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 fluctuations in a system with an infinite number of states. In addition to the energy distribution we discuss the energy-energy time-correlation function in the zero-temperature limit.
We show how many-body ground state entanglement information may be extracted from sub-system energy measurements at zero temperature. Generically, the larger the measured energy fluctuations are, the larger the entanglement is. Examples are given with the two-state system and the harmonic oscillator. Comparisons made with recent qubit experiments show this type of measurement provides another method to quantify entanglement with the environment.
We show how many-body ground state entanglement information may be extracted from sub-system energy measurements at zero temperature. A precise relation between entanglement and energy fluctuations is demonstrated in the weak coupling limit. Examples are given with the two-state system and the harmonic oscillator, and energy probability distributions are calculated. Comparisons made with recent qubit experiments show this type of measurement provides another method to quantify entanglement with the environment.
Producing and certifying entanglement between distant qubits is a highly desirable skill for quantum information technologies. Here we propose a new strategy to monitor and characterize entanglement genesis in a half parity measurement setup, that relies on the continuous readout of an energetic observable which is the half-parity observable itself. Based on a quantum-trajectory approach, we theoretically analyze the statistics of energetic fluctuations for a pair of continuously monitored qubits. We quantitatively relate these energetic fluctuations to the rate of entanglement produced betwee…
An Energetic Constraint for Qubit-Qubit Entanglement
MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Laboratory（MajuLab，CNRS-UCA-SU-NUS-NTU国际联合研究实验室）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Université Paris-Saclay, Centre de Nanosciences et de Nanotechnologies, CNRS（巴黎萨克雷大学，纳米科学与技术中心，CNRS）；Université de Lorraine, CNRS, LPCT（洛林大学，CNRS，LPCT）
Although entropy is a necessary and sufficient quantity to characterize the order of work content for equal energetic (EE) states in the asymptotic limit, for the finite quantum systems, the relation is not so linear and requires detail investigation. Toward this, we have considered a resource theoretic framework taking the energy preserving operations (EPO) as free, to compare the amount of extractable work from two different quantum states. Under EPO, majorization becomes a necessary criterion for state transformation. It is also shown that the passive state energy is a concave function and …
Bipartite entanglement entropies are calculated for the ground state of the two-excitation subspace in a two-site coupled cavity model. Each region in the phase diagram (atomic insulator, polaritonic insulator, photonic superfluid, and polaritonic superfluid) is found to be characterized by unique entanglement properties. In particular, the polaritonic superfluid region exhibits multipartite entanglement among the two atoms and two cavity fields. This system provides a toy model in which a number of intriguing aspects of entanglement can be studied, such as the relationship of entanglement to …
We study the entanglement of thermal and ground states in Heisernberg $XX$ qubit rings with a magnetic field. A general result is found that for even-number rings pairwise entanglement between nearest-neighbor qubits is independent on both the sign of exchange interaction constants and the sign of magnetic fields. As an example we study the entanglement in the four-qubit model and find that the ground state of this model without magnetic fields is shown to be a four-body maximally entangled state measured by the $N$-tangle.
We analytically evaluate the entanglement spectra of the superconductivity states in graphene, primarily focusing on the s-wave and chiral $ d_{x^{2}-y^{2}}+id_{xy} $ superconductivity states. We demonstrate that the topology of the entanglement Hamiltonian can differ from that of the subsystem Hamiltonian. In particular, the topological properties of the entanglement Hamiltonian of the chiral $ d_{x^{2}-y^{2}}+id_{xy} $ superconductivity state obtained by tracing out one spin direction clearly differ from those of the time-reversal invariant Hamiltonian of noninteracting fermions on the honey…
We introduce on physical grounds a new measure of multipartite entanglement for pure states. The function we define is discriminant and monotone under LOCC and moreover can be expressed in terms of observables of the system.
