Entanglement and discord assisted entropic uncertainty relations under decoherence

The uncertainty principle is a crucial aspect of quantum mechanics.It has been shown that quantum entanglement as well as more general notions of correlations,such as quantum discord,can relax or tighten the entropic uncertainty relation in the presence of an ancillary system.We explored the behaviour of entropic uncertainty relations for system of two qubits—one of which subjects to several forms of independent quantum noise,in both Markovian and non-Markovian regimes.The uncertainties and their lower bounds,identified by the entropic uncertainty relations,increase under independent local unital Markovian noisy channels,but they may decrease under non-unital channels.The behaviour of the uncertainties(and lower bounds)exhibit periodical oscillations due to correlation dynamics under independent non-Markovian reservoirs.In addition,we compare different entropic uncertainty relations in several special cases and find that discord-tightened entropic uncertainty relations offer in general a better estimate of the uncertainties in play.     

The uncertainty and quantum correlation of measurement in double quantum-dot systems

In this work, we study the entropic uncertainty and quantum discord in two double-quantum-dot (DQD) system coupled via a transmission line resonator (TLR). Explicitly, the dynamics of the systemic quantum correlation and measured uncertainty are analysed with respect to a general X-type state as the initial state. Interestingly, it is found that the different parameters, including the eigenvalue α of the coherent state, detuning amount δ, frequency ω and the coupling constant g, have subtle effects on the dynamics of the entropic uncertainty, such as the oscillation period of the uncertainty. It is clear to reveal that the quantum discord and the lower bound of the entropic uncertainty are anti-correlated when the initial state of the system is the Werner-type state, while quantum discord and the lower bound of the entropic uncertainty are not anti-correlated when the initial state of the system is the Bell-diagonal state. Thereby, we claim that the current investigation would provide an insight into the entropic uncertainty and quantum correlation in DQDs system, and are basically of importance to quantum precision measurement in practical quantum information processing.     

Relativity,thermodynamics and entropic forces

A recent assertion that inertial and gravitational forces are entropic forces is discussed. A more conventional approach is stressed herein, whereby entropy is treated as a result of relative motion between observers in different frames of reference. It is demonstrated that the entropy associated with inertial and gravitational forces is dependent upon the well known lapse function of general relativity. An interpretation of the temperature and entropy of an accelerating body is then developed, and used to relate the entropic force to Newton's second law of motion. The entropic force is also derived in general coordinates. An expression of the gravitational entropy of in‐falling matter is then derived by way of Schwarzschild coordinates. As a final consideration, the entropy of a weakly gravitating matter distribution is shown to be proportional to the self‐energy and the stress‐energy‐momentum content of the matter distribution.     

General Entropic Approximations for Canonical Systems Described by Kinetic Equations

In this paper we extend the general construction of entropic approximation for kinetic operators modelling canonical systems. More precisely, this paper aims at pursuing to thermalized systems the works of Levermore, Schneider and Junk on moments problems relying on entropy minimization in order to construct BGK approximations and moments based equations.     

Invariance Properties of the Entropy Production,and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems

This study examines the invariance properties of the thermodynamic entropy production in its global (integral), local (differential), bilinear, and macroscopic formulations, including dimensional scaling, invariance to fixed displacements, rotations or reflections of the coordinates, time antisymmetry, Galilean invariance, and Lie point symmetry. The Lie invariance is shown to be the most general, encompassing the other invariances. In a shear-flow system involving fluid flow relative to a solid boundary at steady state, the Galilean invariance property is then shown to preference a unique pair of inertial frames of reference—here termed an entropic pair—respectively moving with the solid or the mean fluid flow. This challenges the Newtonian viewpoint that all inertial frames of reference are equivalent. Furthermore, the existence of a shear flow subsystem with an entropic pair different to that of the surrounding system, or a subsystem with one or more changing entropic pair(s), requires a source of negentropy—a power source scaled by an absolute temperature—to drive the subsystem. Through the analysis of different shear flow subsystems, we present a series of governing principles to describe their entropic pairing properties and sources of negentropy. These are unaffected by Galilean transformations, and so can be understood to “lie above” the Galilean inertial framework of Newtonian mechanics. The analyses provide a new perspective into the field of entropic mechanics, the study of the relative motions of objects with friction.     

