Thermodynamical equilibrium is considered as an effect of quantum entangling of the vacuum state of a system. An explicit mathematical model of multi- particle entangled pure quantum states is developed and analyzed. In the framework, the process of measurement results in probability distributions that exactly correspond to the heat equilibrium of a system in a thermostat.
We argue that on its face, entanglement theory satisfies laws equivalent to thermodynamics if the theory can be made reversible by adding certain bound entangled states as a free resource during entanglement manipulation. Subject to plausible assumptions, we prove that this is not the case in general, and discuss the implications of this for the thermodynamics of entanglement.
Here we investigate the impact of temporal entanglement on a system's ability to perform thermodynamical work. We show that while the quantum version of the Jarzynski equality remains satisfied even in the presence of temporal entanglement, the individual thermodynamical work moments in the expansion of the free energy are, in fact, sensitive to the genuine quantum correlations. Therefore, while individual moments of the amount of thermodynamical work can be larger (or smaller) quantumly than classically, when they are all combined together into the (exponential of) free energy, the total effe…
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.
We provide some new properties of entanglement of formation. In particular, we obtain an additive lower bound for entanglement of formation. Subsequently we develop the concept of local orthogonality of ensembles which leads to the mixed states with distillable entanglement equal to entanglement of formation. Then we consider thermodynamical analogies within the entanglement processing domain. Especially, we exploit analogy entanglement -- energy. In this scheme the total entanglement i.e. the amount of singlet pairs needed for local preparation of a state corresponds to internal energy while …
We show that if the ground state entanglement exceeds the total entropy of a given system, then this system is in an entangled state. This is a universal entanglement witness that applies to any physical system and yields a temperature below which we are certain to find some entanglement. Our witness is then applied to generic bosonic and fermionic many body systems to derive the corresponding "critical" temperatures that have a very broad validity.
We argue that the entanglement entropy for a very small subsystem obeys a property which is analogous to the first law of thermodynamics when we excite the system. In relativistic setups, its effective temperature is proportional to the inverse of the subsystem size. This provides a universal relationship between the energy and the amount of quantum information. We derive the results using holography and confirm them in two dimensional field theories. We will also comment on an example with negative specific heat and suggest a connection between the second law of thermodynamics and the strong …
The first step in quantum information theory is the identification of entanglement as a valuable resource. The next step is learning how to exploit this resource efficiently. We learn how to exploit entanglement efficiently by applying analogues of thermodynamical concepts. These concepts include reversibility, entropy, and the distinction between intensive and extensive quantities. We discuss some of these analogues and show how they lead to a measure of entanglement for pure states. We also ask whether these analogues are more than analogues, and note that, l o c a l l y, entropy of entangle…
Quantum correlation, or entanglement, is now believed to be an indispensable physical resource for certain tasks in quantum information processing, for which classically correlated states cannot be useful. Besides information processing, what kind of physical processes can exploit entanglement? In this paper, we show that there is indeed a more basic relationship between entanglement and its usefulness in thermodynamics. We derive an inequality showing that we can extract more work out of a heat bath via entangled systems than via classically correlated ones. We also analyze the work balance o…
The entanglement in a general mixed spin chain with arbitrary spin $S$ and 1/2 is investigated in the thermodynamical limit. The entanglement is witnessed by the magnetic susceptibility which decides a characteristic temperature for an entangled thermal state. The characteristic temperature is nearly proportional to the interaction $J$ and the mixed spin $S$. The bound of negativity is obtained on the basis of the magnetic susceptibility. It is found that the macroscopic magnetic properties are affected by the quantum entanglement in the real solids. Meanwhile, the entanglement can be quantita…
We introduce a "microcanonical" measure (complying with the "general canonical principle") over the second moments of pure bosonic Gaussian states under an energy constraint. We determine the average fidelity for the teleportation of states distributed according to such a measure and compare it to a threshold obtained from a feasible classical strategy. Furthermore, we show that, under the proposed measure, the distribution of the entanglement concentrates around a finite value at the thermodynamical limit and, in general, the typical entanglement of Gaussian states with maximal energy E is no…