We study a system of qubits that are coupled to each other via only one degree of freedom represented, e.g., by $σ_z$-operators. We prove that, if by changing the Hamiltonian parameters, a non-degenerate ground state of the system is continuously transformed in such a way that the expectation values of $σ_z$ operators of at least two coupled qubits change, this ground state is entangled. Using this proof, we discuss connection between energy level anticrossings and ground state entanglement. Following the same line of thought, we introduce entanglement witnesses, based on cross-susceptibilitie…
We study the entanglement feature of the ground state of a system composed of spin 1 and 1/2 parts. The concurrence vector is shown to be consistent with the measurement of von Neumann entropy for such system. In the light of the ground state degeneracy, we suggest a average concurrence to measure the entanglement of Hilbert subspace. The entanglement property of both a general superposition as well as the mixture of the degenerate ground states are discussed by means of average concurrence and the negativity respectively.
Entanglement in the ground state of a many-body quantum system may arise when the local terms in the system Hamiltonian fail to commute with the interaction terms in the Hamiltonian. We quantify this phenomenon, demonstrating an analogy between ground-state entanglement and the phenomenon of frustration in spin systems. In particular, we prove that the amount of ground-state entanglement is bounded above by a measure of the extent to which interactions frustrate the local terms in the Hamiltonian. As a corollary, we show that the amount of ground-state entanglement is bounded above by a ratio …
We study the entanglement properties of the ground state in Kitaev's model. This is a two-dimensional spin system with a torus topology and nontrivial four-body interactions between its spins. For a generic partition $(A,B)$ of the lattice we calculate analytically the von Neumann entropy of the reduced density matrix $ρ_A$ in the ground state. We prove that the geometric entropy associated with a region $A$ is linear in the length of its boundary. Moreover, we argue that entanglement can probe the topology of the system and reveal topological order. Finally, no partition has zero entanglement…
We study Hofstadter bilayers, i.e. coupled hopping models on two-dimensional square lattices in a perpendicular magnetic field. Upon tracing out one of the layers, we find an explicit expression for the resulting entanglement spectrum in terms of the energy eigenvalues of the underlying monolayer system. For strongly coupled layers the entanglement Hamiltonian is proportional to the energetic Hamiltonian of the monolayer system. The proportionality factor, however, cannot be interpreted as the inverse thermodynamic temperature, but represents a phenomenological temperature scale. We derive an …
We consider how to generate and detect Einstein-Podolsky-Rosen (EPR) entanglement and the steering paradox between groups of atoms in two separated potential wells in a Bose-Einstein condensate (BEC). We present experimental criteria for this form of entanglement, and propose experimental strategies for detecting entanglement using two or four mode ground states. These approaches use spatial and/or internal modes. We also present higher order criteria that act as signatures to detect the multiparticle entanglement present in this system. We point out the difference between spatial entanglement…
Many-body quantum systems in the ground states have zero-point energy due to the uncertainty relation. In many cases, the system in the ground state accompanies spatially-entangled energy density fluctuation via the noncommutativity of the energy density operators, though the total energy takes a fixed value, i.e. the lowest eigenvalue of the Hamiltonian. Quantum energy teleportation (QET) is protocols for extraction of the zero-point energy out of one subsystem using information of a remote measurement of another subsystem. From an operational viewpoint of protocol users, QET can be regarded …
We have studied the symmetric and non-symmetric pairwise ground state and thermal entanglement in three-qubit anisotropic Heisenberg (XXZ) and Ising in a magnetic field models and in the presence of Dzyaloshinskii-Moriya (DM) interaction. We have found that increasing of the DM interaction and magnetic field can enhance and reduce the entanglement of system. We have shown that the non-symmetric pairwise has higher value concurrence and critical temperature (above which the entanglement vanishes) than the symmetric pairwise. For negative anisotropy the non-symmetric entanglement is a monotonic …
We examine whether it is possible for one-dimensional translationally-invariant Hamiltonians to have ground states with a high degree of entanglement. We present a family of translationally invariant Hamiltonians {H_n} for the infinite chain. The spectral gap of H_n is Omega(1/poly(n)). Moreover, for any state in the ground space of H_n and any m, there are regions of size m with entanglement entropy Omega(min{m,n}). A similar construction yields translationally-invariant Hamiltonians for finite chains that have unique ground states exhibiting high entanglement. The area law proven by Hastings…
A method of storing and retrieving quantum states of radiation fields using the ground-state coherences is discussed. We demonstrate the generation of multiparticle entangled states starting from atoms prepared in a coherent state. Use is made of the j=-1/2 to +1/2 atomic transition and its interaction with a far-detuned elliptically polarized field.