Entropic accelerating universe

To accommodate the observed accelerated expansion of the universe, one popular idea is to invoke a driving term in the Friedmann–Lemaître equation of dark energy which must then comprise 70% of the present cosmological energy density. We propose an alternative interpretation which takes into account the entropy and temperature intrinsic to the horizon of the universe due to the information holographically stored there. Dark energy is thereby obviated and the acceleration is due to an entropic force naturally arising from the information storage on the horizon surface screen. We consider an additional quantitative approach inspired by surface terms in general relativity and show that this leads to the entropic accelerating universe.     

Entropic entanglement criteria for Fermion systems

Entanglement criteria for general (pure or mixed) states of systems consisting of two identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total system, on the one hand, and the entropy of the one-particle reduced density matrix, on the other hand. A majorization-related relation between these two density matrices is obtained, leading to a family of entanglement criteria based on Rényi’s entropic measure. These criteria are applied to various illustrative examples of parametrized families of mixed states. The dependence of the entanglement detection efficiency on Rényi’s entropic parameter is investigated. The extension of these criteria to systems of N identical fermions is also considered.     

On thermodynamics and gravity

Physics of Atomic Nuclei - A new entropic gravity inspired derivation of general relativity from thermodynamics is presented. This generalizes the “Thermodynamics of Spacetime” approach...     

Entropy and Entropic Forces to Model Biological Fluids

Living cells are complex systems characterized by fluids crowded by hundreds of different elements, including, in particular, a high density of polymers. They are an excellent and challenging laboratory to study exotic emerging physical phenomena, where entropic forces emerge from the organization processes of many-body interactions. The competition between microscopic and entropic forces may generate complex behaviors, such as phase transitions, which living cells may use to accomplish their functions. In the era of big data, where biological information abounds, but general principles and precise understanding of the microscopic interactions is scarce, entropy methods may offer significant information. In this work, we developed a model where a complex thermodynamic equilibrium resulted from the competition between an effective electrostatic short-range interaction and the entropic forces emerging in a fluid crowded by different sized polymers. The target audience for this article are interdisciplinary researchers in complex systems, particularly in thermodynamics and biophysics modeling.     

No-broadcasting theorem and its classical counterpart

Although it is widely accepted that "no-broadcasting"-the nonclonability of quantum information-is a fundamental principle of quantum mechanics, an impossibility theorem for the broadcasting of general density matrices has not yet been formulated. In this Letter, we present a general proof for the no-broadcasting theorem, which applies to arbitrary density matrices. The proof relies on entropic considerations, and as such can also be directly linked to its classical counterpart, which applies to probabilistic distributions of statistical ensembles.     

Reducing the Entropic Uncertainty via Non-Markovian Effect and Detuning in the Presence of Quantum Memory ∗

The influence of non-Markovian effect and detuning on the entropic uncertainty in the presence of quantum memory is studied by the time-convolutionless master-equation approach. The result shows that the entropic uncertainty in the presence of quantum memory is obviously dependent on both detuning and non-Markovian effect. The bigger the detuning is and the stronger the non-Markovian effect is, the smaller the entropic uncertainty is. Its physical explanation is that the known quantum information stored in the quantum memory can reduce or eliminate the entropic uncertainty about the measurement outcomes of another particle, which is entangled with the quantum memory.     

Controlling Entropic Uncertainty in the Presence of Quantum Memory by Non-Markovian Effects and Atom-Cavity Couplings

Based on the time-convolutionless master-equation approach,the entropic uncertainty in the presence of quantum memory is investigated for a two-atom system in two dissipative cavities.We find that the entropic uncertainty can be controlled by the non-Markovian effect and the atom-cavity coupling.The results show that increasing the atom-cavity coupling can enlarge the oscillating frequencies of the entropic uncertainty and can decrease the minimal value of the entropic uncertainty.Enhancing the non-Markovian effect can reduce the minimal value of the entropic uncertainty.In particular,if the atom-cavity coupling or the non-Markovian effect is very strong,the entropic uncertainty will be very close to zero at certain time points,thus Bob can minimize his uncertainty about Alice's measurement outcomes.     

Entropic Uncertainty in Neutrino and Meson Systems

The dynamics of quantum‐memory‐assisted entropic uncertainty for the closed neutrino system in the context of two flavor oscillations and the meson system within the framework of open quantum system are investigated. It is found that the entropic uncertainty exists in close relation with the quantum correlation, and growing quantum correlation can decrease the uncertainty. The oscillatory behaviors of entropic uncertainty in neutrino system brought about by neutrino oscillating property are different from the decaying behaviors of entropic uncertainty in meson system induced by the meson decaying nature. In addition, the entropic uncertainty is always equal to its lower bound in the two subatomic systems. This study would throw light on the particle behavior characteristics of high energy physics, and may be useful to the tasks of quantum information‐processing implemented with subatomic system since the uncertainty principle plays vital role in quantum information science and technology.     

