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Graph states play an important role in quantum information theory through their connection to measurement-based computing and error correction. Prior work has revealed elegant connections between the graph structure of these states and…
We study the problem of whether all bipartite quantum states having a prescribed spectrum remain positive under the reduction map applied to one subsystem. We provide necessary and sufficient conditions, in the form of a family of linear…
In recent years, the entanglement spectra of quantum states have been identified to be highly valuable for improving our understanding on many problems in quantum physics, such as classification of topological phases, symmetry-breaking…
The problem of entanglement detection is a long standing problem in quantum information theory. One of the primary procedures of detecting entanglement is to find the suitable positive but non-completely positive maps. Here we try to give a…
It is found that the problem of existence of bound entangled states with non-positive partial transpose (NPPT) has the intriguing relation to the Hilbert's 17th problem. More precisely, we compute the expectation value of the partially…
The halting problem for Turing machines is decidable on a set of asymptotic probability one. Specifically, there is a set B of Turing machine programs such that (i) B has asymptotic probability one, so that as the number of states n…
A contraction $T$ on a (complex, separable) Hilbert space is stable, or of class $C_{0\cdot}$, if $T^n\to 0$ in the strong operator topology. It is proved that for a non-stable pure subnormal contraction $T$ there exists a singular inner…
Particle systems admit a variety of tensor product structures (TPSs) depending on the algebra of observables chosen for analysis. Global symmetry transformations and dynamical transformations may be resolved into local unitary operators…
The integrability has been playing an essential role in the field of differential equations. This property may better help us obtain the topological structure and even the global dynamics for the considered system. A system is called…
We will consider completely positive maps defined on tensor products of von Neumann algebras and taking values in the algebra of bounded operators on a Hilbert space and particularly certain convex subsets of the set of such maps. We show…
We apply random matrix and free probability techniques to the study of linear maps of interest in quantum information theory. Random quantum channels have already been widely investigated with spectacular success. Here, we are interested in…
In this paper, we discuss some general connections between the notions of positive map, weak majorization and entropic inequalities in the context of detection of entanglement among bipartite quantum systems. First, basing on the fact that…
It is a well-known result due to E. St{\o}rmer that every positive qubit map is decomposable into a sum of a completely positive map and a completely copositive map. Here, we generalize this result to tensor squares of qubit maps.…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
We define an entanglement witness in a composite quantum system as an observable having nonnegative expectation value in every separable state. Then a state is entangled if and only if it has a negative expectation value of some…
We characterize all translation invariant half planar maps satisfying a certain natural domain Markov property. For p-angulations with p \ge 3 where all faces are simple, we show that these form a one-parameter family of measures…
By the topological argument that the identity matrix is surrounded by a set of separable states follows the result that if a system is entangled at thermal equilibrium for some temperature, then it presents a phase transition (PT) where…
We study positive maps of B(K) into B(H) for finite-dimensional Hilbert spaces K and H. Our main emphasis is on how Choi matrices and estimates of their norms with respect to mapping cones reflect various properties of the maps. Special…
We propose a generalization of the model of classical baker map on the torus, in which the images of two parts of the phase space do overlap. This transformation is irreversible and cannot be quantized by means of a unitary Floquet…
The existence of a maximally entangled pure state is a cornerstone result of entanglement theory that has paramount consequences in quantum information theory. A natural generalization of this property is to consider whether a notion of…