We present a general argument showing that the temperature as well as other thermodynamical state variables can qualify as entanglement witnesses for spatial entanglement. This holds for a variety of systems and we exemplify our ideas using a simple free non-interacting Bosonic gas. We find that entanglement can exist at arbitrarily high temperatures, provided that we can probe smaller and smaller regions of space. We then discuss the relationship between the occurrence of Bose-Einstein condensation and our conditions for the presence of entanglement and compare the respective critical tempera…
We present a new inequality which holds in the thermodynamical processes with measurement and feedback controls with using only the Helmholtz free energy and the entanglement of formation: $W_{\mathrm{ext}}\le-ΔF-k_{B}TΔE_{F}$. The quantity $-ΔE_{F}$, which is positive, expresses the amount of entanglement transfer from the system $S$ to the probe $P$ through the interaction $\hat{U}_{SP}$ during the measurement. It is easier to achieve the upper bound in the new inequality than in the Sagawa-Ueda inequality [Phys. Rev. Lett. 100 080403 (2008)]. The new inequality has clear physical meaning: i…
The current-carrying steady-state that arises in the middle of a metallic wire connected to macroscopic leads is characterized regarding its response functions, correlations and entanglement entropy. The spectral function and the dynamical structure factor show clear non-equilibrium signatures accessible by state-of-the-art techniques. In contrast with the equilibrium case, the entanglement entropy is extensive with logarithmic corrections at zero-temperature that depend on the wire-leads coupling and, in a non-analytic way, on voltage. This shows that some robust universal quantities found in…
We consider a set of fully connected spins models that display first- or second-order transitions and for which we compute the ground-state entanglement in the thermodynamical limit. We analyze several entanglement measures (concurrence, Rényi entropy, and negativity), and show that, in general, discontinuous transitions lead to a jump of these quantities at the transition point. Interestingly, we also find examples where this is not the case.
We consider the amount of work which can be extracted from a heat bath using a bipartite state shared by two parties. In general it is less then the amount of work extractable when one party is in possession of the entire state. We derive bounds for this "work deficit" and calculate it explicitly for a number of different cases. For pure states the work deficit is exactly equal to the distillable entanglement of the state, and this is also achievable for maximally correlated states. In these cases a form of complementarity exists between physical work which can be extracted and distillable ent…
We show that in one-dimensional isotropic Heisenberg model two-qubit thermal entanglement and maximal violation of Bell inequalities are directly related with a thermodynamical state function, i.e., the internal energy. Therefore they are completely determined by the partition function, the central object of thermodynamics. For ferromagnetic ring we prove that there is no thermal entanglement at any temperature. Explicit relations between the concurrence and the measure of maximal Bell inequality violation are given.
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…
We analyze the bipartite and multipartite entanglement for the ground state of the one-dimensional XY model in a transverse magnetic field in the thermodynamical limit. We explicitly take into account the spontaneous symmetry breaking in order to explore the relation between entanglement and quantum phase transitions. As a result we show that while both bipartite and multipartite entanglement can be enhanced by spontaneous symmetry breaking deep into the ferromagnetic phase, only the latter is affected by it in the vicinity of the critical point. This result adds to the evidence that multipart…
When a measurement is carried out on one of the entangled parties, the second party can extract work owing to the reduction in its entropy. Here we inquire the amount of work/energy corresponding to the symmetrization entanglement of identical particles (bosons) in a condensate. One measures the quantum state of a particular boson which can be performed only under some certain conditions. We learn that the extracted work comes out to be the \textit{complete} thermodynamical energy present in the condensate. %We learn that the work extracted by the remaining part of the condensate is equal to t…
We employ a nuclear magnetic resonance (NMR) quantum information processor to simulate the ground state of an XXZ spin chain and measure its NMR analog of entanglement, or pseudo-entanglement. The observed pseudo-entanglement for a small-size system already displays singularity, a signature which is qualitatively similar to that in the thermodynamical limit across quantum phase transitions, including an infinite-order critical point. The experimental results illustrate a successful approach to investigate quantum correlations in many-body systems using quantum simulators.
