Optimal Decompositions with Respect to Entropy and Symmetries

The entropy of a subalgebra, which has been used in quantum ergodic theory to construct a noncommutative dynamical entropy, coincides for N-level systems and Abelian subalgebras with the notion of maximal mutual information of quantum communication theory. The optimal decompositions of mixed quantum states singled out by the entropy of Abelian subalgebras correspond to optimal detection schemes at the receiving end of a quantum channel. It is then worthwhile studying in some detail the structure of the convex hull of quantum states brought about by the variational definition of the entropy of a subalgebra. In this Letter, we extend previous results on the optimal decompositions for 3-level systems.     

Role of nonequilibrium entropy in Einstein’s theory of gravitation

We employ the covariant version of a systematic framework of nonequilibrium thermodynamics to clarify the role of entropy in the classical theory of gravitation. An expression for the global entropy is identified naturally from the covariant formulation, and a dual role of the Einstein equation as a fundamental evolution equation and as a thermodynamic equation of state follows immediately. The covariant time integral of the entropy is a more fundamental quantity than the entropy itself. In the absence of matter, the gravitational entropy alone cannot generate any irreversible processes. Some implications for the structure of a quantum theory of gravity are discussed.     

Intrinsic quantum computation

We introduce ways to measure information storage in quantum systems, using a recently introduced computation-theoretic model that accounts for measurement effects. The first, the quantum excess entropy, quantifies the shared information between a quantum process's past and its future. The second, the quantum transient information, determines the difficulty with which an observer comes to know the internal state of a quantum process through measurements. We contrast these with von Neumann entropy and quantum entropy rate and provide a closed-form expression for the latter for the class of deterministic quantum processes.     

与XY双自旋链耦合的双量子比特系统的关联性与相干性

研究了双量子比特系统中在具有Dzyaloshinsky-Moriya相互作用的独立XY自旋链环境下的相干性与关联性动力学.推导出相干性与关联性的演化规律.发现在自旋链的临界点附近,当tt_0时,系统相干性的演化与经典关联完全相同;而在tt_0时,则与量子关联完全相同;在t_0时刻,量子关联突变为经典关联.     

On Convexity of Generalized Wigner–Yanase–Dyson Information

The convexity of the Wigner–Yanase–Dyson information, as first proved by Lieb, is a deep and fundamental result because it leads to the strong subadditivity of quantum entropy. The Wigner–Yanase–Dyson information is a particular kind of quantum Fisher information with important applications in quantum estimation theory. But unlike the quantum entropy, which is the unique natural quantum extension of the classical Shannon entropy, there are many different variants of quantum Fisher information, and it is desirable to investigate their convexity. This article is devoted to studying the convexity of a direct generalization of the Wigner–Yanase–Dyson information. Some sufficient conditions are obtained, and some necessary conditions are illustrated. In a particular case, a surprising necessary and sufficient condition is obtained. Our results reveal the intricacy and subtlety of the convexity issue for general quantum Fisher information.      

Lieb-Robinson bounds and the generation of correlations and topological quantum order

The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails. We discuss several consequences of this result in the context of quantum information theory. First, we show that the information that leaks out to spacelike separated regions is negligible and that there is a finite speed at which correlations and entanglement can be distributed. Second, we discuss how these ideas can be used to prove lower bounds on the time it takes to convert states without topological quantum order to states with that property. Finally, we show that the rate at which entropy can be created in a block of spins scales like the boundary of that block.     

Perturbation theory of von Neumann entropy

In quantum information theory, von Neumann entropy plays an important role; it is related to quantum channel capacities. Only for a few states can one obtain their entropies. In a continuous variable system, numeric evaluation of entropy is not easy due to infinite dimensions. We develop the perturbation theory for systematically calculating von Neumann entropy of a non-degenerate system as well as a degenerate system.     

