Related papers: Physical transformations between quantum states
Linear maps of matrices describing evolution of density matrices for a quantum system initially entangled with another are identified and found to be not always completely positive. They can even map a positive matrix to a matrix that is…
Two quantum theories are physically equivalent if they are related, not by a unitary transformation, but by an isometric transformation. The conditions under which a quantum canonical transformation is an isometric transformation are given.
A density matrix {\rho}(t) yields probabilistic information about the outcome of measurements on a quantum system. We introduce here the past quantum state, which, at time T, accounts for the state of a quantum system at earlier times t <…
We introduce a generalization of the set of completely positive matrices that we call "pairwise completely positive" (PCP) matrices. These are pairs of matrices that share a joint decomposition so that one of them is necessarily positive…
We study the problem of transforming a set of pure bipartite states into another using deterministic LOCC (local operations and classical communication). Necessary conditions for the existence of such a transformation are obtained using…
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and…
Comparison of statistical models (experiments) is an important branch of mathematical statistics, which gives deep insights in many aspects of foundation of statistics. So far, there are two quantum versions of the concept: Comparison with…
Given a non-empty closed convex subset $\mathsf{F}$ of density matrices, we formulate conditions that guarantee the existence of an $\mathsf{F}$-morphism (namely, a completely positive trace-preserving linear map that maps $\mathsf{F}$ into…
X states are a broad class of two-qubit density matrices that generalize many states of interest in the literature. In this work, we give a comprehensive account of various quantum properties of these states, such as entanglement,…
A system interacting with its environment will give rise to a quantum evolution. After tracing over the environment the net evolution of the system can be described by a linear Hermitian map. It has recently been shown that a necessary and…
Linear maps preserving pure states of a quantum system of any dimension are characterized. This is then used to establish a structure theorem for linear maps that preserve separable pure states in multipartite systems. As an application, a…
The universal transpose of quantum states is an anti-unitary transformation that is not allowed in quantum theory. In this work, we investigate approximating the universal transpose of quantum states of two-level systems (qubits) using the…
Valid transformations between quantum states are necessarily described by completely positive maps, instead of just positive maps. Positive but not completely positive maps such as the transposition map cannot be implemented due to the…
We address the problem of existence of completely positive trace preserving (CPTP) maps between two sets of density matrices. We refine the result of Alberti and Uhlmann and derive a necessary and sufficient condition for the existence of a…
Any evolution described by a completely positive trace-preserving linear map can be imagined as arising from the interaction of the evolving system with an initially uncorrelated ancilla. The interaction is given by a joint unitary…
Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot…
For a system of N identical particles in a random pure state, there is a threshold k_0 = k_0(N) ~ N/5 such that two subsystems of k particles each typically share entanglement if k > k_0, and typically do not share entanglement if k < k_0.…
Looking for a quantum-mechanical implementation of duality, we formulate a relation between coherent states and complex-differentiable structures on classical phase space ${\cal C}$. A necessary and sufficient condition for the existence of…
A basic linearity of quantum dynamics, that density matrices are mapped linearly to density matrices, is proved very simply for a system that does not interact with anything else. It is assumed that at each time the physical quantities and…
The nonlocal properties of arbitrary dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. These invariants give rise to both sufficient and necessary…