We consider a collection of bosonic modes corresponding to the vertices of a graph $Γ.$ Quantum tunneling can occur only along the edges of $Γ$ and a local self-interaction term is present. Quantum entanglement of one vertex with respect the rest of the graph is analyzed in the ground-state of the system as a function of the tunneling amplitude $τ.$ The topology of $Γ$ plays a major role in determining the tunneling amplitude $τ^*$ which leads to the maximum ground-state entanglement. Whereas in most of the cases one finds the intuitively expected result $τ^*=\infty$ we show that it there exis…
Ground state instabilities of the spin-boson model is studied in this work. The existence of sequential ground state instabilities is shown analytically for arbitrary detuning in the two-spin system. In this model, extra discontinuities of concurrence(entanglement measure) are found in the finite system, which do not appear in the on-resonant model. The above results remain intact by including extra boson modes. Moreover, by including extra modes, it is found that ground state entanglement can be obtained and enhanced even in the weak coupling regime.
The ground state entanglement entropy is studied in a many-body bipartite quantum system with either a single or multiple conserved quantities. It is shown that the entanglement entropy exhibits a universal power-law behaviour at large $R$ -- the occupancy ratio between the two subsystems. Single and multiple conserved quantities lead to different power-law exponents, suggesting the entanglement entropy can serve to detect hidden conserved quantities. Moreover, occupancy measurements allow to infer the bipartite entanglement entropy. All the above results are generalized for the Rényi entropy.
What correlations are present in the ground state of a many-body Hamiltonian? We study the relationship between ground-state correlations, especially entanglement, and the energy gap between the ground and first excited states. We prove several general inequalities which show quantitatively that ground-state correlations between systems not directly coupled by the Hamiltonian necessarily imply a small energy gap.
We investigate of the relationship between the entanglement and subsystem Hamiltonians in the perturbative regime of strong coupling between subsystems. One of the two conditions that guarantees the proportionality between these Hamiltonians obtained by using the nondegenerate perturbation theory within the first order is that the unperturbed ground state has a trivial entanglement Hamiltonian. Furthermore, we study the entanglement Hamiltonian of the Heisenberg ladders in a time-dependent magnetic field using the degenerate perturbation theory, where couplings between legs are considered as a…
Ground-state entanglement induces emergence of negative-energy-density regions in quantum systems by squeezing zero-point oscillation, keeping total energy of the systems nonnegative. By use of the negativity of quantum energy density, protocols of quantum energy teleportation are proposed that transport energy to distant sites by local operations and classical communication. The energy is teleported without breaking any physical laws including causality and local energy conservation. Because intermediate subsystems of the energy transfer channel are not excited during the protocol execution, …
In this paper we calculate the block entanglement entropies of spin models whose ground states have perfect antiferromagnetic or ferromagnetic long-range order. In the latter case the definition of entanglement entropy is extended to properly take into account the ground state degeneracy. We find in both cases the entropy grows logarithmically with the block size. Implication of our results on states with general long-range order will be discussed.
An area law is proved for the Renyi entanglement entropy of possibly degenerate ground states in one-dimensional gapped quantum systems. Suppose in a chain of $n$ spins the ground states of a local Hamiltonian with energy gap $ε$ are constant-fold degenerate. Then, the Renyi entanglement entropy $R_α(0<α<1)$ of any ground state across any cut is upper bounded by $\tilde O(α^{-3}/ε)$, and any ground state can be well approximated by a matrix product state of subpolynomial bond dimension $2^{\tilde O(ε^{-1/4}\log^{3/4}n)}$.
