共查询到20条相似文献,搜索用时 111 毫秒
1.
Antonio Zecca 《International Journal of Theoretical Physics》2008,47(9):2230-2236
Aspects of quantum entropy and relative quantum entropy are discussed in the Hilbert model. It is shown that finite values
of the relative entropy of states implies a superposition relation between the states. The property is studied in case of
tensor product of states and for state reductions. A “Schmidt-like” state, derived from the reduced states, is considered.
It is shown that its entropy, relative to the product of the reduced states, is not smaller than the entropy of the reduced
states. The main existing results concerning the changement of superposition and entropy under dynamical map are recalled
in a uniform way. A class of possible dynamical maps, not necessarily linear, is proposed that do not decrease the entropy. 相似文献
2.
The joint state of a system that is in contact with an environment is called lazy, if the entropy rate of the system under any coupling to the environment is zero. Necessary and sufficient conditions have recently been established for a state to be lazy [Phys. Rev. Lett. 106, 050403 (2011)], and it was shown that almost all states of the system and the environment do not have this property [Phys. Rev. A 81, 052318 (2010)]. At first glance, this may lead us to believe that low entropy rates themselves form an exception, in the sense that most states are far from being lazy and have high entropy rates. Here, we show that in fact the opposite is true if the environment is sufficiently large. Almost all states of the system and the environment are pretty lazy-their entropy rates are low for any coupling to the environment. 相似文献
3.
4.
Christopher Briscoe 《Physica A》2010,389(19):3978-455
The nature of randomness in disordered packings of frictional and frictionless spheres is investigated using theory and simulations of identical spherical grains. The entropy of the packings is defined through the force and volume ensemble of jammed matter and this is shown to be difficult to calculate analytically. A mesoscopic ensemble of isostatic states is then utilized in an effort to predict the entropy through the definition of a volume function that is dependent on the coordination number. Equations of state are obtained relating entropy, volume fraction and compactivity characterizing the different states of jammed matter, and elucidating the phase diagram for jammed granular matter. Analytical calculations are compared to numerical simulations using volume fluctuation analysis and graph theoretical methods, with reasonable agreement. The entropy of the jammed system reveals that random loose packings are more disordered than random close packings, allowing for an unambiguous interpretation of both limits. Ensemble calculations show that the entropy vanishes at random close packing (RCP), while numerical simulations show that a finite entropy remains in the microscopic states at RCP. The notion of a negative compactivity, which explores states with volume fractions below those achievable by existing simulation protocols, is also explored, expanding the equations of state. The mesoscopic theory reproduces the simulations results in shape well, though a difference in magnitude implies that the entire entropy of the packing may not be captured by the methods presented herein. We discuss possible extensions to the present mesoscopic approach describing packings from random loose packing (RLP) to RCP to the ordered branch of the equation of state in an effort to understand the entropy of jammed matter in the full range of densities from RLP to face-centered cubic (FCC) packing. 相似文献
5.
A generalized definition of entropy for any state on aC* algebra is given and studied. We prove that the entropy characterizes uniquely the normal states. 相似文献
6.
Two closest single-qubit states could be diagonalised by the same unitary matrix,which helps to find the relative entropy of entanglement of a two-qubit ’X’ state.We formulate two binary equations for the relative entropy of entanglement and the corresponding closest separable state of a given two-qubit ’X’ state.This approach can be applied to get the relative entropy of entanglement of many widely-discussed two-qubit states,such as pure states,Werner states,and so on. 相似文献
7.
Vladimir N. Chernega Olga V. Man’ko Vladimir I. Man’ko Oleg V. Pilyavets Vadim G. Zborovskii 《Journal of Russian Laser Research》2006,27(2):132-166
Spin states are studied in the tomographic-probability representation. The standard probability distribution of spin projection
onto a direction in space is used instead of the spinor or the density matrix to identify the quantum state. The Shannon entropy
and information are associated with the spin tomographic probability. A short review of the probability-theory notions is
presented. Analysis of tomographic entropy and tomographic information for the Werner state is considered. The probability
representation is used to describe a spin-3/2 particle and two qubits. The connection of tomographic entropy with the von
Neumann entropy is discussed. 相似文献
8.
