Related papers: Minimal and Maximal Operator Spaces and Operator S…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
Operator entanglement of two-qubit joint unitary operations is revisited. Schmidt number is an important attribute of a two-qubit unitary operation, and may have connection with the entanglement measure of the unitary operator. We found the…
We give a criterion for a positive mapping on the space of operators on a Hilbert space to be indecomposable. We show that this criterion can be applied to two families of positive maps. These families of maps can then be used to form…
We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e., the difference between the two largest…
Research on Koopman operator theory has focused on three key areas for several decades: the mathematical structure of the Koopman eigenfunction space, the basis of this space, and the ability to represent nonlinear dynamics as linear. This…
In this article, we study absolutely norm attaining operators ($\mathcal{AN}$-operators, in short), that is, operators that attain their norm on every non-zero closed subspace of a Hilbert space. Our focus is primarily on positive…
Linear maps between finite-dimensional ordered vector spaces with orders induced by proper cones $C_A$ and $C_B$ are called entanglement breaking if their partial application sends the maximal tensor product $K\otimes_{\max} C_A$ into the…
Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct…
In this paper, we consider the problem of quantization of classical St\"ackel systems and the problem of separability of related quantum Hamiltonians. First, using the concept of St\"ackel transform, all considered systems are expressed by…
In this paper, we combine the k-reduction map, the moment method, and the classical shadow method into a practical protocol for certifying the entanglement dimensionality. Our approach is based on the observation that a state with…
Classical matching theory can be defined in terms of matrices with nonnegative entries. The notion of Positive operator, central in Quantum Theory, is a natural generalization of matrices with nonnegative entries. Based on this point of…
There are several important abstract operator systems with the convex cone of positive semidefinite matrices at the first level. Well-known are the operator systems of separable matrices, of positive semidefinite matrices, and of block…
The property of linear discrete-time time-invariant system operators mapping inputs with at most $k-1$ sign changes to outputs with at most $k-1$ sign changes is investigated. We show that this property is tractable via the notion of…
In this work we solve, for given bounded operators $B,C$ and Hilbert-Schmidt operator $M$ acting on potentially infinite-dimensional separable Hilbert spaces, the reduced rank approximation problem, $\min\{\lVert M-BXC\rVert_{L_2}:\…
We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral…
Quantum resource theory under different classes of quantum operations advances multiperspective understandings of inherent quantum-mechanical properties, such as quantum coherence and quantum entanglement. We establish hierarchies of…
Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt…
We present a survey on mathematical topics relating to separable states and entanglement witnesses. The convex cone duality between separable states and entanglement witnesses is discussed and later generalized to other families of…
We study two abstract scenarios, where an operator family has a certain minimality property. In both scenarios, it is shown that norm, spectrum and resolvent are the same for all family members. Both abstract settings are illustrated by…
Many problems in information theory can be reduced to optimizations over matrices, where the rank of the matrices is constrained. We establish a link between rank-constrained optimization and the theory of quantum entanglement. More…