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A reanalysis of unpolarized electron-proton elastic scattering data is done in terms of the electric to magnetic form factor squared ratio. This observable is in principle more robust against experimental correlations and global normalizations. The present analysis shows indeed that it is a useful quantity that contains reliable and coherent information. The comparison with the ratio extracted from the measurement of the longitudinal to transverse polarization of the recoil proton in polarized electron-proton scattering shows that the results are compatible within the experimental errors. Limits are set on the kinematics where the physical information on the form factors can be safely extracted. The results presented in this work bring a decisive piece of information to the controversy on the deviation of the proton form factors from the dipole dependence., 18 pages 13 figures, 11 tables- Updated version for Phys. Rev. C

In the present article we address the question 'What is quantum information?' from a conceptual viewpoint. In particular, we argue that there seems to be no sufficiently good reasons to accept that quantum information is qualitatively different from classical information. The view that, in the communicational context, there is only one kind of information, physically neutral, which can be encoded by means of classical or quantum states has, in turn, interesting conceptual advantages. First, it dissolves the widely discussed puzzles of teleportation without the need to assume a particular interpretation of information. Second, and from a more general viewpoint, it frees the attempts to reconstruct quantum mechanics on the basis of informational constraints from any risk of circularity; furthermore, it endows them with a strong conceptual appealing and, derivatively, opens the way to the possibility of a non-reductive unification of physics. Finally, in the light of the idea of the physical neutrality of information, the wide field of research about classical models for quantum information acquires a particular conceptual and philosophical interest., Instituto de Física La Plata

This chapter aims to introduce the main concepts of the classical zero-error information theory. We begin by defining the zero-error capacity of a discrete memoryless channel and presenting some basic concepts, like adjacency and adjacency-reducing mappings. Then, we show how the problem of finding the zero-error capacity can be stated in terms of a graph quantity. The Lovasz theta function and some of its properties are presented and, lastly, the zero-error capacity of the sum and product of channels is discussed.

2016 IEEE International Symposium on Information Theory (ISIT), ISBN:978-1-5090-1806-2

As well known, wireless channels are characterized by temporal and spatial variations due to different reasons such as multipath propagation of the signals, and mobility of the communicating devices or their surrounding environment. This has two consequences. First, the channel quality (i.e. amplitude) varies resulting in changes in the amount of data rate (in bits/sec) that can be received reliably over the channel. Second, the channel “phase” varies, which necessities the ability of the receiver to track these changes reliably in order to demodulate the transmitted signal correctly. This is called “coherent” transmission. If the receiver is unable to track the phase variations, then the transmitter should use “non-coherent” modulation schemes, which can be detected without phase knowledge at the receiver. However, this will be at the cost of significant degradation of the data rate that can be transmitted reliably. Therefore, modern communication systems are supported with channel estimation algorithms in order to enable coherent reception. However, this is not always feasible. Channel estimation is usually accomplished by transmitting pilot signals with some frequency. Depending on the frequency of pilot transmission and the channel coherence time, some receivers might have reliable channel estimates and other receivers might not have that reliable channel estimates. This is one reason why each mobile wireless standard supports some maximum velocities for the mobile users, limited by the frequency of pilot transmission. Mobile users moving at higher speeds might not have reliable channel estimates and this means that they will not be able to receive any information via coherent transmission.Having this in mind, we are mainly interested in this work in broadcasting systems like mobile TVs. These systems are usually transmitted using coherent modulation schemes in order to enable good quality of reception which cannot be maintained using the “low-rate” non-coherent modulation schemes. Therefore, mobile users with unreliable channel estimates will not be able to receive such applications, while the users with reliable channel estimates can receive the transmitted stream reliably. Therefore, broadcasting applications are characterized by “all or nothing” reception depending on the mobility and the channel conditions of the receiving terminals.Alternatively, we propose a layered coding scheme from a new viewpoint that has not been addressed before in the literature. We propose a layered transmission scheme with two layers, one layer, base-layer (non-coherent-layer), that can be decoded by any receiver even if it does not have reliable channel estimates, and the other, refining-layer (coherent-layer) that can be only decoded at receivers with reliable channel estimates. The basic bits could be transmitted on the first layer and the extra bits that improve quality could be transmitted on the second layer. Therefore, receivers with unreliable channel estimates can decode the non-coherent layer and the receivers with reliable channel estimates can decode all the information and experience better service quality.This proposed scheme can be designed using multi-resolution broadcast space-time coding, which allows the simultaneous transmission of low rate (LR) non-coherent information for all receivers, including those with no channel state information (CSI), and high rate (HR) coherent information to those receivers that have reliable CSI. The proposed scheme ensures that the communication of the HR layer is transparent to the underlying LR layer. We can show that both the non-coherent and coherent receivers achieve full diversity, and that the proposed scheme achieves the maximum number of communication degrees of freedom for non-coherent LR channels and coherent HR channels with unitarily-constrained input signals.

