Related papers: Negative Conditional Entropy of Post-Selected Stat…
The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In…
The goal of the present paper is to derive some conditions on saturation of (strong) subadditivity inequality for the stochastic matrices. The notion of relative entropy of stochastic matrices is introduced by mimicking quantum relative…
We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of…
Non Gaussian states and processes are useful resources in quantum information with continuous variables. An experimentally accessible criterion has been proposed to measure the degree of non Gaussianity of quantum states, based on the…
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when…
It is well-known that pure quantum states are typically almost maximally entangled, and thus have close to maximally mixed subsystems. We consider whether this is true for probabilistic theories more generally, and not just for quantum…
We approach the physical implications of the non-commutative nature of Complementary Observable Algebras (COA) from an information theoretic perspective. In particular, we derive a general \textit{entropic certainty principle} stating that…
We consider a quantum state shared between many distant locations, and define a quantum information processing primitive, state merging, that optimally merges the state into one location. As announced in [Horodecki, Oppenheim, Winter,…
A problem of statistical estimation of a Hermitian nonnegatively definite matrix of unit trace (for instance, a density matrix in quantum state tomography) is studied. The approach is based on penalized least squares method with a…
In physics, entanglement 'reduces' the entropy of an entity, because the (von Neumann) entropy of, e.g., a composite bipartite entity in a pure entangled state is systematically lower than the entropy of the component sub-entities. We show…
In this paper we derive a new quantum entropic uncertainty relation, bounding the conditional smooth quantum min entropy based on the result of a measurement using a two outcome POVM and the failure probability of a classical sampling…
We study the entanglement entropy arising from coherent states and one--particle states. We show that it is possible to define a finite entanglement entropy by subtracting the vacuum entropy from that of the considered states, when the…
Information, in its communications sense, is a transactional property. If the received signals communicate choices made by the sender of the signals, then information has been transmitter by the sender to the receiver. Given this reality,…
New exact results about the nonequilibrium thermodynamics of open quantum systems at arbitrary timescales are obtained by considering all possible variations of initial conditions of a system, its environment, and correlations between them.…
A state $\rho=(\rho_n)_{n=1}^{\infty}$ is a sequence such that $\rho_n$ is a density matrix on $n$ qubits. It formalizes the notion of an infinite sequence of qubits. The von Neumann entropy $H(d)$ of a density matrix $d$ is the Shannon…
In this paper, we investigate and compare two well-developed definitions of entropy relevant for describing the dynamics of isolated quantum systems: bipartite entanglement entropy and observational entropy. In a model system of interacting…
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of…
We derive a universal inequality that provides a lower bound on the ensemble-averaged von Neumann entropy change in a quantum system subject to continuous measurement and dissipation. Our result clarifies how entropy production is…
Weak measurements of photon position can be used to obtain direct experimental evidence of the wavefunction of a photon between generation and ultimate detection. Significantly, these measurement results can also be understood as complex…
We discuss the concept of connection states (or connection matrices) that describe posterior ensembles, post-selected according to the outcomes of a quantum measurement. Connection matrices allow one to obtain results of any weak and some…