Entropic uncertainty relation of a qubit-qutrit Heisenberg spin model and its steering

We investigate the quantum-memory-assisted entropic uncertainty relation (QMA-EUR) in a Heisenberg XYZ mixed-spin (1/2, 1) model. Coupling strength, Dzyaloshinskii-Moriya (DM) interaction and inhomogeneous magnetic field, respectively, contributing to QMA-EUR by a thermal entanglement in the hybrid-spin model are studied in detail. Furthermore, we compare the uncertainty of the bipartite hybrid model with those of qubit-qubit and qutrit-qutrit systems. Meanwhile, the effects of local PT-symmetric operation and weak measurement on the steering of entropic uncertainty are analyzed. We find that the local PT-symmetric operation can reduce the entropic uncertainty, and the entropic uncertainty can also be decreased by weak measurement reversal.     

A Tsallis’ statistics based neural network model for novel word learning

We invoke the Tsallis entropy formalism, a nonextensive entropy measure, to include some degree of non-locality in a neural network that is used for simulation of novel word learning in adults. A generalization of the gradient descent dynamics, realized via nonextensive cost functions, is used as a learning rule in a simple perceptron. The model is first investigated for general properties, and then tested against the empirical data, gathered from simple memorization experiments involving two populations of linguistically different subjects. Numerical solutions of the model equations corresponded to the measured performance states of human learners. In particular, we found that the memorization tasks were executed with rather small but population-specific amounts of nonextensivity, quantified by the entropic index q. Our findings raise the possibility of using entropic nonextensivity as a means of characterizing the degree of complexity of learning in both natural and artificial systems.     

Improving statistical keyword detection in short texts: Entropic and clustering approaches

In the last years, two successful approaches have been introduced to tackle the problem of statistical keyword detection in a text without the use of external information: (i) The entropic approach, where Shannon’s entropy of information is used to quantify the information content of the sequence of occurrences of each word in the text; and (ii) The clustering approach, which links the heterogeneity of the spatial distribution of a word in the text (clustering) with its relevance. In this paper, first we present some modifications to both techniques which improve their results. Then, we propose new metrics to evaluate the performance of keyword detectors based specifically on the needs of a typical user, and we employ them to find out which approach performs better. Although both approaches work well in long texts, we obtain in general that measures based on word-clustering perform at least as well as the entropic measure, which needs a convenient partition of the text to be applied, such as chapters of a book. In the latter approach we also show that the partition of the text chosen affects strongly its results. Finally, we focus on short texts, a case of high practical importance, such as short reports, web pages, scientific articles, etc. We show that the performance of word-clustering measures is also good in generic short texts since these measures are able to discriminate better the degree of relevance of low frequency words than the entropic approach.     

Subadditivity Condition for Spin Tomograms and Density Matrices of Arbitrary Composite and Noncomposite Qudit Systems

We obtain a new quantum entropic inequality for the states of a system of n ≥ 1 qudits. The inequality has the form of the quantum subadditivity condition of a bipartite qudit system and coincides with the subadditivity condition for the system of two qudits. We formulate a general statement on the existence of the subadditivity condition for an arbitrary probability distribution and an arbitrary qudit-system tomogram. We discuss the nonlinear quantum channels creating the entangled states from separable states.     

Reduction of entropic uncertainty in entangled qubits system by local PT-symmetric operation

We investigate the quantum-memory-assisted entropic uncertainty for an entangled two-qubit system in a local quantum noise channel with PT-symmetric operation performing on one of the two particles. Our results show that the quantum-memory-assisted entropic uncertainty in the qubits system can be reduced effectively by the local PT-symmetric operation. Physical explanations for the behavior of the quantum-memory-assisted entropic uncertainty are given based on the property of entanglement of the qubits system and the non-locality induced by the re-normalization procedure for the non-Hermitian PT-symmetric operation.     

Correct thermodynamic forces in Tsallis thermodynamics: connection with Hill nanothermodynamics

The equivalence between Tsallis thermodynamics and Hill's nanothermodynamics is established. The correct thermodynamic forces in Tsallis thermodynamics are pointed out. Through this connection we also find a general expression for the entropic index q which we illustrate with two physical examples, allowing in both cases to relate q to the underlying dynamics of the Hamiltonian systems.