In this chapter, we provide the basic concepts of quantum information processing and quantum information theory. The following topics from quantum information processing will be covered: state vectors, operators, density operators, measurements, dynamics of a quantum system, superposition principle, quantum parallelism, no-cloning theorem, and entanglement. The following concepts from quantum information theory will be provided: Holevo information, accessible information, Holevo bound, Shannon entropy and von Neumann entropy, Schumacher’s noiseless quantum coding theorem, and Holevo–Schumacher–Westmoreland theorem.

We propose constellations of finitely-many coherent states for high-rate quantum and classical communication over the thermal noise Bosonic Gaussian channel. Our constructions are based on constellations for the classical additive white Gaussian noise (AWGN) channel, and we adapt the results of Wu and Verdu [Allerton 2010, pp. 620] for the AWGN to determine achievable rates of classical and quantum information transmission for the thermal noise channel. Several constellations allow classical rates approaching the classical capacity, recently determined by Giovannetti et al. [Nature Photonics 8, 796 (2014)], while in the quantum case the rates approach the Gaussian coherent information. The constellations can also be used for private transmission of classical information at the coherent information rate.

Recently the theory of communication developed by Shannon has been extended to the quantum realm by exploiting the rules of quantum theory. This latter stems on complex vector spaces. However complex (as well as real) numbers are just idealizations and they are not available in practice where we can only deal with rational numbers. This fact naturally leads to the question of whether the developed notions of capacities for quantum channels truly catch their ability to transmit information. Here we answer this question for the quantum capacity. To this end we resort to the notion of semi-computability in order to approximately (by rational numbers) describe quantum states and quantum channel maps. Then we introduce algorithmic entropies (like algorithmic quantum coherent information) and derive relevant properties for them. Finally we define algorithmic quantum capacity and prove that it equals the standard one.

The combination of quantum mechanics and information science results in the quantum information science. Now, conversely, the progress in quantum information field promotes the progress of quantum physics. Here, we review some recent research progress in physics foundation for quantum information, including the concept of quantum correlation and its application, entanglement-assisted entropic uncertainty principle, environmental control and quantitative research of non-Markonianity in dynamics of open quantum systems.

The entropic perspective on the molecular electronic structure is investigated. Information-theoretic description of electron probabilities is extended to cover the complex amplitudes (wave functions) of quantum mechanics. This analysis emphasizes the entropic concepts due to the phase part of electronic states, which generates the probability current density, thus allowing one to distinguish the information content of states generating the same electron density and differing in their current densities. The classical information measures of Fisher and Shannon, due to the probability/density distributions themselves, are supplemented by the nonclassical terms generated by the wave-function phase or the associated probability current. A complementary character of the Fisher and Shannon information measures is explored and the relationship between these classical information densities is derived. It is postulated to characterize also their nonclassical (phase/current-dependent) contributions. The continuity equations of the generalized information densities are examined and the associated nonclassical information sources are identified. The variational rules involving the quantum-generalized Shannon entropy, which generate the stationary and time-dependent Schrodinger equations from the relevant maximum entropy principles, are discussed and their implications for the system “thermodynamic” equilibrium states are examined. It is demonstrated that the lowest, stationary “thermodynamic” state differs from the true ground state of the system, by exhibiting the space-dependent phase, linked to the modulus part of the wave function, and hence also a nonvanishing probability current.

