynamics of cosmological inflation and discuss the possibility of having observable effects of the early gravitational entanglement at the level of the universe.
We study thermal entanglement in some low-dimensional Heisenberg models. It is found that in each model there is a critical temperature above which thermal entanglement is absent.
In this work the degree of entanglement of two-photon states generated by parametric-down conversion with a phase mismatch is computed in terms of the temperature of the nonlinear medium where the interaction takes place. The minimum interaction time, named {\it birth time of entanglement}, needed before entanglement is attained, is computed in terms of the temperature and of the phase mismatch. Our results show that, for each value of the phase mismatch, there is a critical temperature above which entanglement disappears. We are able to identify the regions of parameters, temperature and mism…
We study the dynamics of two two-level atoms embedded near to the interface of paired meta-material slabs, one of negative permeability and the other of negative permittivity. The interface behaves as a plasmonic waveguide composed of surface-plasmon polariton modes. It is found that significantly different dynamics occur for the resonant and an off-resonant couplings of the plasma field to the atoms. In the case of the resonant coupling, the plasma field does not appear as a dissipative reservoir to the atoms. We adopt the image method and show that the dynamics of the two atoms are completel…
We examine the entanglement of general mixed states of a two qubit Heisenberg XYZ chain in the presence of a magnetic field, and its detection by means of different criteria. Both the exact separability conditions and the weaker conditions implied by the disorder and the von Neumann entropic criteria are analyzed. The ensuing limit temperatures for entanglement in thermal states of different XYZ models are then examined and compared with the limit temperature of the symmetry-breaking solution in a mean field type approximation. The latter, though generally lower, can also be higher than the ex…
A potential experimental system, based on the Silicon Nitride (SiN) material, is proposed to generate steady-state room-temperature optomechanical entanglement. In the proposed structure, the nanostring interacts dispersively and reactively with the microdisk cavity via the evanescent field. We study the role of both dispersive and reactive coupling in generating optomechanical entanglement, and show that the room-temperature entanglement can be effectively obtained through the dispersive couplings within the reasonable experimental parameters. In particular, we find, in the high Temperature (…
The dynamics evolutions of discord and entanglement of two atoms in two independent Lorentzian reservoirs at zero or finite temperature have been investigated by using the time-convolutionless master-equation method. Our results show that, when both the non-Markovian effect and the detuning are present simultaneously, due to the memory and feedback effect of the non-Markovian reservoirs, the discord and the entanglement can be effectively protected even at nonzero temperature by increasing the non-Markovian effect and the detuning. The discord and the entanglement have different robustness for…
We investigate the emerging properties of quantum walks with temporal disorder engineered from a binary Markov chain with tailored correlation, $C$, and disorder strength, $r$. We show that when the disorder is weak -- $r \ll 1$ -- the introduction of negative correlation leads to a counter-intuitive higher production of spin-lattice entanglement entropy, $S_e$, than the setting with positive correlation, that is $S_e(-|C|)>S_e(|C|)$. These results show that negatively correlated disorder plays a more important role in quantum entanglement than it has been assumed in the literature.
We compare the entanglement of formation with a measure defined as the modulus of the negative eigenvalue of the partial transpose. In particular, we investigate whether both measures give the same ordering of density operators with respect to the amount of entanglement.
In this paper we consider the decay of quantum entanglement, quantified by the concurrence, of a pair of two-level systems each of which is interacting with a reservoir at finite temperature T. For a broad class of initially entangled states, we demonstrate that the system always becomes disentangled in a finite time i.e."entanglement sudden death" (ESD) occurs. This class includes all states which previously had been found to have long-lived entanglement in zero temperature reservoirs. Our general result is illustrated by an example.
We calculate the entanglement between two spins in the ferromagnetic Heisenberg chain at low temperatures, and show that when only the ground state and the one particle states are populated, the entanglement profile is a gaussian with a characteristic length depending on the temperature and the coupling between spins. The magnetic field only affects the amplitude of the profile and not its characteristic length.
We propose a scheme for creating of a maximally entangled state comprising two field quanta. In our scheme, two weak light fields, which are initially prepared in either coherent or polarization states, interact with a composite medium near an interface between a dielectric and a negative index metamaterial. Such interaction leads to a large Kerr nonlinearity, reduction of the group velocity of the light and significant confinement of the light fields while simultaneously avoiding amplitude losses of the incoming radiation. All these considerations make our scheme efficient.