A simple two-qubit model showing Quantum Phase Transitions as a consequence of ground state level crossings is studied in detail. Using the Concurrence of the system as an entanglement measure and heat capacity as a marker of thermodynamical properties, an analytical expression giving the latter in terms of the former is obtained. A protocol allowing an experimental measure of entanglement is then presented and compared with a related proposal recently reported by Wieśniak, Vedral and Brukner
The work extractable from correlated bipartite quantum systems can be used to distinguish entanglement from classical correlation. A natural question is now whether it can be generalised to multipartite systems. In this paper, we devise a protocol to distinguish the GHZ, the W, and separable states in terms of the thermodynamically extractable work under local operations and classical communication, and compare the results with those obtained from Mermin's inequalities.
A review is given on the thermodynamical structure of bipartite entanglement. By comparing it to the axiomatic formulation of thermodynamics presented by Giles it is shown that for finite dimensional systems the two theories are formally inequivalent. The same approach is used to demonstrate the full equivalence in the asymptotic limit for pure quantum states. For mixed states a different method for obtaining the second law is described applied to two different classes of operations, PPT-preserving and asymptotically non-entangling operations.
Evidencing Quantum Gravity with Thermodynamical Observables
Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences（奥地利科学院维也纳量子光学与量子信息研究所）；Department of Physics, Royal Holloway, University of London（伦敦大学皇家霍洛威学院物理系）；Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna（维也纳大学物理学院维也纳量子科学与技术中心）
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 define and analyse the concept of entanglement production during the evolution of a general quantum mechanical dissipative system. While it is important to minimise entropy production in order to achieve thermodynamical efficiency, maximising the rate of change of entanglement is important in quantum information processing. Quantitative relations are obtained between entropy and entanglement productions, under specific assumptions detailed in the text. We apply these to the processes of dephasing and decay of correlations between two initially entangled qubits. Both the Master equation trea…
The entanglement properties of the phase transition in a two dimensional harmonic lattice, similar to the one observed in recent ion trap experiments, are discussed both, for finite number of particles and thermodynamical limit. We show that for the ground state at the critical value of the trapping potential two entanglement measures, the negativity between two neighbouring sites and the block entropy for blocks of size 1, 2 and 3, change abruptly. Entanglement thus indicates quantum phase transitions in general; not only in the finite dimensional case considered in [Phys. Rev. Lett. {\bf 93}…
We demonstrate that the presence of entanglement in macroscopic bodies (e.g. solids) in thermodynamical equilibrium could be revealed by measuring heat-capacity. The idea is that if the system were in a separable state, then for certain Hamiltonians heat capacity would not tend asymptotically to zero as the temperature approaches absolute zero. Since this would contradict the third law of thermodynamics, one concludes that the system must contain entanglement. The separable bounds are obtained by minimization of the heat capacity over separable states and using its universal low-temperature be…
Motivated by the recent interest in thermodynamics of micro- and mesoscopic quantum systems we study the maximal amount of work that can be reversibly extracted from a quantum system used to store temporarily energy. Guided by the notion of passivity of a quantum state we show that entangling unitary controls extract in general more work than independent ones. In the limit of large number of copies one can reach the thermodynamical bound given by the variational principle for free energy.
In the discussion about the quantumness of NMR computation a conclusion is done that computational states are separable and therefore can not be entangled. This conclusion is based on the assumption that the initial density matrix of an individual molecule coincides with whole sample molecules distribution over single molecule energy levels. This means that quantum stochasticity is replaced by classical stochasticity. In the present paper it is shown, that quantum NMR computation can create genuine entangled states if initial system states are thermodynamical equilibrium ones. A separability a…
It is shown that if a mixed state can be distilled to the singlet form, it must violate partial transposition criterion [A. Peres, Phys. Rev. Lett. 76, 1413 (1996)]. It implies that there are two qualitatively different types of entanglement: ``free'' entanglement which is distillable, and ``bound'' entanglement which cannot be brought to the singlet form useful for quantum communication purposes. Possible physical meaning of the result is discussed.
Some thermodynamical properties of solids, such as heat capacity and magnetic susceptibility, have recently been shown to be linked to the amount of entanglement in a solid. However this entanglement may appear a mere mathematical artifact of the typical symmetrization procedure of many-body wave function in solid state physics. Here we show that this entanglement is physical demonstrating the principles of its extraction from a typical solid state system by scattering two particles off the system. Moreover we show how to simulate this process using present-day optical lattices technology. Thi…
We study the threshold temperature for pairwise thermal entanglement in the spin-1/2 isotropic Heisenberg model up to 11 spins and find that the threshold temperature for odd and even number of qubits approaches the thermal dynamical limit from below and above, respectively. The threshold temperature in the thermodynamical limit is estimated. We investigate the many-particle entanglement in both ground states and thermal states of the system, and find that the thermal state in the four-qubit model is four-particle entangled before a threshold temperature.