For a pure non-markovian dephasing model we derive analytic expressions of coherent information, quantum discord, and entanglement. We find that for the cases of the initial Werner states, the dynamical behavior of coherent information is similar to that of quantum discord but different from that of entanglement. Coherent information, as well as quantum discord, can reveal the quantum correlations in some mixed-states, in which the entanglement is zero.

By using a generalized Greenberger---Horne---Zeilinger (GHZ) state in which is locally unitarily connected with standard GHZ state as a communication channel, semi-quantum key distribution is extended to study semi-quantum information splitting protocols for secret sharing of quantum information. In our scheme, quantum Alice splits arbitrary two, three and N-qubit states with two classical parties, Bob and Charlie, in a way that both parties are sufficient to reconstruct Alice's original states only under the condition of which she/he obtains the help from another one, but one of them cannot. The presented protocols are helpful for both secure against certain eavesdropping attacks and economical in processing of quantum information.

In a realistic situation, the secret sharing of classical or quantum information will involve the transmission of this information through noisy channels. We consider a three qubit pure state. This state becomes a mixed-state when the qubits are distributed over noisy channels. We focus on a specific noisy channel, the phase-damping channel. We propose a protocol for secret sharing of classical information with this and related noisy channels. This protocol can also be thought of as cooperative superdense coding. We also discuss other noisy channels to examine the possibility of secret sharing of classical information.

Conventional information science considers an information process, but traditionally uses the probability measure for random states and Shannon's entropy as the uncertainty function of these states. This paper presents a new approach, based on an integral information measure of the random process. An entropy functional (EF) on the trajectories of the process accumulates and encodes the process'inner connections between the information states. The application of a variation principle (VP) to the EF determines the process' information path functional (IPF), whose extremal trajectories describe the informational dynamics of this process. Information dynamics with the VP invariant relations evaluate the information content of a random process, expose its information code and reveal a conserved (hidden) information, produced at an acquisition of the process information. By introducing both objective and subjective information observers, we consider the observers information cognitive dynamics and neurodynamics, based on the EF-IPF approach. The universal nature of information process' dynamics and regularities, discovered in the information observers, have many applications not only in cognitive and intelligent systems, but also in different biological, social and economic systems.

In this work some charicteristics and applications for quantum information is revealed. The various dynamical equations of quantum information density have been investigated, transmission characteristics of the dynamical mutual information have been studied, and the decoherence-free controlling procedure has been considered, which exposes that quantum information is holographic through the similarity structure of subdynamic kinetic equations for quantum information density.

Shannon’s noisy channel coding theorem is a cornerstone in the history of classical information theory. A proof of Shannon’s noisy channel coding theorem using quantum notations is presented, which sets up a bridge between classical information theory and the developing quantum information theory.

We discuss the correlations on classical and quantum systems from the information theoretical points of view. There exists an essential difference between such two types of correlation. How can we understand such difference? This report is a review of our recent works on the quantum information theory with entanglement.

Application of nanoelectromechanical systems (NEMSs) as one of the structural components of quantum computers assumes a high level of coherent control of their state. In this case, such objects could perform certain functions in the coding, storing, and transportation of quantum information, and serve as auxiliary elements for processing such information. This paper contains a survey of basic theoretical and experimental results proving the possibility of coherent manipulations with phonon states of NEMSs, their cooling to the ground vibrational state, and organization of controllable interaction between them and other quantum information carriers.