We present a quantum information theory that allows for the consistent description of quantum entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices, rather than probability distributions, for the description of quantum ensembles. We find that, unlike in Shannon theory, conditional entropies can be negative when considering quantum entangled systems such as an Einstein-Podolsky-Rosen pair, which leads to a violation of well-known bounds of classical information theory. Negative quantum entropy can be traced back to ``conditional'' density ma…
Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized, but these states display Gaussian spin distribution functions with a non-negative Wigner function. Non-Gaussian entangled states have been produced in small ensembles of ions, and very recently in large atomic ensembles. Here, we generate entanglement in a large atomic ensemble via the interaction with a very weak laser pulse; remarkably, the detec…
We investigate the end-to-end entanglement of a general XYZ-spin chain at the non-zero temperatures. The entanglement usually vanishes at a certain critical temperature $T_c$, but external fields can make $T_c$ higher. We obtain a general statement on the increase of the critical temperature $T_c$ by the external fields. We prove that if the two end spins are separated by two spins or more, the critical temperature cannot be higher than a certain finite temperature $bar{T}_c$ ($T_c le bar{T}_c$), that is, the entanglement must vanish above the temperature $bar{T}_c$ for any values of the exter…
We study spin squeezing, negative correlations, and concurrence in the quantum kicked top model. We prove that the spin squeezing and negative correlations are equivalent for spin systems with only symmetric Dicke states populated. We numerically analyze spin squeezing parameters and concurrence in this model, and find that the maximal spin squeezing direction, which refers to the minimal pairwise correlation direction, is strongly influenced by quantum chaos. Entanglement (spin squeezing) sudden death and sudden birth occur alternatively for the periodic and quasi-periodic cases, while only e…
In the present work, we investigate the quantum thermal entanglement in molecular magnets composed of dimers of spin $S$, using an Entanglement Witness built from measurements of magnetic susceptibility. An entanglement temperature, $T_{e}$, is then obtained for some values of spin $S$. From this, it is shown that $T_{e}$ is proportional to the intradimer exchange interaction $J$ and that entanglement appears only for antiferromagnetic coupling. The results are compared to experiments carried on three isostructural materials: KNaMSi$_{4}$O$_{10}$ (M$=$Mn, Fe or Cu).
In composed quantum systems, the presence of local dissipative channels causes loss of coherence and entanglement at a rate that grows with the temperature of the reservoirs. However, here we show that if temperature is artificially added to the system, entanglement decay can be significantly slowed down or even suppressed conditioned on suitable local monitoring of the reservoirs. We propose a scheme to implement the joint reservoir monitoring applicable in different experimental setups like trapped ions, circuit and cavity QED or quantum dots coupled to nanowires and we analyze its general r…
Local hidden variables theories didn't succeed to explain the correlations revealed by entanglements. It is obvious that the explanation of the correlations stands in non-local effects, but nobody has ever detected any carriers that travel with superluminal velocity s.t. they could candidate for some superluminal connection between distant particles, in order to adjust the results to the correlations. This text explains that the role of creating the correlations is played by what is called here the "Negative". This is the part that was removed from the wave function of the independent particle…
Performances of the symmetric universal and phase-covariant cloning transformations and entanglement cloners -- qubit case -- are investigated when the initial state of the hardware or the original state to be cloned is weakly coupled to a thermal environment. Different behaviors of each of these transformations are analyzed and contrasted with the ideal cases.
In the present paper we study the entanglement properties of thermal (a.k.a. Gibbs) states of quantum harmonic oscillator systems as functions of the Hamiltonian and the temperature. We prove the physical intuition that at sufficiently high temperatures the thermal state becomes fully separable and we deduce bounds on the critical temperature at which this happens. We show that the bound becomes tight for a wide class of Hamiltonians with sufficient translation symmetry. We find, that at the crossover the thermal energy is of the order of the energy of the strongest normal mode of the system a…
Stationary entanglement in a four-mode optomechanical system, especially under roomtemperature, is discussed. In this scheme, when the coupling strengths between the two target modes and the mechanical resonator are equal, the results cannot be explained by the Bogoliubov mode- based scheme. This is related to the idea of quantum-mechanics-free subspace, which plays an important role when the thermal noise of the mechanical modes is considered. Significantly prominent steady-state entanglement can be available under room-temperature.