A new method to study phase transition in 3D Heisenberg model

It is shown that partial entropy, which is the classical analog of von Neumann entropy in quantum theory, is an effective tool to study the thermodynamic phase transitions in the physical systems. This method captures the intrinsic characters of critical fluctuations and does not need the pre-assumed order parameter. As an example, the finite temperature phase transition in the quantum three-dimensional spin-1/2 Heisenberg model is studied, where the stochastic series expansion quantum Monte Carlo method with operator-loop update is used. It is found that close to the critical temperature, the derivative of partial entropy displays a maximum value and shows finite size scaling behaviors, from which the critical temperature and critical exponents are determined.     

A Measure of Quantum Correlation Based on von Neumann Entropy and Positive Operator-Valued Measurement

Quantum correlations in composite quantum systems are at the origin of the most peculiar features of quantum mechanics such as the violation of Bells inequalities and non-locality. In quantum information theory, they are viewed as quantum resources used by quantum algorithms and communication protocols to outperform their classical analogs. In this paper, we define a new measure of quantum correlation based on von Neumann entropy and positive operator-valued measurement,which has clear physical meaning and we can prove that it satisfying many good property for a measure of quantumness.     

Entanglement dynamics in Coriolis coupled rovibrational states of formaldehyde

The entanglement dynamics of two vibrational modes of a polyatomic molecule coupled by Coriolis interaction to overall molecular rotation is studied in terms of two negativities, N(t) and N_s(t), respectively, defined by the minimum of the eigenvalues and by the sum of the negative eigenvalues of the partial transpose of a density matrix. Various initial states are the products of Dicke states and the products of coherent states of vibrations and rotations. Formaldehyde is taken as an example, and the von Neumann entropy s(t) is simulated for the comparison with both negativities. It is shown that negativity N_s(t) is positively correlated with entropy s(t), and the correlated behavior between negativity N(t) and entropy s(t) strongly depends on initial states. However, these three indicators of entanglement display a dominantly positive correlation for the coherent states with small or large parameters. In addition, for the latter state two quantities N(t) and s(t) are nearly unchanged for a long time. This time can be further increased by the increasing of vibrational quantum number so that molecular information processing and quantum computing is allowed. These results are useful in quantum information theory.     

Information-Probabilistic Description of the Universe

We describe the universe as a single entangled ensemble of quantum particles. The total entropy of this world ensemble, which can be expressed as a sum of information, thermodynamic and entanglement components, is assumed to be always zero. This condition suggests information quantization, which we associate with the Planck’s action. Then the entropy neutrality condition for the universe leads to the zero-action principle. We show that the main concepts of classical space-time and gravity naturally emerge in this picture. A generalized least action principle, which embraces the maximal entropy principles of information theory, is introduced.     

Entanglement Degree in the Time Development of the Jaynes–Cummings Model

Recently, it has been become known that a quantum entangled state plays an important role in fields of quantum information theory, such as quantum teleportation and quantum computation. Research on quantifying entangled states has been carried out using several measures. In this Letter, we will adopt this method using quantum mutual entropy to measure the degree of entanglement in the time development of the Jaynes–Cummings model.     

多光子Jaynes-Cummings模型中与Glauber-Lachs态相互作用原子的熵压缩

利用全量子理论,研究了多光子Jaynes-Cummings模型中与Glauber-Lachs态相互作用的混合态原子的信息熵压缩。讨论了相干平均光子数、热平均光子数、跃迁光子数、原子初态参量对原子信息熵压缩的影响。结果表明原子信息熵 分量没有熵压缩性质;相干平均光子数取值适当时,原子信息熵 分量呈现熵压缩效应;热平均光子数、跃迁光子数会破坏原子信息熵 分量的熵压缩效应;原子初态参量对原子信息熵 分量能否呈现熵压缩效应没有决定性作用;伴随双光子跃迁时,原子的熵压缩因子的时间演化曲线呈现周期性。     

Information Erasure and the Generalized Second Law of Black Hole Thermodynamics

We consider the generalized second law of black hole thermodynamics in the light of quantum information theory, in particular information erasure and Landauer’s principle (namely, that erasure of information produces at least the equivalent amount of entropy). A small quantum system outside a black hole in the Hartle-Hawking state is studied, and the quantum system comes into thermal equilibrium with the radiation surrounding the black hole. For this scenario, we present a simple proof of the generalized second law based on quantum relative entropy. We then analyze the corresponding information erasure process, and confirm our proof of the generalized second law by applying Landauer’s principle.     