Reverse coherent information, as a symmetric counterpart of the coherent information, has been firstly defined by R. Garcia-Patron et al. This quantity allows to define reverse coherent information capacity which is additive. In this Letter, we prove the convexity of such capacity for a general quantum channel, and investigate the effect of convex decomposition of quantum channel on its (reverse) coherent information. Finally, we apply the convexity property to provide an upper bound on the reverse coherent information capacity for some important channels.

In this paper we review a particular connection between information theory and group theory. We formalize the notions of information elements and information lattices, first proposed by Shannon. Exploiting this formalization, we expose a comprehensive parallelism between information lattices and subgroup lattices. Qualitatively, isomorphisms between information lattices and subgroup lattices are demonstrated. Quantitatively, a decisive approximation relation between the entropy structures of information lattices and the log-index structures of the corresponding subgroup lattices, first discovered by Chan and Yeung, is highlighted. This approximation, addressing both joint and common entropies, extends the work of Chan and Yeung on joint entropy. A consequence of this approximation result is that any continuous law holds in general for the entropies of information elements if and only if the same law holds in general for the log-indices of subgroups. As an application, by constructing subgroup counterexamples, we find surprisingly that common information, unlike joint information, obeys neither the submodularity nor the supermodularity law. We emphasize that the notion of information elements is conceptually significant—formalizing it helps to reveal the deep connection between information theory and group theory. The parallelism established in this paper admits an appealing group-action explanation and provides useful insights into the intrinsic structure among information elements from a group-theoretic perspective.

Feedback is proposed for distinguishing between two weak coherent states with phases differing by ∼π. The mutual nonorthogonality of such states gives rise to a discrimination error, which can be reduced by using feedback. An optical quantum channel is discussed where the input is classical information encoded in two weak coherent states. For a channel with feedback, the discrimination error probability is calculated, and the mutual entropy that quantifies the fidelity between input and output is evaluated. We find that the use of a feedback loop in a quantum communication channel can increase the mutual entropy when canonical position or photon number is measured.

As was mentioned by Nicolas Lori in his (Found Sci, 2010) commentary, the definition of Information in Physics is something about which not all authors agreed. According to physicists like me Information decreases when Entropy increases (so entropy would be a negative measure of information), while many physicists, seemingly the majority of them, are convinced of the contrary (even in the camp of Quantum Information Theoreticians). In this reply I reproduce, and make more precise, some of my arguments, that appeared here and there in my (2010) paper, in order to clarify the presentation of my personal point of view on the subject.

The physics of consciousness and universal mind is shown on the base of theory of byuons, the theory of “life’ of special unobservable discrete objects—byuons from which the surrounding space and the world of elementary particles are formed. An essential distinction of that theory from the modern models in the classical and quantum field theories is that the potentials of physical fields (gravitational, electromagnetic, asf.) gain exactly fixable, measurable values. Basic axioms and some conclusions of this theory are discussed. The theory of byuons predicts the existence of a new force and a new quantum information channel in nature. All objects of the Universe are shown to be united into the unique information field due to the huge interval of uncertainty in the coordinate (Δx = L = 1028 cm) of objects 4b (object formed during four-contact byuon-byuon interaction ( mc24b = 33 eV)) forming the surrounding physical space. It is a new quantum information channel.

We consider the entropy gain for infinite-dimensional evolutions and show that unlike in the finitedimensional case, there are many channels with positive minimal entropy gain. We obtain a new lower bound and compute the minimal entropy gain for a broad class of bosonic Gaussian channels. We mathematically formulate the Choi-Jamiolkowski (CJ) correspondence between channels and states in the infinite-dimensional case in a form close to the form used in quantum information theory. In particular, we obtain an explicit expression for the CJ operator defining a general nondegenerate bosonic Gaussian channel and compute its norm.

