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1.
In this paper, we introduce and investigate the mutual information and relative entropy on the sequential effect algebra, we also give a comparison of these mutual information and relative entropy with the classical ones by the venn diagrams. Finally, a nice example shows that the entropies of sequential effect algebra depend extremely on the order of its sequential product. 相似文献
2.
Jiamei Wang Xiaomin Gao Minhyung Cho 《International Journal of Theoretical Physics》2014,53(8):2739-2745
In this paper, for a given quantum state s on the sequential effect algebra, we introduce the sequential independence of two partitions and refinements with respect to the quantum state s. Under these conditions, we study some interesting properties of partition entropy. 相似文献
3.
Using standard statistical method, we discover the existence of correlations among Hawking radiations (of tunneled particles) from a black hole. The information carried by such correlations is quantified by mutual information between sequential emissions. Through a careful counting of the entropy taken out by the emitted particles, we show that the black hole radiation as tunneling is an entropy conservation process. While information is leaked out through the radiation, the total entropy is conserved. Thus, we conclude the black hole evaporation process is unitary. 相似文献
4.
Belavkin–Staszewski relative entropy can naturally characterize the effects of the possible noncommutativity of quantum states. In this paper, two new conditional entropy terms and four new mutual information terms are first defined by replacing quantum relative entropy with Belavkin–Staszewski relative entropy. Next, their basic properties are investigated, especially in classical-quantum settings. In particular, we show the weak concavity of the Belavkin–Staszewski conditional entropy and obtain the chain rule for the Belavkin–Staszewski mutual information. Finally, the subadditivity of the Belavkin–Staszewski relative entropy is established, i.e., the Belavkin–Staszewski relative entropy of a joint system is less than the sum of that of its corresponding subsystems with the help of some multiplicative and additive factors. Meanwhile, we also provide a certain subadditivity of the geometric Rényi relative entropy. 相似文献
5.
从量子相干性包括l1 norm相干性和量子相对熵相干性的角度建立了判定开放量子系统中非马尔可夫过程的方法, 并给出了相应的判别条件. 作为它们的具体应用, 研究了一个两能级系统分别经历相位衰减通道、 随机幺正通道和振幅耗散通道作用时对应的非马尔可夫过程发生必须满足的条件. 对于三种通道模型, 得到了l1 norm相干性对系统任意态非马尔可夫过程发生的判别条件, 并发现在相位衰减通道和振幅耗散通道中其非马尔可夫过程发生 的条件与用其他方式如信息回流、可分性和量子互熵给出的条件是相同的, 而在随机幺正通道中给出了一个新的且不完全等价于基于信息回流和可分性对应的条件. 至于量子相对熵相干性, 在相位衰减通道中得到了对系统任意态的非马尔可夫过程发生的具体条件, 并发现该条件也等同于基于信息回流、可分性和量子互熵给出的条件. 而在随机幺正通道和振幅耗散通道中得到了系统最大相干态对应的非马尔可夫过程发生的条件. 相似文献
6.
Jonas Maziero 《Brazilian Journal of Physics》2014,44(2-3):194-201
Using the relative entropy of total correlation, we derive an expression relating the mutual information of n-partite pure states to the sum of the mutual informations and entropies of its marginals and analyze some of its implications. Besides, by utilizing the extended strong subadditivity of von Neumann entropy, we obtain generalized monogamy relations for the total correlation in three-partite mixed states. These inequalities lead to a tight lower bound for this correlation in terms of the sum of the bipartite mutual informations. We use this bound to propose a measure for residual three-partite total correlation and discuss the non-applicability of this kind of quantifier to measure genuine multiparty correlations. 相似文献
7.