Quantum transmission processes and their entropies

In classical information theory, one of the most important theorems are the coding theorems, which were discussed by calculating the mean entropy and the mean mutual entropy defined by the classical dynamical entropy (Kolmogorov-Sinai). The quantum dynamical entropy was first studied by Emch [13] and Connes-Stormer [11]. After that, several approaches for introducing the quantum dynamical entropy are done [10, 3, 8, 39, 15, 44, 9, 27, 28, 2, 19, 45]. The efficiency of information transmission for the quantum processes is investigated by using the von Neumann entropy [22] and the Ohya mutual entropy [24]. These entropies were extended to S- mixing entropy by Ohya [26, 27] in general quantum systems. The mean entropy and the mean mutual entropy for the quantum dynamical systems were introduced based on the S- mixing entropy. In this paper, we discuss the efficiency of information transmission to calculate the mean mutual entropy with respect to the modulated initial states and the connected channel for the quantum dynamical systems.     

Quantum Computation Toward Quantum Gravity

The aim of this paper is to enlighten the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of Quantum Mechanics (the "It from bit" proposal). Here we suggest that quantum information must play a relevant role in Quantum Gravity (the "It from qubit" proposal). The conjecture is that Quantum Gravity, the theory which will reconcile Quantum Mechanics with General Relativity, can be formulated in terms of quantum bits of information (qubits) stored in space at the Planck scale. This conjecture is based on the following arguments: a) The holographic principle, b) The loop quantum gravity approach and spin networks, c) Quantum geometry and black hole entropy. From the above arguments, as they stand in the literature, it follows that the edges of spin networks pierce the black hole horizon and excite curvature degrees of freedom on the surface. These excitations are micro-states of Chern-Simons theory and account of the black hole entropy which turns out to be a quarter of the area of the horizon, (in units of Planck area), in accordance with the holographic principle. Moreover, the states which dominate the counting correspond to punctures of spin j = 1/2 and one can in fact visualize each micro-state as a bit of information. The obvious generalization of this result is to consider open spin networks with edges labeled by the spin –1/ 2 representation of SU(2) in a superposed state of spin "on" and spin "down." The micro-state corresponding to such a puncture will be a pixel of area which is "on" and "off" at the same time, and it will encode a qubit of information. This picture, when applied to quantum cosmology, describes an early inflationary universe which is a discrete version of the de Sitter universe.     

与二项式光场相互作用的运动原子熵压缩

运用量子信息熵理论,研究了二项式光场与运动二能级原子相互作用过程中运动原子的信息熵压缩。讨论了不同的原子初态和场的有关参数对原子信息熵压缩的影响。结果表明：选择原子初态、场模结构、场调节参数及原子运动速度可以调控原子信息熵的压缩方向、偶极矩分量值和压缩周期;适当的选择参数可得到持续性的原子信息熵压缩。     

Comments on the Kolmogorov-Sinai-Sąsiada entropy and the quantum information theory

Commenting the recent generalization by S$\text{a}\text{?}$siada of the Kolmogorov-Sinai entropy to the quantum case (KSSentropy), it is remarked that this entropy refers to the process of evolution as a whole and to the initial state (t = 0), not to the state at any time (t ? 0). Therefore, the KSS entropy has no direct relation to the von Neumann entropy or A-entropy at time t. Secondly, the proof of the no-increase theorem of S$\text{a}\text{?}$siada (referring to the initial time) is valid only for the Markov type of time evolution, while the KSS entropy can be generalized to time evolution with arbitrary time correlations. Some important consequences of the new concept for the formulation of the quantum information theory are also presented.