We present quantum mechanics (QM) as theory of special classical random signals. On one hand, this approach provides a possibility to go beyond conventional QM: to create a finer description of micro processes than given by the QM-formalism. In fact, we present a model with hidden variables of the wave-type. On the other hand, our approach establishes coupling between quantum and classical information theories. We recall that quantum information theory has already been used for description of the entropy of Gaussian input signals for noisy channels. The entropy of a classical random input was invented as the entropy of the quantum density operator corresponding to the covariance operator of the input process.1 In this paper, we proceed the other way around: we apply classical signal theory to create a measurement model which reproduces quantum probabilities.

In this work, we develop non-equilibrium information theory formalism for the investigation of the steady-state heterogeneous electron transfer. In order to analyze the information transfer, we introduce the concept of information potential and information affinity. These new functions allow us to describe the transformation from the initial to final state by means of Fokker–Planck type equation. Accordingly, the transformation can be viewed as a diffusion process within the phase space. Also, we are able to determine the information entropy production. We show that the Shannon information entropy production is equal to zero for a reversible system. However, the change in the relative entropy or Kullback–Leibler measure of information distance is positive for an irreversible system. In all cases, we find that a non-negative information entropy production is always observed during the experiments. Here, we demonstrate the self-consistency of the non-equilibrium formalism in the information theory for studying steady-state electrochemical systems.

The dynamics of four fidelities is studied for mixed coherent states and mixed squeezed states of Fermi-resonance coupling vibrations in molecule CS2. It is demonstrated that those fidelities are dominant-positively correlated with each other, one of which by Wang et al. (Phys. Lett. A 373, 58 (2008)) is the most striking in dominant anti-correlation with quantum mutual entropy. That is useful for molecular quantum computing and quantum information.

In this paper, we develop dynamic statistical information theory established by the author. Starting from the ideas that the state variable evolution equations of stochastic dynamic systems, classical and quantum nonequilibrium statistical physical systems and special electromagnetic field systems can be regarded as their information symbol evolution equations and the definitions of dynamic information and dynamic entropy, we derive the evolution equations of dynamic information and dynamic entropy that describe the evolution laws of dynamic information. These four kinds of evolution equations are of the same mathematical type. They show in unison when information transmits in coordinate space outside the systems 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, and 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. When space noise can be neglected, an information wave will appear. If we only consider the information change inside the systems, dynamic information evolution equations reduce to information equations corresponding to the dynamic equations which describe evolution laws of the above dynamic systems. This reveals that the evolution laws of respective dynamic systems can be described by information equations in a unified fashion. Hence, the evolution processes of these dynamic systems can be abstracted as the evolution processes of information. Furthermore, we present the formulas for information flow, information dissipation rate, and entropy production rate. We prove that the information production probably emerges in a dynamic system with internal attractive interaction between the elements, and derive a formula for this information production rate. Thereby, we obtain an expression for the time rate of total information change of a dynamic system, which is equal to the algebraic sum of the formulas for information dissipation rate, information production rate and information inflow rate, and which exhibits a unified information description for the evolution including degradation and self-organizing evolution of dynamic systems.

We discuss the possibility of a relativistic relationship between information and entropy, closely analogous to the classical Maxwell electro-magnetic wave equations. Inherent to the analysis is the description of information as residing in points of non-analyticity; yet ultimately also exhibiting a distributed characteristic: additionally analogous, therefore, to the wave-particle duality of light. At cosmological scales our vector differential equations predict conservation of information in black holes, whereas regular- and Z-DNA molecules correspond to helical solutions at microscopic levels. We further propose that regular- and Z-DNA are equivalent to the alternative words chosen from an alphabet to maintain the equilibrium of an information transmission system.