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…
In this paper it is shown that the quantum state of a multiverse made up of classically disconnected regions of the space-time, whose dynamical evolution is dominated by a homogeneous and isotropic fluid, is given by a squeezed state. These are typical quantum states that have no classical counterpart and, therefore, they allow us to analyze the violation of classical inequalities as well as the EPR argument in the context of the quantum multiverse. The thermodynamical properties of entanglement are calculated for a composite quantum state of two universes whose states are quantum mechanically…
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 show that quantum mechanical entanglement can prevail even in noisy open quantum systems at high temperature and far from thermodynamical equilibrium, despite the deteriorating effect of decoherence. The system consists of a number N of interacting quantum particles, and it can interact and exchange particles with some environment. The effect of decoherence is counteracted by a simple mechanism, where system particles are randomly reset to some standard initial state, e.g. by replacing them with particles from the environment. We present a master equation that describes this process, which …
We give an analytical description of long distance entanglement (LDE) mediated by one-dimensional quantum spin chains recently found in numerical studies. We develop a formalism that allows the computation of LDE for weakly interacting probes with gapped many-body systems. At zero temperature, a DC response function determines the ability of the physical system to generate genuine quantum correlations between the probes. We show that the biquadratic Heisenberg spin-1 chain is able to produce LDE in the thermodynamical limit and that the finite antiferromagnetic Heisenberg chain maximally entan…
Recently, it has been suggested that operational properties connected to quantum computation can be alternative indicators of quantum phase transitions. In this work we systematically study these operational properties in 1D systems that present phase transitions of different orders. For this purpose, we evaluate the local convertibility between bipartite ground states. Our results suggest that the operational properties, related to non-analyticities of the entanglement spectrum, are good detectors of explicit symmetries of the model, but not necessarily of phase transitions. We also show that…
We theoretically explore quantum correlation properties of a dissipative Bose-Hubbard dimer in presence of a coherent drive. In particular, we focus on the regime where the semiclassical theory predicts a bifurcation with a spontaneous spatial symmetry breaking. The critical behavior in a well defined thermodynamical limit of large excitation numbers is considered and analyzed within a Gaussian approach. The case of a finite boson density is also examined by numerically integrating the Lindblad master equation for the density matrix. We predict the critical behavior around the bifurcation poin…
We present a framework, compliant with the general canonical principle of statistical mechanics, to define measures on the set of pure Gaussian states of continuous variable systems. Within such a framework, we define two specific measures, referred to as `micro-canonical' and `canonical', and apply them to study systematically the statistical properties of the bipartite entanglement of n-mode pure Gaussian states (as quantified by the entropy of a subsystem). We rigorously prove the "concentration of measure" around a finite average, occurring for the entanglement in the thermodynamical limit…
Entanglement is a critical resource used in many current quantum information schemes. As such entanglement has been extensively studied in two qubit systems and its entanglement nature has been exhibited by violations of the Bell inequality. Can the amount of violation of the Bell inequality be used to quantify the degree of entanglement. What do Bell inequalities indicate about the nature of entanglement?