We compare a star and a ring network of interacting spins in terms of the entanglement they can provide between the nearest and the next to nearest neighbor spins in the ground state. We then investigate whether this entanglement can be optimized by allowing the system to interact through a weighted combination of the star and the ring geometries. We find that such a weighted combination is indeed optimal in certain circumstances for providing the highest entanglement between two chosen spins. The entanglement shows jumps and counterintuitive behavior as the relative weighting of the star and …
We consider the ground-state entanglement in highly connected many-body systems, consisting of harmonic oscillators and spin-1/2 systems. Varying their degree of connectivity, we investigate the interplay between the enhancement of entanglement, due to connections, and its frustration, due to monogamy constraints. Remarkably, we see that in many situations the degree of entanglement in a highly connected system is essentially of the same order as in a low connected one. We also identify instances in which the entanglement decreases as the degree of connectivity increases.
We study the correlation function and concurrence for the eigenstates with zero spin of engineered Heisenberg models to explore the entanglement property. It is shown that the total nearest neighbor (NN) correlation function of zero-spin eigenstates reaches its local extremum when the coupling strength is uniform, and correspondingly the groundstate entanglement of $d$-D cubic AF Heisenberg model is locally maximized. Moreover, numerical calculations for a $N$-site quantum spin ring with cosinusoidally modulated exchange coupling, i.e. $J_i=J(1+\cos(2πi/N))$, indicate that the uniform coupling…
In this paper, we investigate spin entanglement in the $XXZ$ model defined on a $d$-dimensional bipartite lattice. The concurrence, a measure of the entanglement between two spins, is analyzed. We prove rigorously that the ground state concurrence reaches maximum at the isotropic point. For dimensionality $d \ge 2$, the concurrence develops a cusp at the isotropic point and we attribute it to the existence of magnetic long-range order.
For cavity-assisted optomechanical cooling experiments, it has been shown in the literature that the cavity bandwidth needs to be smaller than the mechanical frequency in order to achieve the quantum ground state of the mechanical oscillator, which is the so-called resolved-sideband or good-cavity limit. We provide a new but physically equivalent insight into the origin of such a limit: that is information loss due to a finite cavity bandwidth. With an optimal feedback control to recover those information, we can surpass the resolved-sideband limit and achieve the quantum ground state. Interes…
We discuss the creation of many-particle entanglement in an ion trap where all ions are simultaneously coupled to bichromatic laser fields. It is shown that in a time-averaged, coarse-grained picture the system can be mapped onto a spin ensemble with controllable collective interactions. An adiabatic change of laser parameters allows a transfer from separable to entangled eigenstates of the many-particle Hamiltonian. Of particular interest is a transition in the ground state which in some cases corresponds to a quantum phase transition. The influence of decoherence mechanisms can be substantia…
We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The $E\otimesβ$ system models the coupling of a two-level electronic system, or qubit, to a single oscillator mode, while the $E\otimesε$ models the qubit coupled to two independent, degenerate oscillator modes. In the absence of a transverse magnetic field applied to the qubit, both systems exhibit a degenerate ground state. Whereas there always exists a completely separable ground state in the $E\otimesβ$ system, the ground states of the $E\otimesε$ model always exhibit entanglement. For the $E\otimesβ$ c…
We show that a singlet of many multi-level quantum systems arises naturally as the ground state of a physically-motivated Hamiltonian. The Hamiltonian simply exchanges the states of nearest-neighbours in some network of qudits (d-level systems); the results are independent of the strength of the couplings or the network's topology. We show that local measurements on some of these qudits project the unmeasured qudits onto a smaller singlet, regardless of the choice of measurement basis at each measurement. It follows that the entanglement is highly persistent, and that through local measurement…
Polarization maintenance is a key technology for free-space quantum communication. In this paper, we describe a polarization maintenance design of a transmitting antenna with an average polarization extinction ratio of 887 : 1 by a local test. We implemented a feasible polarization-compensation scheme for satellite motions that has a polarization fidelity more than 0.995. Finally, we distribute entanglement to a satellite from ground for the first time with a violation of Bell inequality by 2.312+-0.096.