Lin Zhang 《Letters in Mathematical Physics》2016,106(4):557-573
We derive a strengthened monotonicity inequality for quantum relative entropy by employing properties of \({\alpha}\)-Rényi relative entropy. We develop a unifying treatment toward the improvement of some quantum entropy inequalities. In particular, an emphasis is put on a lower bound of quantum conditional mutual information (QCMI) as it gives a Pinsker-like lower bound for the QCMI. We also give some improved entropy inequalities based on Rényi relative entropy. The inequalities obtained, thus, extend some well-known ones. We also obtain a condition under which a tripartite operator becomes a Markov state. As a by-product we provide some trace inequalities of operators, which are of independent interest. 相似文献
8.
Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is shown to depend on the availability of classical information about particular members of the ensemble. Based on this, relations between relative entropy of entanglement and mutual information are derived. 相似文献
9.
N. Watanabe 《Russian Journal of Mathematical Physics》2014,21(3):408-420
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. 相似文献
10.
Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states. In contrast, Petz showed that the measured relative entropy, defined as a maximization of the Kullback–Leibler divergence over projective measurement statistics, is strictly smaller than Umegaki’s quantum relative entropy whenever the states do not commute. We extend this result in two ways. First, we show that Petz’ conclusion remains true if we allow general positive operator-valued measures. Second, we extend the result to Rényi relative entropies and show that for non-commuting states the sandwiched Rényi relative entropy is strictly larger than the measured Rényi relative entropy for \(\alpha \in (\frac{1}{2}, \infty )\) and strictly smaller for \(\alpha \in [0,\frac{1}{2})\). The latter statement provides counterexamples for the data processing inequality of the sandwiched Rényi relative entropy for \(\alpha < \frac{1}{2}\). Our main tool is a new variational expression for the measured Rényi relative entropy, which we further exploit to show that certain lower bounds on quantum conditional mutual information are superadditive. 相似文献
11.
Eissa D. Habil 《International Journal of Theoretical Physics》2008,47(1):280-290
A distributive sequential effect algebra (DSEA) is an effect algebra on which a distributive sequential product with natural
properties is defined. We define the tensor product of two arbitrary DSEA’s and we give a necessary and sufficient condition
for it to exist. As a corollary we obtain the result (see Gudder, S. in Math. Slovaca 54:1–11, 2004, to appear) that the tensor product of a pair of commutative sequential effect algebras exists if and only if they admit
a bimorphism. We further obtain a similar result for the tensor product of a pair of product effect algebras. 相似文献
12.
Uniqueness and Order in Sequential Effect Algebras 总被引:2,自引:0,他引:2
A sequential effect algebra (SEA) is an effect algebra on which a sequential product is defined. We present examples of effect
algebras that admit a unique, many and no sequential product. Some general theorems concerning unique sequential products
are proved. We discuss sequentially ordered SEAs in which the order is completely determined by the sequential product. It
is demonstrated that intervals in a sequential ordered SEA admit a sequential product. 相似文献
13.
14.
Josef Tkadlec 《International Journal of Theoretical Physics》2008,47(1):185-192
Various conditions ensuring that a sequential effect algebra or the set of sharp elements of a sequential effect algebra is
a Boolean algebra are presented. 相似文献
15.
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
16.
J. S. Zhang L. Chen M. Abdel-Aty A. X. Chen 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2012,66(1):2
We study the dynamics of quantum discord and entanglement of two entangled two-level
atoms within two isolated and dissipative cavities in the weak- or strong-coupling regime.
The quantum entanglement are measured by concurrence and relative entropy. The quantum
discord of two atoms based on quantum mutual information and relative entropy are also
calculated. In the weak-coupling regime, the sudden death of quantum discord and
entanglement of two atoms can occur simultaneously within a short interaction time. When
the interaction time is long, quantum discord and entanglement of two atoms could be
partially preserved due to the long-lived nature of quantum discord and entanglement.
However, in the strong-coupling regime, there is no sudden death of quantum discord though
the entanglement sudden death phenomenon occurs. In addition, we observe that entanglement
and discord will be destroyed eventually when the atom-field interactions are strong. We
also address the issue of experimental realization briefly. 相似文献
17.