We study the robustness of multipartite entanglement of the ground state of the one-dimensional spin 1/2 XY model with a transverse magnetic field in the presence of thermal excitations, by investigating a threshold temperature, below which the thermal state is guaranteed to be entangled. We obtain the threshold temperature based on the geometric measure of entanglement of the ground state. The threshold temperature reflects three characteristic lines in the phase diagram of the correlation function. Our approach reveals a region where multipartite entanglement at zero temperature is high but …
We analyze the quantum entanglement at the equilibrium in a class of exactly solvable one-dimensional spin models at finite temperatures and identify a region where the quantum fluctuations determine the behavior of the system. We probe the response of the system in this region by studying the spin dynamics after projective measurement of one local spin which leads to the appearance of the ``decoherence wave''. We investigate time-dependent spin correlation functions, the entanglement dynamics, and the fidelity of the quantum information transfer after the measurement.
In this paper I intend to show that macroscopic entanglement is possible at high temperatures. I analyze multipartite entanglement produced by the $η$ pairing mechanism which features strongly in the fermionic lattice models of high $T_c$ superconductivity. This problem is shown to be equivalent to calculating multipartite entanglement in totally symmetric states of qubits. I demonstrate that we can conclusively calculate the relative entropy of entanglement within any subset of qubits in an overall symmetric state. Three main results then follow. First, I show that the condition for supercond…
We study different architectures for a photonic crystal in the microwave regime based on superconducting transmission lines interrupted by Josephson junctions, both in one and two dimensions. A study of the scattering properties of a single junction in the line shows that the junction behaves as a perfect mirror when the photon frequency matches the Josephson plasma frequency. We generalize our calculations to periodic arrangements of junctions, demonstrating that they can be used for tunable band engineering, forming what we call a quantum circuit crystal. Two applications are discussed in de…
We use multiple quantum (MQ) NMR dynamics of a gas of spin-carrying molecules in nanocavities at high and low temperatures for an investigation of many-particle entanglement. A distribution of MQ NMR intensities is obtained at high and low temperatures in a system of 201 spins 1/2. The second moment of the distribution, which provides a lower bound on the quantum Fisher information, sheds light on the many-particle entanglement in the system. The dependence of the many-particle entanglement on the temperature is investigated. Almost all spins are entangled at low temperatures.
Both direct and indirect weak nonresonant interactions are shown to produce entanglement between two initially disentangled systems prepared as a tensor product of thermal states, provided the initial temperature is sufficiently low. Entanglement is determined by the Peres-Horodeckii criterion, which establishes that a composite state is entangled if its partial transpose is not positive. If the initial temperature of the thermal states is higher than an upper critical value $T_{uc}$ the minimal eigenvalue of the partially transposed density matrix of the composite state remains positive in th…
The role of spin-orbit interaction on the ground state and thermal entanglement of a Heisenberg XYZ two-qubit system in the presence of an inhomogeneous magnetic field is investigated. For a certain value of spin-orbit parameter $D$, the ground state entanglement tends to vanish suddenly and when $D$ crosses its critical value $D_c$, the entanglement undergoes a revival. The maximum value of the entanglement occurs in the revival region. In finite temperatures there are revival regions in $D-T$ plane. In these regions, entanglement first increases with increasing temperature and then decreases…
We study and compare the persistence of bipartite entanglement (BE) and multipartite entanglement (ME) in one-dimensional and two-dimensional spin XY models in an external transverse magnetic field under the effect of thermal excitations. We compare the threshold temperature at which the entanglement vanishes in both types of entanglement. We use the entanglement of formation as a measure of the BE and the geometric measure to evaluate the ME of the system. We have found that in both dimensions in the anisotropic and partially anisotropic spin systems at zero temperatures, all types of entangl…
The entanglement in a general Heisenberg antiferromagnetic chain of arbitrary spin-$s$ is investigated. The entanglement is witnessed by the thermal energy which equals to the minimum energy of any separable state. There is a characteristic temperature below that an entangled thermal state exists. The characteristic temperature for thermal entanglement is increased with spin $s$. When the total number of lattice is increased, the characteristic temperature decreases and then approaches a constant. This effect shows that the thermal entanglement can be detected in a real solid state system of l…
A formula to evaluate the entanglement in an one-dimensional ferrimagnetic system is derived. Based on the formula, we find that the thermal entanglement in a small size spin-1/2 and spin-s ferrimagnetic chain is rather robust against temperature, and the threshold temperature may be arbitrarily high when s is sufficiently large. This intriguing result answers unambiguously a fundamental question: ``can entanglement and quantum behavior in physical systems survive at arbitrary high temperatures?"