Giacomo De Palma 《Letters in Mathematical Physics》2018,108(9):2139-2152
We prove two new fundamental uncertainty relations with quantum memory for the Wehrl entropy. The first relation applies to the bipartite memory scenario. It determines the minimum conditional Wehrl entropy among all the quantum states with a given conditional von Neumann entropy and proves that this minimum is asymptotically achieved by a suitable sequence of quantum Gaussian states. The second relation applies to the tripartite memory scenario. It determines the minimum of the sum of the Wehrl entropy of a quantum state conditioned on the first memory quantum system with the Wehrl entropy of the same state conditioned on the second memory quantum system and proves that also this minimum is asymptotically achieved by a suitable sequence of quantum Gaussian states. The Wehrl entropy of a quantum state is the Shannon differential entropy of the outcome of a heterodyne measurement performed on the state. The heterodyne measurement is one of the main measurements in quantum optics and lies at the basis of one of the most promising protocols for quantum key distribution. These fundamental entropic uncertainty relations will be a valuable tool in quantum information and will, for example, find application in security proofs of quantum key distribution protocols in the asymptotic regime and in entanglement witnessing in quantum optics. 相似文献
9.
Z. Alexandrowicz 《Journal of statistical physics》1976,14(1):1-9
Entropy is related to the frequency of states for individual particles. Taking the Ising lattice as an example, a local state for an individual spin is defined by the orientation of the spin and of its neighbors. The ratio of the frequencies of two local states involved in a spin-flipping conflgurational transition is related to an entropy change. Implementation is by computer simulation. A stochastic process is used to construct an initial lattice configuration, corresponding to state of known entropy. This configuration is subsequently relaxed to a desired equilibrium state, with the help of a (uniform Metropolis) Monte Carlo spin flipping and the attendant entropy change is calculated from the sequence of frequency ratios for all transitions. The calculation is approximate since it treats a process that can be described by a hypothetical sequence of states at internal equilibrium, which cannot be true for a relaxation at finite rate. Nonetheless, the results obtained have been quite accurate. The theory, therefore, provides an additional method for measuring the entropy of systems simulated with the help of a computer. It also indicates a practical way for bridging the Boltzmann entropy of individual particle states (which Jaynes has shown to be incorrect, in its original form, for strongly interacting particles), to the Gibbs entropy ofN-particle configurations. 相似文献
10.
A fundamental difficulty in demonstrating quantum state tomography is that the required resources grow exponentially with the system size. For pure states and nearly pure states, the task of tomography can be more efficient. We proposed two methods for state reconstruction, by (1) minimizing entropy and (2) maximizing likelihood. The algorithm of compressed sampling is employed to solve the optimization problem. Experiments are demonstrated considering 4-qubit photonic states. The results show that (1) much fewer measurements than the standard tomography are sufficient to obtain high fidelity, and (2) the method of maximizing likelihood is more accurate and noise robust than the original reconstruction method of compressed sampling. Furthermore, the physical meaning of the methods of minimizing entropy and maximizing likelihood is clear. 相似文献
11.
Etang Chen 《Reports on Mathematical Physics》1977,11(2):189-195
Given a faithful normal state ? of a von Neumann algebra M, entropy and relative entropy for normal states of M are defined by Radon-Nikodyn derivatives of normal states with respect to ?. Most properties of entropy and relative entropy in finite quantum systems are shown to hold. It is also shown that the finiteness of relative entropy is related to the facial superposition principle in quantum theory [5]. 相似文献
12.
Subhash Kak 《International Journal of Theoretical Physics》2007,46(4):860-876
Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. This entropy for an unknown
pure state is zero, although repeated measurements on copies of such a pure state do communicate information. In view of this,
we propose a new measure for the informational entropy of a quantum state that includes information in the pure states and
the thermodynamic entropy. The origin of information is explained in terms of an interplay between unitary and non-unitary
evolution. Such complementarity is also at the basis of the so-called interaction-free measurement. 相似文献
13.
14.
Partovi MH 《Physical review letters》2004,92(7):077904
A general framework is developed for separating classical and quantum correlations in a multipartite system. Entanglement is defined as the difference in the correlation information encoded by the state of a system and a suitably defined separable state with the same marginals. A generalization of the Schmidt decomposition is developed to implement the separation of correlations for any pure, multipartite state. The measure based on this decomposition is a generalization of the entanglement of formation to multipartite systems, provides an upper bound for the relative entropy of entanglement, and is directly computable on pure states. The example of pure three-qubit states is analyzed in detail, and a classification based on minimal, four-term decompositions is developed. 相似文献
15.