We propose a mechanism of ground-state blockade between two $N$-type Rydberg atoms in virtue of Rydberg-antiblockade effect and Raman transition. Inspired by the quantum Zeno effect, the strong Rydberg antiblockade interaction plays a role in frequently measuring one ground state of two, leading to a blockade effect for double occupation of the corresponding quantum state. By encoding the logic qubits into the ground states, we efficiently avoid the spontaneous emission of the excited Rydberg state, and maintain the nonlinear Rydberg-Rydberg interaction at the same time. As applications, we di…
Using an NMR quantum computer, we experimentally simulate the quantum phase transition of a Heisenberg spin chain. The Hamiltonian is generated by a multiple pulse sequence, the nuclear spin system is prepared in its (pseudo-pure) ground state and the effective Hamiltonian varied in such a way that the Heisenberg chain is taken from a product state to an entangled state and finally to a different product state.
Using tools of quantum information theory we show that the ground state of the Dicke model exhibits an infinite sequence of instabilities (quantum-phase-like transitions). These transitions are characterized by abrupt changes of the bi-partite entanglement between atoms at critical values $κ_j$ of the atom-field coupling parameter $κ$ and are accompanied by discontinuities of the first derivative of the energy of the ground state. We show that in a weak-coupling limit ($κ_1\leq κ\leq κ_2$) the Coffman-Kundu-Wootters (CKW) inequalities are saturated which proves that for these values of the cou…
A microscopic calculation of ground state entanglement for the XY and Heisenberg models shows the emergence of universal scaling behavior at quantum phase transitions. Entanglement is thus controlled by conformal symmetry. Away from the critical point, entanglement gets saturated by a mass scale. Results borrowed from conformal field theory imply irreversibility of entanglement loss along renormalization group trajectories. Entanglement does not saturate in higher dimensions which appears to limit the success of the density matrix renormalization group technique. A possible connection between …
In this paper, we study the entanglement properties of a spin-1 model the exact ground state of which is given by a Matrix Product state. The model exhibits a critical point transition at a parameter value a=0. The longitudinal and transverse correlation lengths are known to diverge as a tends to zero. We use three different entanglement measures S(i) (the one-site von Neumann entropy), S(i,j) (the two-body entanglement) and G(2,n) (the generalized global entanglement) to determine the entanglement content of the MP ground state as the parameter a is varied. The entanglement length, associated…
The purpose of this study is to calculate the entanglement measure for a bipartite system where the two subsystems interact via a central potential, and more importantly, to analyze the conceptual implication in the case of gravitational potential. Through numerical calculation, we confirm that the ground state of such quantum system is an entangled state. This raises a question whether a quantum ground state describing masses interacting through gravity can ever be a separable state. Entanglement seems to be an intrinsic characteristic for the ground state when mutual gravitational interactio…
We study the ground state as well as the dynamics of chains of bosons with local repulsive interactions and nearest-neighbour exchange using numerical techniques based on density matrix decimation. We explore the development of entanglement between the terminal sites of such chains as mechanisms are invoked to concentrate population in these sites. We find that long-range entanglement in the ground state emerges as a result of hopping taking place at the whole chain length in systems with appropriate hopping coefficients. Additionally, we find appropriate perturbations to increase the entangle…
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 introduce a method for analyzing ground state properties of quantum many body systems, based on the characterization of separability and entanglement by single subsystem unitary operations. We apply the method to the study of the ground state structure of several interacting spin-1/2 models, described by Hamiltonians with different degrees of symmetry. We show that the approach based on single qubit unitary operations allows to introduce {\it ``entanglement excitation energies''}, a set of observables that can characterize ground state properties, including the quantification of single-site…
The pairwise entanglement and local polarization of the ground state are discussed by studying the Heisenberg XX model in finite qubit case. The results show that: the ground state is composed by the micro state with the minimal total spin 0 (for even qubit) or 1/2 (for odd qubit), local polarization (LP) has intimate relation with the probability of the micro state in the ground state, the stronger the LP the smaller the probability, the same LP corresponding to the same probability; the pairwise entanglement of the ground state is the biggest in all the eigenvectors. We find when the qubit i…
We examine particle entanglement, characterized by pseudo-spin squeezing, of spin-1 bosonic atoms with coupled ground states in a one-dimensional optical lattice. Both the superfluid and Mott-insulator phases are investigated separately for ferromagnetic and antiferromagnetic interactions. Mode entanglement is also discussed in the Mott insulating phase. The role of a small but nonzero angle between the polarization vectors of counter-propagating lasers forming the optical lattice on quantum correlations is investigated as well.
