Sandu Popescu, Daniel Rohrlich
We point out formal correspondences between thermodynamics and entanglement. By applying them to previous work, we show that entropy of entanglement is the unique measure of entanglement for pure states.
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We apply the axiomatic approach to thermodynamics presented by Giles to derive a unique measure of entanglement for bi-partite pure states. This implies that local manipulations of entanglement in quantum information theory and adiabatic transformations of states in thermodynamics have the same underlying mathematical structure. We discuss possible extensions of our results to mixed and multi-partite states.
Quantifying entanglement in quantum thermodynamics via separability constraints
本文通过限制非平衡动力学至分离态，量化量子系统中因纠缠导致的热量和功，探讨纠缠对热力学的影响，验证了其在量子电池和制冷器中的应用。
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…
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.
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…
Multipartite entanglement measures based on the thermodynamic framework
本文基于热力学框架提出新的多体纠缠度量，通过区分GHZ和W态及检测四体星量子网络态验证其有效性。
We present the minimal energy costs for the measurement and the information erase, using only the Helmholtz free energy and the entanglement of formation. The entanglement of formation appears in the form of difference which indicates the amount of entanglement transfer on the memory during the processes; the cost of the measurement is given by the entanglement gain, whereas the cost of the information erase is given by the loss of available entanglement. Putting together the present Letter and Rev. E 88, 042143 (2013), we can describe the violation and the restoration of the second law only i…
Entanglement is central both to the foundations of quantum theory and, as a novel resource, to quantum information science. The theory of entanglement establishes basic laws, such as the non-increase of entanglement under local operations, that govern its manipulation and aims to draw from them formal analogies to the second law of thermodynamics. However, while in the second law the entropy uniquely determines whether a state is adiabatically accessible from another, the manipulation of entanglement under local operations exhibits a fundamental irreversibility which prevents the existence of …
Theory of bipartite entanglement shares profound similarities with thermodynamics. In this letter we extend this connection to multipartite quantum systems where entanglement appears in different forms with genuine entanglement being the most exotic one. We propose thermodynamic quantities that capture signature of genuineness in multipartite entangled states. Instead of entropy, these quantities are defined in terms of energy -- particularly the difference between global and local extractable works (ergotropies) that can be stored in quantum batteries. Some of these quantities suffice as fait…
Hierarchies of Gaussian multimode entanglement from thermodynamic quantifiers
该研究通过热力学量化器提出多模纠缠的分层结构，利用ergotropic间隙量化纠缠，并为多模纠缠提供了可计算的实验框架。
We discuss quantum entanglement in the context of the thermodynamic arrow of time. We review the role of correlations in entropy-decreasing events and prove that the occurrence of a transformation between two thermodynamic states constitutes a new type of entanglement witness, one not defined as a separating plane in state space between separable and entangled states, but as a physical process dependent on the local initial properties of the states. Extending work by Partovi, we consider a general entangled multipartite system that allows large reversals of the thermodynamic arrow of time. We …
We construct a rigourous model of quantum measurement. A two-state model of a negative temperature amplifier, such as a laser, is taken to a classical thermodynamic limit. In the limit, it becomes a classical measurement apparatus obeying the stochastic axioms of quantum mechanics. Thus we derive the probabilities from a deterministic Schroedinger's equation by procedures analogous to those of classical statistical mechanics. This requires making precise the notion of `macroscopic.'
Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement. Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories. We first address the question whether an entangled state can be transformed into another by means of local operations and classical co…
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.
We show that entanglement can be utilized to extract thermodynamic work beyond classical correlation via feedback control based on measurement on part of a composite system. The net work gain due to entanglement is determined by the change in the mutual information content between the subsystems that is accessible by the memory.
The quantum deformation of the Hopf algebra describes the skeleton of quantum field theory, namely its characterizing feature consisting in the existence of infinitely many unitarily inequivalent representations of the canonical commutation relations. From this we derive the thermal properties of quantum field theory, with the entropy playing the role of the generator of the non-unitary time evolution. The entanglement of the quantum vacuum appears to be robust against interaction with the environment: on cannot ``unknot the knots" in the infinite volume limit.