A Gaussian degree of entanglement for a symmetric two-mode Gaussian
state can be defined as its distance to the set of all separable two-mode Gaussian
states. The principal property that enables us to evaluate both Bures distance and relative entropy between symmetric two-mode
Gaussian
states is the diagonalization of their covariance matrices under the same beam-splitter transformation. The multiplicativity
property of the Uhlmann fidelity and the additivity of the relative entropy allow one to finally deal with a single-mode optimization
problem in both cases. We find that only
the Bures-distance Gaussian entanglement
is consistent with the exact entanglement of formation. 相似文献
16.
为了研究三光子过程中原子与相干态耦合量子体系信息熵压缩随时间演化规律及原子最佳信息熵压缩态的制备,我们采用全量子理论,推导出运动原子与单模简并三光子依赖强度耦合量子体系的精确解;理论上给出制备原子最佳信息熵压缩态的充分及必要条件,并进行了数值模拟验证.研究结果表明:控制相干态场与原子作用时间,切断相干态场与原子的纠缠,选择二能级原子处于等权重相干叠加态,适当选取相干态场与原子的初始位相,可以制备出原子最佳量子信息熵压缩态;调节光腔中场模结构参量,能够得到连续的量子信息熵压缩态.该研究结果在多光子过程低噪声量子信息处理中具有一定意义. 相似文献
17.
为了研究三光子过程中原子与相干态耦合量子体系信息熵压缩随时间演化规律及原子最佳信息熵压缩态的制备,我们采用全量子理论,推导出运动原子与单模简并三光子依赖强度耦合量子体系的精确解;理论上给出制备原子最佳信息熵压缩态的充分及必要条件,并进行了数值模拟验证。研究结果表明:控制相干态场与原子作用时间,切断相干态场与原子的纠缠,选择二能级原子处于等权重相干叠加态,适当选取相干态场与原子的初始位相,可以制备出原子最佳量子信息熵压缩态;调节光腔中场模结构参量,能够得到连续的量子信息熵压缩态。该研究结果在多光子过程低噪声量子信息处理中具有一定意义。 相似文献
18.
19.
C. Pinzari Y. Watatani--RID=""--> K. Yonetani 《Communications in Mathematical Physics》2000,213(2):331-379
To any periodic and full C
*-dynamical system , an invertible operator s acting on the Banach space of trace functionals of the fixed point algebra is canonically associated. KMS states correspond
to positive eigenvectors of s. A Perron–Frobenius type theorem asserts the existence of KMS states at inverse temperatures equals the logarithms of the
inner and outer spectral radii of s (extremal KMS states). Examples arising from subshifts in symbolic dynamics, self-similar sets in fractal geometry and noncommutative
metric spaces are discussed.
Certain subshifts are naturally associated to the system, and criteria for the equality of their topological entropy and inverse
temperatures of extremal KMS states are given.
Unital completely positive maps implemented by partitions of unity {x
j
} of grade 1 are considered, resembling the “canonical endomorphism” of the Cuntz algebras. The relationship between the Voiculescu
topological entropy of and the topological entropy of the associated subshift is studied. Examples where the equality holds are discussed among
Matsumoto algebras associated to non finite type subshifts. In the general case is bounded by the sum of the entropy of the subshift and a suitable entropic quantity of the homogeneous subalgebra. Both
summands are necessary.
The measure-theoretic entropy of , in the sense of Connes–Narnhofer–Thirring, is compared to the classical measure-theoretic entropy of the subshift.
A noncommutative analogue of the classical variational principle for the entropy is obtained for the “canonical endomorphism”
of certain Matsumoto algebras. More generally, a necessary condition is discussed. In the case of Cuntz–Krieger algebras an
explicit construction of the state with maximal entropy from the unique KMS state is done.
Received: 1 February 2000 / Accepted: 23 February 2000 相似文献
20.
According to the chemical kinetic model of lysogeny/lysis switch in Escherichia coli (E. coli) infected by bacteriophage λ, the entropy production rates of steady states are calculated. The results show that the lysogenic state has lower entropy production rate than lytic state, which provides an explanation on why the lysogenic state of λ phage is so stable. We also notice that the entropy production rates of both lysogenic state and lytic state are lower than that of saddle-point and bifurcation state, which is consistent with the principle of minimum entropy production for living organism in nonequilibrium stationary state. Subsequently, the relations between CI and Cro degradation rates at two bifurcations and the changes of entropy production rate with CI and Cro degradation are deduced. The theory and method can be used to calculate entropy change in other molecular network. 相似文献