Related papers: Integral representations of separable states
The invertable map of spin state density operator onto quasiprobability distribution of three continuous variables is constructed. The connection with two-mode electromagnetic field oscillators is discussed. The inversion formula for…
We argue that Hilbert spaces are not suitable to represent quantum states mathematically, in the sense that they require properties that are untenable by physical entities. We first demonstrate that the requirements posited by complex inner…
Study of an N qubit mixed symmetric separable states is a long standing challenging problem as there exist no unique separability criterion. In this regard, we take up the N-qubit mixed symmetric separable states for a detailed study as…
Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…
The construction of exactly-solvable models has recently been advanced by considering integrable $T\bar{T}$ deformations and related Hamiltonian deformations in quantum mechanics. We introduce a broader class of non-Hermitian Hamiltonian…
We consider the following class of unitary representations $\pi $ of some (real) Lie group $G$ which has a matched pair of symmetries described as follows: (i) Suppose $G$ has a period-2 automorphism $\tau $, and that the Hilbert space…
The symmetric subspace of multi-qubit systems, that is, the space of states invariant under permutations, is commonly encountered in applications in the context of quantum information and communication theory. It is known that the symmetric…
The possible spectra of one-particle reduced density matrices that are compatible with a pure multipartite quantum system of finite dimension form a convex polytope. We introduce a new construction of inner- and outer-bounding polytopes…
We investigate the equivalence of bipartite quantum mixed states under local unitary transformations by introducing representation classes from a geometrical approach. It is shown that two bipartite mixed states are equivalent under local…
In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result…
P-representability is a necessary and sufficient condition for separability of bipartite Gaussian states only for the special subset of states whose covariance matrix are $Sp(2,R)\otimes Sp(2,R)$ locally invariant. Although this special…
We present two sets of computable entanglement measures for multipartite systems where each subsystem can have different degrees of freedom (so-called qudits). One set, called 'separability' measure, reveals which of the subsystems are…
Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one…
The complete reducibility property for bipartite states reduced the separability problem to a proper subset of positive under partial transpose states and was used to prove several theorems inside and outside entanglement theory. So far…
One of the most challenging problems in quantum physics is to quantify the entanglement of $d$-partite states and their separability. We show here that these problems are best addressed using tensors. The geometric measure of entanglement…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
We prove that Bargmann representations exist for some deformed harmonic oscillators that admit non-Fock representations. In specific cases, we explicitly obtain the resolution of the identity in terms of a true integral on the complex…
We introduce a new technique to detect separable states using semidefinite programs. This approach provides a sufficient condition for separability of a state that is based on the existence of a certain local linear map applied to a known…
Two families of bipartite mixed quantum states are studied for which it is proved that the number of members in the optimal-decomposition ensemble --- the ensemble realizing the entanglement of formation --- is greater than the rank of the…
A measure representation result for a functional modelling optimal design problems for plastic deformations, under linear growth conditions, is obtained. Departing from an energy with a bulk term depending on the deformation gradient and…