Recently David Jennings and Terry Rudolph published two papers as reaction on Maccone's paper "Quantum Solution to the Arrow-of-Time Dilemma". In these papers, the authors suppose that second law of thermodynamics is not relevant for quantum systems. Unfortunately, these papers did not get relevant reply from Maccone. The reason of this is following. Both Maccone and the above-mentioned authors use thermodynamic law and thermodynamic-like terminology for non-thermodynamic systems, for example, microscopic system of three qubits. However, big size of a system (quantum or classic) is also not an…
Thermodynamic Probes of Multipartite Entanglement in Strongly Interacting Quantum Systems
提出基于ergotropy的热力学框架，通过可控淬灭或局部测量评估强相互作用量子系统的多体纠缠，适用于多种物理模型和含噪量子电路。
We study the entanglement spectra of bilayer quantum Hall systems at total filling factor nu=1. In the interlayer-coherent phase at layer separations smaller than a critical value, the entanglement spectra show a striking similarity to the energy spectra of the corresponding monolayer systems around half filling. The transition to the incoherent phase can be followed in terms of low-lying entanglement levels. Finally, we describe the connection between those two types of spectra in terms of an effective temperature leading to relations for the entanglement entropy which are in full analogy to …
We discuss the possibility of existence of entanglement in biological systems. Our arguments centre on the fact that biological systems are thermodynamic open driven systems far from equilibrium. In such systems error correction can occur which may maintain entanglement despite high levels of de-coherence. We also discuss the possibility of cooling (classical or quantum) at molecular level.
The entanglement between the position and coin state of a $N$-dimensional quantum walker is shown to lead to a thermodynamic theory. The entropy, in this thermodynamics, is associated to the reduced density operator for the evolution of chirality, taking a partial trace over positions. From the asymptotic reduced density matrix it is possible to define thermodynamic quantities, such as the asymptotic entanglement entropy, temperature, Helmholz free energy, etc. We study in detail the case of a $2$-dimensional quantum walk, in the case of two different initial conditions: a non-separable coin-p…
Advantage of flexible catalysis for entanglement and quantum thermodynamics
研究灵活催化在纠缠和量子热力学中的能力，发现其比标准催化更强大，能实现确定性转换和提高成功概率。
Classical and quantum error correction are presented in the form of Maxwell's demon and their efficiency analyzed from the thermodynamic point of view. We explain how Landauer's principle of information erasure applies to both cases. By then extending this principle to entanglement manipulations we rederive upper bounds on purification procedures thereby linking the ''no local increase of entanglement'' principle to the Second Law of thermodynamics.
