Related papers: Quantum Information and Entropy
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
When discriminating between two pure quantum states, there exists a quantitative tradeoff between the information retrieved by the measurement and the disturbance caused on the unknown state. We derive the optimal tradeoff and provide the…
Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes…
A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and…
We investigate the following generalisation of the entropy of quantum measurement. Let H be an infinite-dimensional separable Hilbert space with a 'density' operator {\rho}, tr {\rho}=1. Let I(P)\in R be defined for any partition P =…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
Observational entropy is interpreted as the uncertainty an observer making measurements associates with a system. So far, properties that make such an interpretation possible rely on the assumption of ideal projective measurements. We show…
The evolution of a quasi-isolated finite quantum system from a nonequilibrium initial state is considered. The condition of quasi-isolation allows for the description of the system dynamics on the general basis, without specifying the…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
In standard quantum theory, the ideas of information-entropy and of pure states are closely linked. States are represented by density matrices $\rho$ on a Hilbert space and the information-entropy $-tr(\rho\log\rho)$ is minimised on pure…
Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies, such as quantum computation, quantum communication and quantum metrology. Yet, their quantification, rather than…
Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics, respectively. In the last decade the study of quantum quenches revealed that these two concepts are intricately intertwined.…
The pure quantum entanglement is generalized to the case of mixed compound states on an operator algebra to include the classical and quantum encodings as particular cases. The true quantum entanglements are characterized by quantum…
The paper analyzes the entropy of a system composed by non-interacting and indistinguishable particles whose quantum state numbers are modelled as independent and identically distributed classical random variables. The crucial observation…
We consider conservative quantum evolutions possibly interrupted by macroscopic measurements. When started in a nonequilibrium state, the resulting path-space measure is not time-reversal invariant and the weight of time-reversal breaking…
In this work, we use the theory of quantum states over time to define an entropy $S(\rho,\mathcal{E})$ associated with quantum processes $(\rho,\mathcal{E})$, where $\rho$ is a state and $\mathcal{E}$ is a quantum channel responsible for…
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…
Within an inherently classical perspective, there is always an unavoidable energy cost associated with the information deletion and this common lore is at the heart of the Landauer's conjecture that does not impose, per se, any relevant…
A pure quantum state can fully describe thermal equilibrium as long as one focuses on local observables. Thermodynamic entropy can also be recovered as the entanglement entropy of small subsystems. When the size of the subsystem increases,…
We address the framework of analysing quantum metrology in the information-theoretic picture. Firstly we show how to extract the maximum amount of information in general via suitable state initialization of the probes at the beginning and a…