One of the basic results of classical information theory is that error-free information transmission is possible even through an imperfect binary communication channel with noise up to an error of Qc = 1/2. There is a fundamental and applied question of whether quantum-mechanical constraints can ensure error-free classical-information transmission with quantum states and, moreover, guarantee the security of distributed keys up to the theoretical limit in the error Qc. It has been shown that the secure key distribution is possible up to the error Qc in the asymptotic limit of a large number of bases.

The theoretical formalism of the implementation of the Deutsch-Jozsa algorithm relies on von Neumann’s theory. We try to investigate whether von Neumann’s theory meet our physical world. We derive a proposition concerning a quantum expectation value under the assumption of the existence of the orientation of reference frames in N spin-1/2 systems (1≤N

We investigate the usefulness of the highly entangled five-partite cluster and Brown states for the quantum information splitting (QIS) of a special kind of two-qubit state using remote state preparation. In our schemes, the information that is to be shared is known to the sender. We show that, QIS can be accomplished with just two classical bits, as opposed to four classical bits, when the information that is to be shared is unknown to the sender. The present algorithm, demonstrated through the cluster and Brown states is deterministic as compared to the previous works in which it was probabilistic.

Optimal utilization of complex synthetic aperture radar imagery for coherent change detection (CCD) is achieved by maximizing the amount of information extracted from the coherent correlation of images. Conventional techniques cannot fully exploit the coherent information due to limited application of few products or indicators, e.g., correlation factor and phase maps. Also, considering the lack of a systematic formulation of change observables and their nature, unsupervised change detection or classification is not feasible. To address this, an analytic framework is established by taking advantage of the analogy to partially polarized electromagnetic fields to introduce vectors and observables that can establish a complete change space. Decomposition of the coherent correlation or change characteristics into this basis set can provide a better understanding of the associated change phenomenology.

An information-theoretic description of induced transitions between stationary states in the space of control parameters is given for nonextensive self-organized systems. The S- and I-theorems on changes in nonadditive entropy and information difference measures are proved in the general form when the effective Hamiltonian function is unknown. The statistical method is used to derive the q-entropy and q-information difference depending on the distribution seminorm.

In quantum information theory it is generally accepted that quantum mutual information is an information-theoretic measure of total correlations of a bipartite quantum state. We argue that there exist quantum states for which quantum mutual information cannot be considered as a measure of total correlations. Moreover, for these states we propose a different way of quantifying total correlations., Comment: 6 pages, 3 figures, published version

We review the basics of classical algorithmic complexity theory and two of its quantum extensions that have been prompted by the foreseeable existence of quantum computing devices. In particular, we will examine the relations between these extensions and the von Neumann entropy rate of generic quantum information sources of ergodic type.

Dynamic propagation and storing-retrieving of a weak infrared (IR)-light pulse in a coupled semiconductor double-quantum-dot (SDQD) structure are studied theoretically with feasible parameters. Two characteristic features are found. First, it is shown that, with a constant control field, the SDQD medium is transparent to the probe pulse which propagates over sufficiently long distances. Furthermore, the pulse shape remains unchanged on propagation. Second, with a time-varying control field, we are able to store and retrieve the probe pulse in this four-subband SDQD medium by adiabatically switching off and on the control field. Such a four-subband SDQD system for storing and retrieving coherent information is much more practical than its atomic counterpart as a result of its flexible design and the controllable (tunable) interference strength and thus provides a new possibility for technological applications in quantum information science in the SDQD solid-state nanostructure.

We present a quantum information splitting scheme of a two-qubit state by using two Greenberger–Horne–Zeilinger (GHZ) states as quantum channels. In this scheme, since the sender Alice knows the quantum information in priori, she only needs to perform a two-qubit measurement and publish two classical bits for her two agents Bob and Charlie to reconstruct the quantum information via their mutual assistance. We calculate the success probability and classical communication cost within the scheme. In the general case, Alice can successfully split the state with probability 25% (probabilistic) and the classical communication cost is 4 classical bits. However, in some special cases, the secret states are chosen from a special ensemble, the success probability of our scheme can be increased to 50% or even to 100% (deterministic) after consuming some extra classical bits.

