Related papers: Linear maps preserving separability of pure states
We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable, c) completely positive, d) extended by identity impose…
The positive and not completely positive maps of density matrices, which are contractive maps, are discussed as elements of a semigroup. A new kind of positive map (the purification map), which is nonlinear map, is introduced. The density…
We consider quantum state transfer on finite graphs which are attached to infinite paths. The finite graph represents an operational quantum system for performing useful quantum information tasks. In contrast, the infinite paths represent…
We investigate the geometrical structure of multipartite states based on the construction of toric varieties. We show that the toric variety represents the space of general pure states and projective toric variety defines the space of…
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…
We show that quantum computation circuits with coherent states as the logical qubits can be constructed using very simple linear networks, conditional measurements and coherent superposition resource states.
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…
We call a function $f: X\to Y$ $P$-preserving if, for every subspace $A \subset X$ with property $P$, its image $f(A)$ also has property $P$. Of course, all continuous maps are both compactness- and connectedness-preserving and the natural…
A system of plane curves defined by prescribing n points of multiplicity m in general position is regular if n > (2m)^2. The proof uses computation of limits of linear systems acquiring fixed divisors, an interesting problem in itself.
Neural networks are being used to improve the probing of the state spaces of many particle systems as approximations to wavefunctions and in order to avoid the recurring sign problem of quantum monte-carlo. One may ask whether the usual…
The rules in a shape grammar apply in terms of embedding to take advantage of the parts that emerge visually in the appearance of shapes. While the shapes are kept unanalyzed as a computation moves forward, part-structures for shapes can be…
We provide a new characterisation of quantum supermaps in terms of an axiom that refers only to sequential and parallel composition. Consequently, we generalize quantum supermaps to arbitrary monoidal categories and operational…
This work characterizes the general form of a bijective linear map $\Psi:\mathscr{M}_n(\mathbb{C}) \to \mathscr{M}_n(\mathbb{C})$ such that $[\Psi(A_1),~\Psi(A_2)]=D_2$ whenever $[A_1,~A_2]=D_1$ where $D_1~\text{and}~D_2$ are fixed…
In this paper, I will discuss the geometrical structures of multipartite quantum systems based on complex projective schemes. In particular, I will explicitly construct multi-qubit states in terms of these schemes and also discuss…
By introducing an operator sum representation for arbitrary linear maps, we develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory…
Quantum state elimination measurements tell us what states a quantum system does not have. This is different from state discrimination, where one tries to determine what the state of a quantum system is, rather than what it is not. Apart…
We show that any quantum family of maps from a non commutative space to a compact quantum metric space has a canonical quantum semi metric structure.
Convex geometry has recently attracted great attention as a framework to formulate general probabilistic theories. In this framework, convex sets and affine maps represent the state spaces of physical systems and the possible dynamics,…
The distinguishability between two quantum states can be defined in terms of their trace distance. The operational meaning of this definition involves a maximization over measurement projectors. Here we introduce an alternative definition…
Consider a situation in which a quantum system is secretly prepared in a state chosen from the known set of states. We present a principle that gives a definite distinction between the operations that preserve the states of the system and…