We demonstrate that both Wigner's form of Bell's inequalities as well as a form of the second law of thermodynamics, as manifest in Carathéodory's principle, can be derived from the same simple experimental and statistical mechanical assumptions combined with the trivial behavior of integers. This suggests that Bell's theorem is merely a well-disguised statement of the second law. It also suggests that entanglement is necessary for quantum theory to be in full accord with the second law and thus builds on the results of Wiesniak, Vedral, and Brukner \cite{Marcin-Wiesniak:2008fv} who showed it …
The relation between the theory of entanglement and thermodynamics is very tight: a thermodynamic theory of quantum entanglement, as well as the establishment of rigorous formal connections between the laws of thermodynamics and the phenomenology of entanglement are currently open areas of investigation. In this quest, an interesting problem is embodied by the role played by entanglement in processes of work extraction from a working medium embodied by quantum information carriers. In this work, we experimentally address the question "Is there any intrinsic advantage for work extraction given …
We investigate an asymptotically spatially flat Robertson-Walker spacetime from two different perspectives. First, using von Neumann entropy, we evaluate the entanglement generation due to the encoded information in spacetime. Then, we work out the entropy of particle creation based on the quantum thermodynamics of the scalar field on the underlying spacetime. We show that the general behavior of both entropies are the same. Therefore, the entanglement can be applied to the customary quantum thermodynamics of the universe. Also, using these entropies, we can recover some information about the …
Explaining the influence of strong coupling in the dynamics of open quantum systems is one of the most challenging issues in the rapidly growing field of quantum thermodynamics. By using a particular definition of heat, we develop a new approach to study thermodynamics in the strong coupling regime, which takes into account quantum resources as coherence and entanglement. We apply the method to calculate the time-dependent thermodynamic properties of a system and an environment interacting via the generalized amplitude-damping channel (GADC). The results indicate that the transient imbalance b…
Pure state entanglement transformations have been thought of as irreversible, with reversible transformations generally only possible in the limit of many copies. Here, we show that reversible entanglement transformations do not require processing on the many copy level, but can instead be undertaken on individual systems, provided the amount of entanglement which is produced or consumed is allowed to fluctuate. We derive necessary and sufficient conditions for entanglement manipulations in this case. As a corollary, we derive an equation which quantifies the fluctuations of entanglement, whic…
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 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 investigate further the relationship between the entanglement spectrum of a composite many-body system and the energy spectrum of a subsystem making use of concepts of canonical thermodynamics. In many important cases the entanglement Hamiltonian is, in the limit of strong coupling between subsystems, proportional to the energy Hamiltonian of the subsystem. The proportionality factor is an appropriately defined coupling parameter, suggesting to interpret the latter as a inverse temperature. We identify a condition on the entanglement Hamiltonian which rigorously guarantees this interpretati…
Unlocking thermodynamic multitasking: Exploring the functioning of two-qubit engines through coherence and entanglement
本文研究双量子比特热机在双热浴和耗散环境下的运行，揭示纠缠与相干性对运行模式、信息流和效率的影响，并确定热机与制冷机模式的最优参数区域。
We develop a general approach to compute the symmetry-resolved Rényi and von Neumann entanglement entropies (SREE) of thermodynamic macrostates in interacting integrable systems. Our method is based on a combination of the thermodynamic Bethe ansatz and the Gärtner-Ellis theorem from large deviation theory. We derive an explicit simple formula for the von Neumann SREE, which we show to coincide with the thermodynamic Yang-Yang entropy of an effective macrostate determined by the charge sector. Focusing on the XXZ Heisenberg spin chain, we test our result against iTEBD calculations for thermal …