We examine the entanglement in the ground states of helium and helium-like ions using an original Hylleraas expansion. The von Neumann and linear entropies of the reduced density matrix are accurately computed by performing the Schmidt decomposition of the S singlet spatial wavefunctions. The results presented are more accurate than currently available in published literature.
The entanglement in a Hubbard chain of hardcore bosons is investigated. The analytic expression of the global entanglement in ground state is derived. The divergence of the derivative of the global entanglement shows the quantum criticality of the ground state. For the thermal equilibrium state, the bipartite and the multipartite entanglement are evaluated. The entanglement decreases to zero at a certain temperature. The thermal entanglement is rapidly decreasing with the increase of the number of sites in the lattice. The bipartite thermal entanglement approaches a constant value at a certain…
Quantum entanglement is analyzed thoroughly in the case of the ground and lowest states of two-electron axially symmetric quantum dots under a perpendicular magnetic field. The individual-particle and the center-of-mass representations are used to study the entanglement variation at the transition from interacting to noninteracting particle regimes. The mechanism of symmetry breaking due to the interaction, that results in the states with symmetries related to the later representation only, being entangled even at the vanishing interaction, is discussed. The analytical expression for the entan…
In certain special circumstances, such as in the vicinity of a black hole or in a uniformly accelerating frame, vacuum fluctuations appear to give rise to a finite-temperature environment. This effect, currently without experimental confirmation, can be interpreted as a manifestation of quantum entanglement after tracing out vacuum modes in an unobserved region. In this work, we identify a class of experimentally accessible quantum systems where thermal density matrices emerge from vacuum entanglement. We show that reduced density matrices of lower-dimensional subsystems embedded in $D$-dimens…
In this work we analyse three quantum communication schemes for the generation of Gaussian entanglement between two ground stations. Communication occurs via a satellite over two independent atmospheric fading channels dominated by turbulence-induced beam wander. In our first scheme the engineering complexity remains largely on the ground transceivers, with the satellite acting simply as a reflector. Although the channel state information of the two atmospheric channels remains unknown in this scheme, the Gaussian entanglement generation between the ground stations can still be determined. On …
For a general quantum many-body system, we show that its ground-state entanglement imposes a fundamental constraint on the low-energy excitations. For two-dimensional systems, our result implies that any system that supports anyons must have a nonvanishing topological entanglement entropy. We demonstrate the generality of this argument by applying it to three-dimensional quantum many-body systems, and showing that there is a pair of ground state topological invariants that are associated to their physical boundaries. From the pair, one can determine whether the given boundary can or cannot abs…
We study pairwise entanglements in spin-half and spin-one Heisenberg chains with an open boundary condition, respectively. We find out that the ground-state and the first-excited-state entanglements are equal for the three-site spin-one chain. When the number of sites L>3, the concurrences and negativities display oscillatory behaviors, and the oscillations of the ground-state and the first-excited-state entanglements are out of phase or in phase.
We present a quantum analysis of three-mode optoacoustic parametric interactions in an optical cavity, in which two orthogonal transverse optical-cavity modes are coupled to one acoustic mode through radiation pressure. Due to the optimal frequency matching -- the frequency separation of two cavity modes is equal to the acoustic-mode frequency -- the carrier and sideband fields simultaneously resonate and coherently build up. This mechanism significantly enhances the optoacoustic couplings in the quantum regime. It allows exploration of quantum behavior of optoacoustic interactions in small-sc…