We present a quantum information theory that allows for a consistent description of entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices (rather than probability distributions) for the description of quantum ensembles. We find that quantum conditional entropies can be negative for entangled systems, which leads to a violation of well-known bounds in Shannon information theory. Such a unified information-theoretic description of classical correlation and quantum entanglement clarifies the link between them: the latter can be viewed as ``sup…
Making use of the master equation and effective Hamiltonian approach, we investigate the steady state entanglement in a three-qubit $XX$ model. Both symmetric and nonsymmetric qubit-qubit couplings are considered. The system (the three qubits) is coupled to two bosonic baths at different temperatures. We calculate the steady state by the effective Hamiltonian approach and discuss the dependence of the steady state entanglement on the temperatures and couplings. The results show that for symmetric qubit-qubit couplings, the entanglements between the nearest neighbor are equal, independent of th…
The non-Markovia dynamics of quantum evolution plays an important role in open quantum sytem. However, how to quantify non-Markovian behavior and what can be obtained from non- Markovianity are still open questions, especially in complex solid systems. Here we address the problem of quantifying non-Markovianity with entanglement in a genuine noisy solid state system at room temperature. We observed the non-Markovianity of quantum evolution with entanglement. By prolonging entanglement with dynamical decoupling, we can reveal the non-Markovianity usually concealed in the environment and obtain …
We show the existence of an entangled nonequilibrium state at very high temperatures when two linearly coupled harmonic oscillators are parametrically driven and dissipate into two independent heat baths. This result has a twofold meaning: first, it fundamentally shifts the classical-quantum border to temperatures as high as our experimental ability allows us, and second, it can help increase by at least one order of magnitude the temperature at which current experimental setups are operated.
Entanglement is the central yet fleeting phenomena of quantum physics. Once being considered a peculiar counter-intuitive property of quantum theory it has developed into the most central element of quantum technology providing speed up to quantum computers, a path towards long distance quantum cryptography and increased sensitivity in quantum metrology. Consequently, there have been a number of experimental demonstration of entanglement between photons, atoms, ions as well as solid state systems like spins or quantum dots, superconducting circuits and macroscopic diamond. Here we experimental…
In the present work we show that a special family of materials, the metal carboxylates, may have entangled states up to very high temperatures. From magnetic susceptibility measurements, we have estimated the critical temperature below which entanglement exists in the cooper carboxylate \{Cu$_2$(O$_2$CH)$_4$\}\{Cu(O$_2$CH)$_2$(2-methylpyridine)$_2$\}, and we have found this to be above room temperature ($T_e \sim 630$ K). Furthermore, the results show that the system remains maximally entangled until close to $\sim 100$ K and the Bell's inequality is violated up to nearly room temperature ($\s…
Equilibrium states of infinite extended lattice systems at high temperature are studied with respect to their entanglement. Two notions of separability are offered. They coincide for finite systems but differ for infinitely extended ones. It is shown that for lattice systems with localized interaction for high enough temperature there exists no local entanglement. Even more quasifree states at high temperature are also not distillably entangled for all local regions of arbitrary size. For continuous systems entanglement survives for all temperatures. In mean field theories it is possible, that…
The dynamics of a simple spin chain (2 spins) coupled to bosonic baths at different temperatures is studied. The analytical solution for the reduced density matrix of the system is found. The dynamics and temperature dependence of spin-spin entanglement is analyzed. It is shown that the system converges to a steady-state. If the energy levels of the two spins are different, the steady-state concurrence assumes its maximum at unequal bath temperatures. It is found that a difference in local energy levels can make the steady-state entanglement more stable against high temperatures.
We consider a system of two iso-spectral bosonic modes coupled with a single two-level systems i.e., a qubit. The dynamics is described by a mode-symmetric two-modes Jaynes-Cummings. The entanglement, induced between the two bosonic modes, is analyzed and quantified by negativity. We computed the time evolution of negativity starting from an initial thermal state of the bosonic sector for both zero and finite temperature. We also studied the entangling power of the interaction as a function of mode-qubit detuning and its resilience against temperature increase. Finally a two-qubit gates based …
We show that macroscopic thermodynamical properties - such as functions of internal energy and magnetization - can detect quantum entanglement in solids at nonzero temperatures in the thermodynamical limit. We identify the parameter regions (critical values of magnetic field and temperature) within which entanglement is witnessed by these thermodynamical quantities.
