Related papers: On a quantum version of Shannon's conditional entr…

We present a formula for the relative entropy S(rho||sigma) of two n mode gaussian states rho, sigma in the boson Fock space. It is shown that the relative entropy has a classical and a quantum part: The classical part consists of a…

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…

We comment on a formulation of quantum statistical mechanics, which incorporates the statistical inference of Shannon. Our basic idea is to distinguish the dynamical entropy of von Neumann, $H = -k Tr \hat{\rho}\ln\hat{\rho}$, in terms of…

The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[\rho]= - Tr (\rho \ln \rho) of a density matrix \rho_{123} on the product of three Hilbert spaces satisfies…

Let $S(\rho)=- Tr (\rho \log\rho)$ be the von Neumann entropy of an $N$-dimensional quantum state $\rho$ and $e_2(\rho)$ the second elementary symmetric polynomial of the eigenvalues of $\rho$. We prove the inequality $S(\rho) \le c(N)…

We introduce a new notion of entropy for quantum states, called contextual entropy, and show how it unifies Shannon and von Neumann entropy. The main result is that from the knowledge of the contextual entropy of a quantum state of a…

For a quantum state represented as an $n\times n$ density matrix $\sigma \in M_n$, let ${\cal S}(\sigma)$ be the compact convex set of quantum states $\rho = (\rho_{ij}) \in M_{m\cdot n}$ with the first partial trace equal to $\sigma$,…

Let $S(\rho)$ be the von Neumann entropy of a density matrix $\rho$. Weak monotonicity asserts that $S(\rho_{AB}) - S(\rho_A) + S(\rho_{BC}) - S(\rho_C)\geq 0$ for any tripartite density matrix $\rho_{ABC}$, a fact that is equivalent to the…

We consider a ${\mu}$-deformation of the Segal-Bargmann transform, which is a unitary map from a ${\mu}$-deformed quantum configuration space onto a ${\mu}$-deformed quantum phase space (the ${\mu}$-deformed Segal-Bargmann space). Both of…

We consider the properties of the Shannon entropy for two probability distributions which stand in the relationship of majorization. Then we give a generalization of a theorem due to Uhlmann, extending it to infinite dimensional Hilbert…

The Tsallis relative entropy $S_q (\hat{\rho},\hat{\sigma})$ measures the distance between two arbitrary density matrices $\hat{\rho}$ and $\hat{\sigma}$. In this work the approximation to this quantity when $q=1+\delta$ ($\delta\ll 1$) is…

In this paper we investigate the inequality $S_q(\rho_{123})+S_q(\rho_2)\leq S_q(\rho_{12})+S_q(\rho_{23}) \, (*)$ where $\rho_{123}$ is a state on a finite dimensional Hilbert space $\mathcal{H}_1\otimes \mathcal{H}_2\otimes…

A finite dimensional quantum mechanical system is modeled by a density rho, a trace one, positive semi-definite matrix on a suitable tensor product space H[N] . For the system to demonstrate experimentally certain non-classical behavior,…

The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $\rho$…

The quantum entropy power inequality, proven by K\"onig and Smith (2012), states that $\exp(S(\rho \boxplus \sigma)/m)\geq \frac 12 (\exp(S(\rho)/m) + \exp(S(\sigma)/m))$ for two $m$-mode bosonic quantum states $\rho$ and $\sigma$. One…

This work explores connections between the quantum relative entropy of two faithful states $\rho,\sigma$ (i.e. full-rank density matrices) and the Kullback-Leibler divergences of classical measures $\mu,\nu$. Here, $\mu$ and $\nu$ are…

In the framework of Quantum Field Theory, we provide a rigorous, operator algebraic notion of entanglement entropy associated with a pair of open double cones $O \subset \tilde O$ of the spacetime, where the closure of $O$ is contained in…

For a quantum pure state in conformal field theory, we generate the Shannon entropy of its coherence, that is, the von Neumann entropy obtained by introducing quantum measurement errors. We give a holographic interpretation of this Shannon…

We construct for a Schur concave function $f$ on the set of quantum states a tight upper bound on the difference $f(\rho)-f(\sigma)$ for a quantum state $\rho$ with finite $f(\rho)$ and any quantum state $\sigma$ $m$-partially majorized by…

We introduce a simple geometrical construction similar to covariant holographic entanglement entropy but with the addition of a new term proportional to boundary region volume. This new procedure has properties strongly resembling classical…