Jiyong Park 《Entropy (Basel, Switzerland)》2022,24(7)
We derive accessible upper and lower bounds for continuous-variable (CV) quantum states on quantum mutual information. The derivations are based on the observation that some functions of purities bound the difference between quantum mutual information of a quantum state and its Gaussian reference. The bounds are efficiently obtainable by measuring purities and the covariance matrix without multimode quantum state reconstruction. We extend our approach to the upper and lower bounds for the quantum total correlation of CV multimode quantum states. Furthermore, we investigate the relations of the bounds for the quantum mutual information with the bounds for the quantum conditional entropy. 相似文献
18.
XING Xiusan 《中国科学G辑(英文版)》2006,49(1):1-37
In recent years we extended Shannon static statistical information theory to dynamic processes and established a Shannon dynamic
statistical information theory, whose core is the evolution law of dynamic entropy and dynamic information. We also proposed
a corresponding Boltzmman dynamic statistical information theory. Based on the fact that the state variable evolution equation
of respective dynamic systems, i.e. Fokker-Planck equation and Liouville diffusion equation can be regarded as their information
symbol evolution equation, we derived the nonlinear evolution equations of Shannon dynamic entropy density and dynamic information
density and the nonlinear evolution equations of Boltzmann dynamic entropy density and dynamic information density, that describe
respectively the evolution law of dynamic entropy and dynamic information. The evolution equations of these two kinds of dynamic
entropies and dynamic informations show in unison that the time rate of change of dynamic entropy densities is caused by their
drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes;
and that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in
state variable space inside the systems and coordinate space in the transmission processes. Entropy and information have been
combined with the state and its law of motion of the systems. Furthermore we presented the formulas of two kinds of entropy
production rates and information dissipation rates, the expressions of two kinds of drift information flows and diffusion
information flows. We proved that two kinds of information dissipation rates (or the decrease rates of the total information)
were equal to their corresponding entropy production rates (or the increase rates of the total entropy) in the same dynamic
system. We obtained the formulas of two kinds of dynamic mutual informations and dynamic channel capacities reflecting the
dynamic dissipation characteristics in the transmission processes, which change into their maximum—the present static mutual
information and static channel capacity under the limit case where the proportion of channel length to information transmission
rate approaches to zero. All these unified and rigorous theoretical formulas and results are derived from the evolution equations
of dynamic information and dynamic entropy without adding any extra assumption. In this review, we give an overview on the
above main ideas, methods and results, and discuss the similarity and difference between two kinds of dynamic statistical
information theories. 相似文献
19.
J. Cao S.-J. Gu Y. Wang H.-Q. Lin 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,63(1):147-151
The critical behaviors of the entropy correlation
effects in the one dimensional J1-J2 Heisenberg model are
studied. It is shown that the mutual information or the
correlation entropy captures the key features of information about
critical fluctuations and can be used to quantify the quantum and
finite-temperature phase transitions. At the critical point, the
mutual information is power-law decay and the entanglement
correlation length is infinite. While far away from the critical
point, the mutual information is exponential decay and the
entanglement correlation length is finite. A universal property of
the mutual information is also found. Based on the critical
behaviors of the mutual information, a new method to quantify the
infinite order phase transition in the system is proposed. 相似文献
20.
Giovanazzi S 《Physical review letters》2011,106(1):011302
A method to investigate acoustic Hawking radiation is proposed, where entanglement entropy and mutual information are measured from the fluctuations of the number of particles. The rate of entropy radiated per one-dimensional (1D) channel is given by S=κ/12, where κ is the sound acceleration on the sonic horizon. This entropy production is accompanied by a corresponding formation of mutual information to ensure the overall conservation of information. The predictions are confirmed using an ab initio analytical approach in transonic flows of 1D degenerate ideal Fermi fluids. 相似文献