Related papers: Sequences of resource monotones from modular Hamil…
We propose a method to generate entanglement measures systematically by using the irreducible decomposition of some copies of a state under the local unitary (LU) transformations. It is applicable to general multipartite systems. We show…
We investigate the fundamental limits of entanglement generation under bipartite Hamiltonian dynamics when only finite physical resources-specifically, bounded energy variance-are available. Using the relative entropy of entanglement, we…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
It is well-known that entanglement entropy in field theory at its ground state is dominated by an area law term, presenting a similarity to the entropy of black holes. It is interesting to investigate whether this similarity can be extended…
We review the theory of entanglement measures, concentrating mostly on the finite dimensional two-party case. Topics covered include: single-copy and asymptotic entanglement manipulation; the entanglement of formation; the entanglement…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…
Distinguishability and predictability are part of complementarity relations which apply to two different kinds of interference experiments, with and without a path-detector, respectively. In [Opt. Comm. 179, 337 (2000)], Englert and Bergou…
Two new relative entropy quantities, called the min- and max-relative entropies, are introduced and their properties are investigated. The well-known min- and max- entropies, introduced by Renner, are obtained from these. We define a new…
We develop a framework to extend resource measures from one domain to a larger one. We find that all extensions of resource measures are bounded between two quantities that we call the minimal and maximal extensions. We discuss various…
Entropic uncertainty relations in a finite dimensional Hilbert space are investigated. Making use of the majorization technique we derive explicit lower bounds for the sum of R\'enyi entropies describing probability distributions associated…
The entanglement production in bipartite quantum systems is studied for initially unentangled product eigenstates of the subsystems, which are assumed to be quantum chaotic. Based on a perturbative computation of the Schmidt eigenvalues of…
Entropies associated with spatial subsystems in conventional local quantum field theories are typically divergent when the spatial regions have boundaries. However, in certain linear combinations of the entropies for various subsystems,…
We find the analytic expression of the trace of powers of the reduced density matrix on an interval of length L, for a massive boson field in 1+1 dimensions. This is given exactly (except for a non universal factor) in terms of a finite sum…
We introduce a new class of real-valued monotones in preordered spaces, injective monotones. We show that the class of preorders for which they exist lies in between the class of preorders with strict monotones and preorders with countable…
We prove that the entanglement cost equals the regularized entanglement of formation for any infinite-dimensional quantum state $\rho_{AB}$ with finite quantum entropy on at least one of the subsystems $A$ or $B$. This generalizes a…
We initiate the systematic study of resource theories of quantum channels, i.e. of the dynamics that quantum systems undergo by completely positive maps, in abstracto: Resources are in principle all maps from one quantum system to another,…
In order to understand the detailed mechanism by which a fundamental discreteness can provide a finite entanglement entropy, we consider the entanglement entropy of two classes of free massless scalar fields on causal sets that are well…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
A combination of a finite number of linear independent states forms superposition in a way that cannot be conceived classically. Here, using the tools of resource theory of superposition, we give the conditions for a class of superposition…
We extend the definition of concurrence into a family of entanglement monotones, which we call concurrence monotones. We discuss their properties and advantages as computational manageable measures of entanglement, and show that for pure…