Related papers: Infinitely entangled states
We investigate entanglement measures in the infinite-dimensional regime. First, we discuss the peculiarities that may occur if the Hilbert space of a bi-partite system is infinite-dimensional, most notably the fact that the set of states…
Investigating a class of models that is familiar in studies of cellular automata, we find that quantum operators can be employed to describe their long distance behavior. These operators span a Hilbert space that appears to turn such a…
Two-qubit states occupy a large and relatively unexplored Hilbert space. Such states can be succinctly characterized by their degree of entanglement and purity. In this letter we investigate entangled mixed states and present a class of…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
We introduce a class of states of a composite quantum system, the so-called cross states, that turn out to play a major role in the theory of entanglement for a genuinely infinite-dimensional bipartite system. In the case where at least one…
An example is given of an interaction that produces an infinite amount of entanglement in an infinitely short time, but only a finite amount in longer times. The interaction arises from a standard Kerr nonlinearity and a 50/50 beamsplitter,…
In the problem of entanglement there exist two different notions. One is the entanglement of a quantum state, characterizing the state structure. The other is entanglement production by quantum operators, describing the action of operators…
We show that for a finite-dimensional Hilbert space, there exist observables that induce a tensor product structure such that the entanglement properties of any pure state can be tailored. In particular, we provide an explicit, finite…
It is shown that the order property of pure bipartite states under SLOCC (stochastic local operations and classical communications) changes radically when dimensionality shifts from finite to infinite. In contrast to finite dimensional…
We consider an infinite spin chain as a bipartite system consisting of the left and right half-chain and analyze entanglement properties of pure states with respect to this splitting. In this context we show that the amount of entanglement…
We report the creation of a wide range of quantum states with controllable degrees of entanglement and entropy using an optical two-qubit source based on spontaneous parametric downconversion. The states are characterised using measures of…
Given a bipartite quantum system represented by a tensor product of two Hilbert spaces, we give an elementary argument showing that if either component space is infinite-dimensional, then the set of nonseparable density operators is…
It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom, becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is…
We introduce the idea that the knowable quantum reality depends not only on the state but also on measurements. Mathematically, we map the states from the ordinary Hilbert space into new states in what we call the measurement space. The…
Teleportation of finite dimensional quantum states by a non-local entangled state is studied. For a generally given entangled state, an explicit equation that governs the teleportation is presented. Detailed examples and the roles played by…
We identify a class of two-mode squeezed states which are parametrized by an angular variable ${0\le\theta<2\pi}$ and a squeezing parameter $r$. We show that, for a large squeezing value, these states are either (almost) maximally entangled…
Optimal universal entanglement processes are discussed which entangle two quantum systems in an optimal way for all possible initial states. It is demonstrated that the linear character of quantum theory which enforces the peaceful…
The hybrid entangled states generated, e.g., in a trapped-ion or atom-cavity system, have exactly one ebit of entanglement, but are not maximally entangled. We demonstrate this by showing that they violate, but in general do not maximally…
Entanglement is the powerful and enigmatic resource central to quantum information processing, which promises capabilities in computing, simulation, secure communication, and metrology beyond what is possible for classical devices. Exactly…
We provide generalizations of known two-qubit entanglement distillation protocols for arbitrary Hilbert space dimensions. The protocols, which are analogues of the hashing and breeding procedures, are adapted to bipartite quantum states…