A common framework for quantum mechanics, thermodynamics and information theory is presented. It is accomplished by reinterpreting the mathematical formalism of Everett's many-worlds theory of quantum mechanics and augmenting it to include preparation according to a given ensemble. The notion of \emph{directed entanglement} is introduced through which both classical and quantum communication over quantum channels are viewed as entanglement transfer. This point is illustrated by proving the Holevo bound and quantum data processing inequality relying exclusively on the properties of directed ent…
Quantum entanglement and extractable work for Gaussian states
本研究探讨了双模高斯态中可提取功与量子关联的关系，发现可提取功的定量差异取决于状态属于可分态、纠缠态还是可导态。
Entanglement within a given device provides a potential resource for quantum information processing. Entanglement between system and environment leads to decoherence (thus suppressing non-classical features within the system) but also opens up a route to robust and universal control. The latter is related to thermodynamic equilibrium, a generic behavior of bi-partite quantum systems. Fingerprints of this equilibrium behavior (including relaxation and stability) show up already far from the thermodynamic limit, where a complete solution of the underlying Schroedinger dynamics of the total syste…
We investigate the entanglement properties of an ensemble of atoms interacting with a single bosonic field mode via the Dicke (superradiance) Hamiltonian. The model exhibits a quantum phase transition and a well-understood thermodynamic limit, allowing the identification of both quantum and semi-classical many-body features in the behaviour of the entanglement. We consider the entanglement between the atoms and the field, an investigation initiated in [N. Lambert, C. Emary and T. Brandes, Phys. Rev. Lett. {\bf 92}, %073602 (2004)]. In the thermodynamic limit, we give exact results for all enta…
Fermionic one-body entanglement as a thermodynamic resource
本文证明双模费米子态的纠缠可在开放系统热力学过程中作为真正的量子资源，完成可分态无法实现的任务，从而为费米子纠缠的操作意义提供新见解。
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 …
Entropy from Entanglement in Quantum State Reduction
研究指出，即使在仅两个自由度的系统中，量子纠缠熵无法单向转化为热熵，且量子态缩减的随机动力学允许多种熵定义，从而区分量子态缩减与环境退相干的热力学特征。
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 a…
We study the bipartite entanglement entropy of the two-dimensional (2D) transverse-field Ising model in the thermodynamic limit using series expansion methods. Expansions are developed for the Renyi entropy around both the small-field and large-field limits, allowing the separate calculation of the entanglement associated with lines and corners at the boundary between sub-systems. Series extrapolations are used to extract subleading power laws and logarithmic singularities as the quantum critical point is approached. In 1D, we find excellent agreement with exact results as well as quantum Mont…
Quantumness Speeds up Quantum Thermodynamics Processes
针对缺乏量化量子相干与纠缠在功提取中作用的通用方法的问题，提出热力学速度量化功提取，证明相干和真纠缠可加速功提取，提供无态层析的纠缠见证新热力学方法。
Experimental Verification of Many-Body Entanglement Using Thermodynamic Quantities
本文提出利用全局与局域可提取功之差作为热力学判据，在核磁共振平台上对多达10个量子比特的含噪纠缠态进行实验认证，并扩展至状态信息未知的多体系统。
Ergotropic characterization of continuous variable entanglement
本文提出了一种基于ergotropy的无熵标准，用于检测连续变量纠缠，通过分析ergotropic间隙推导出区分纠缠与分离态的界限，并展示了其在混合系统中的应用。
The first exact quantum simulation of a real molecular system (HD$^+$) under strong ro-vibrational coupling to a quantized optical cavity mode in thermal equilibrium is presented. Theoretical challenges in describing strongly coupled systems of mixed quantum statistics (Bosons and Fermions) are discussed and circumvented by the specific choice of our molecular system. Our exact simulations reveal the absence of a zero temperature for the strongly coupled matter and light subsystems, due to cavity induced non-equilibrium conditions. Furthermore, we explore the temperature dependency of light-ma…
The free rider problem is one of the most well-studied problems in economics. The solution proposed mainly is punitive in order to deter people from free riding. In this work, we introduce quantum strategies and study the problem in the thermodynamic limit by drawing analogies with the 1D Ising model. We observe that for maximum entanglement, irrespective of the payoffs, quantum strategy is the equilibrium solution, solving the free rider problem.