In the first part of the paper we give a representation for entanglement-breaking channels in separable Hilbert space that generalizes the "Kraus decomposition with rank-one operators" and use it to describe complementary channels. We also note that coherent information for antidegradable channel is always nonpositive. In the second part, we give necessary and sufficient condition for entanglement breaking for the general quantum Gaussian channel. Application of this condition to one-mode channels provides several new cases where the additivity conjecture holds in the strongest form.

We consider the problem of updating non-monotonic knowledge bases represented by epistemic logic programs where disjunctive information and notions of knowledge and belief can be explicitly expressed. We propose a formulation for epistemic logic program update based on a principle called minimal change and maximal coherence. The central feature of our approach is that during an update or a sequence of updates, contradictory information is removed on a basis of minimal change under the semantics of epistemic logic programs and then coherent information is maximally retained in the update result. Through various update scenarios, we show that our approach provides both semantic and syntactic characterizations for an update problem. We also investigate essential semantic properties of epistemic logic program update.

Entanglement of pure states of bipartite quantum systems has been shown to have a unique measure in terms of the von Neumann entropy of the reduced states of either of its subsystems. The measure is established under entanglement manipulation of an asymptotically large number of copies of the states. In this paper, different asymptotic measures of entanglement assigned to arbitrary sequences of bipartite pure states are shown to coincide only when the sequence is information stable, in terms of the quantum spectral information rates of the sequence of subsystem states. Additional bounds on the optimal rates of entanglement manipulation protocols in quantum information are also presented, including bounds given by generalizations of the coherent information and the relative entropy of entanglement., Comment: 7 pages, requires IEEEtran.cls

We obtain a maximizer for the quantum mutual information for classical information sent over the quantum qubit amplitude damping channel. This is achieved by limiting the ensemble of input states to antipodal states, in the calculation of the product-state capacity for the channel, the resulting maximizing ensemble consisting of just two non-orthogonal states. We also consider the product-state capacity of a convex combination of two memoryless channels and demonstrate in particular that it is in general not given by the minimum of the capacities of the respective memoryless channels., Comment: Published in IJQI (2008). One figure added

We construct a complete representation of the atomic information entropy of an arbitrary multi-level system. Our approach is applicable to all scenarios in which the quantum state shared by a single particle and fields is known. As illustrations we apply our findings to a single four-level atom strongly coupled to a cavity field and driven by a coherent laser field. In this framework, we discuss connections with entanglement frustration and entropic forms. We conclude by showing how the atomic information entropy can be extended to examine entanglement in multi-level atomic systems.

The Wigner-Yanase-Dyson information is an important variant of quantum Fisher information. Two fundamental requirements concerning this notion of information content originally postulated by Wigner and Yanase are convexity and superadditivity. The former was fully established by Lieb in 1973, and led to the first proof of the strong subadditivity of quantum entropy. The latter, although widely believed to be true, was quite recently disproved by Hansen. Nevertheless, superadditivity has also been established in two extreme cases, i.e., when the states are pure or classical. In this paper, we first review a scheme to classify bipartite states into a hierarchy of classical, semi-quantum, and quantum states, which are arranged in the order of increasing quantumness. We then prove the superadditivity of the Wigner-Yanase-Dyson information for all semi-quantum states. The convexity of the Wigner-Yanase-Dyson information plays a crucial role here.

We show that the conservation and the non-additivity of the information, together with the additivity of the entropy make the entropy increase in an isolated system. The collapse of the entangled quantum state offers an example of the information non-additivity. Nevertheless, the later is also true in other fields, in which the interaction information is important. Examples are classical statistical mechanics, social statistics and financial processes. The second law of thermodynamics is thus proven in its most general form. It is exactly true, not only in quantum and classical physics but also in other processes, in which the information is conservative and non-additive., Comment: 4 pages