We show that quantum decoherence, in the context of observational cosmology, can be connected to the cosmic dark energy. The decoherence signature could be characterized by the existence of quantum entanglement between cosmological eras. As a consequence, the Von Neumann entropy related to the entanglement process, can be compared to the thermodynamical entropy in a homogeneous and isotropic universe. The corresponding cosmological models are compatible with the current observational bounds being able to reproduce viable equations of state without introducing {\it a priori} any cosmological co…
Wave-particle duality is the most fundamental description of the nature of a quantum object which behaves like a classical particle or wave depending on the measurement apparatus. On the other hand, entanglement represents nonclassical correlations of composite quantum systems, being also a key resource in quantum information. Despite the very recent observations of wave-particle superposition and entanglement, whether these two fundamental traits of quantum mechanics can emerge simultaneously remains an open issue. Here we introduce and experimentally realize a scheme that deterministically g…
How to prepare deterministically non-Gaussian entangled states is a fundamental question for continuous-variable quantum information technology. Here, we theoretically demonstrate through numerical methods that the triple-photon state generated by three-photon spontaneous parametric down-conversion is a pure super-Gaussian resource of non-Gaussian entanglement. Interestingly, the degree of entanglement between the modes of the triple-photon state is stronger than that corresponding to the two-mode squeezed vacuum state produced by a quadratic Hamiltonian with the same parameters. Furthermore, …
We study quantum coarse-grained entropy and demonstrate that the gap in entropy between local and global coarse-grainings is a natural generalization of entanglement entropy to mixed states and multipartite systems. This "quantum correlation entropy" $S^{\rm QC}$ is additive over independent systems, is invariant under local unitary operations, measures total nonclassical correlations (vanishing on states with strictly classical correlation), and reduces to the entanglement entropy for bipartite pure states. It quantifies how well a quantum system can be understood via local measurements, and …
Quantum mechanical entanglement can exist in noisy open quantum systems at high temperature. A simple mechanism, where system particles are randomly reset to some standard initial state, can counteract the deteriorating effect of decoherence, resulting in an entangled steady state far from thermodynamical equilibrium. We present models for both gas-type systems and for strongly coupled systems. We point out in which way the entanglement resulting from such a reset mechanism is different from the entanglement that one can find in thermal states. We develop master equations to describe the syste…
It has been observed by numerous authors that a quantum system being entangled with another one limits its possible entanglement with a third system: this has been dubbed the "monogamous nature of entanglement". In this paper we present a simple identity which captures the trade-off between entanglement and classical correlation, which can be used to derive rigorous monogamy relations. We also prove various other trade-offs of a monogamy nature for other entanglement measures and secret and total correlation measures.
Quantum-enhanced measurements exploit quantum mechanical effects for increasing the sensitivity of measurements of certain physical parameters and have great potential for both fundamental science and concrete applications. Most of the research has so far focused on using highly entangled states, which are, however, difficult to produce and to stabilize for a large number of constituents. In the following we review alternative mechanisms, notably the use of more general quantum correlations such as quantum discord, identical particles, or non-trivial hamiltonians; the estimation of thermodynam…
Quantum technologies based on the particle nature of a photon has been progressed over the last several decades, where the fundamental quantum feature of entanglement has been tested by Hong-Ou-Mandel (HOM) type anticorrelation as well as Bell-type nonlocal correlation. Mutually exclusive quantum natures of the wave-particle duality of a single photon have been intensively investigated to understand the fundamental physics of mysterious quantum nature. Here, we revisit the HOM-type quantum correlation to answer the question whether the HOM-type anticorrelation can be a test tool for quantum en…
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…
Recently, it was shown that quantum entanglement is an indispensable part of the duality behavior of light. Here, we report a surprisingly intimate connection between the stereographic projection and the duality--entanglement nature of a single photon. We show that, the duality--entanglement relation [Optica \textbf{5}, 942 (2018)], naturally emerges from the stereographic projection geometry. We demonstrate that this geometry is complementarity sensitive; in the sense that, it is sensitive to the particle nature, wave nature, and entanglement nature of a single photon.
The relationship between the mean-field approximations in various interacting models of statistical physics and measures of classical and quantum correlations is explored. We present a method that allows us to bound the total amount of correlations (and hence entanglement) in a physical system in thermal equilibrium at some temperature in terms of its free energy and internal energy. This method is first illustrated using two qubits interacting through the Heisenberg coupling, where entanglement and correlations can be computed exactly. It is then applied to the one dimensional Ising model in …
Observation of gravitationally induced entanglement between two massive particles can be viewed as implying the existence of the nonclassical nature of gravity. However, weak interaction in the gravitational field is extremely small so that gravitationally induced entanglement is exceptionally challenging to test in practice. For addressing this key challenge, here we propose a criterion based on the logical contradictions of weak entanglement, which may boost the sensitivity of the signal due to the gravitationally induced entanglement. Specifically, we make use of the weak-value scenario and…