Tracking Entanglement Transfer: Emergence of Thermodynamics from Quantum Information
通过两个量子比特与反铁磁海森堡交换耦合的极小模型，研究纠缠从子系统向环境的转移，发现其行为与黑洞热力学中的纠缠熵、霍金熵和佩奇曲线类似，并涌现出有效温度和奇异金属行为。
We demonstrate an area law bound on the ground state entanglement entropy of a wide class of gapless quantum states of matter using a strategy called local entanglement thermodynamics. The bound depends only on thermodynamic data, actually a single exponent, the hyper-scaling violation exponent $θ$. All systems in $d$ spatial dimensions obeying our scaling assumptions and with $θ< d-1$ obey the area law, while systems with $θ= d-1$ can violate the area law at most logarithmically. We also discuss the case of frustration-free Hamiltonians and show that to violate the area law more than logarith…
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…
Over the last decade, significant progresses have been achieved to create Bose-Einstein condensates (BEC) of magnetic excitations, i.e., magnons, at the room temperature, which is a novel quantum many-body system with a strong spin-spin correlation, and contains potential applications in magnonic spintronics. For quantum information science, the magnonic condensates can become an attractive source of quantum entanglement, which plays a central role in most of the quantum information processing tasks. Here we theoretically study the entanglement properties of a magnon gas above and below the co…
Many fruitful analogies have emerged between the theories of quantum entanglement and thermodynamics, motivating the pursuit of an axiomatic description of entanglement akin to the laws of thermodynamics. A long-standing open problem has been to establish a true second law of entanglement, and in particular a unique function which governs all transformations between entangled systems, mirroring the role of entropy in thermodynamics. Contrary to previous promising evidence, here we show that this is impossible, and no direct counterpart to the second law of thermodynamics can be established. Th…
Thermal Entanglement and Out-of-Equilibrium Thermodynamics in 1D Bose gases
研究一维玻色气体在低能玻色-爱因斯坦凝聚态中热与非平衡态的纠缠特性，通过协方差矩阵框架量化纠缠，并揭示非平衡动态中纠缠的生成机制。
Entanglement Islands and Thermodynamics of the Black Hole in Asymptotically Safe Quantum Gravity
本研究通过引入纠缠岛解决黑洞辐射熵悖论，揭示了渐近安全量子引力中黑洞热力学性质及信息守恒机制。
Entanglement entropy of proton and its relation to thermodynamics entropy
该研究基于热力学、饱和效应与Unruh效应推导胶子系统纠缠熵公式，验证其在高能极限下与质子二分密度矩阵法结果的一致性，并探讨了BFKL（DLL近似）和BK方程所得熵的关联。
We investigate the fundamental limitations imposed by thermodynamics for creating correlations. Considering a collection of initially uncorrelated thermal quantum systems, we ask how much classical and quantum correlations can be obtained via a cyclic Hamiltonian process. We derive bounds on both the mutual information and entanglement of formation, as a function of the temperature of the systems and the available energy. While for a finite number of systems there is a maximal temperature allowing for the creation of entanglement, we show that genuine multipartite entanglement---the strongest …
In this paper the geometric entanglement (GE) of systems in one spatial dimension (1D) and in the thermodynamic limit is analyzed focusing on two aspects. First, we reexamine the calculation of the GE for translation-invariant matrix product states (MPSs) in the limit of infinite system size. We obtain a lower bound to the GE which collapses to an equality under certain sufficient conditions that are fulfilled by many physical systems, such as those having unbroken space (P) or space-time (PT) inversion symmetry. Our analysis justifies the validity of several derivations carried out in previou…
We consider an special dynamics of a quantum walk (QW) on a line. Initially, the walker localized at the origin of the line with arbitrary chirality, evolves to an asymptotic stationary state. In this stationary state a measurement is performed and the state resulting from this measurement is used to start a second QW evolution to achieve a second asymptotic stationary state. In previous works, we developed the thermodynamics associated with the entanglement between the coin and position degrees of freedom in the QW. Here we study the application of the first and second laws of thermodynamics …
In this paper, the impact of temperature fluctuations in the entanglement of two qubits described by a spin-1/2 XX model is studied. To describe the out-of-equilibrium situation, super-statistics is used with fluctuations given by a $χ^2$ distribution function, and its free parameters are chosen in such a way that resembles the non-additive Tsallis thermodynamics. In order to preserve the Legendre structure of the thermal functions, particular energy constraints are imposed on the density operator and the internal energy. Analytical results are obtained using an additional set of constraints a…
The Rényi entanglement entropy is calculated exactly for mode-partitioned isolated systems such as the two-mode squeezed state and the multi-mode Silbey-Harris polaron ansatz state. Effective thermodynamic descriptions of the correlated partitions are constructed to present quantum information theory concepts in the language of thermodynamics. Boltzmann weights are obtained from the entanglement spectrum by deriving the exact relationship between an effective temperature and the physical entanglement parameters. The partition function of the resulting effective thermal theory can be obtained d…
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