Related papers: Pure-state transformations and catalysis under ope…
Alice and Bob are given an unknown initial state chosen from a set of pure quantum states. Their task is to transform the initial state to a corresponding final pure state using local operations only. We prove necessary and sufficient…
We study the problem of transforming a tripartite pure state to a bipartite one using stochastic local operations and classical communication (SLOCC). It is known that the tripartite-to-bipartite SLOCC convertibility is characterized by the…
A complete analysis of entangled bipartite qutrit pure states is carried out based on a simple entanglement measure. An analysis of all possible extremally entangled pure bipartite qutrit states is shown to reduce, with the help of SLOCC…
The structure of all completely positive quantum operations is investigated which transform pure two-qubit input states of a given degree of entanglement in a covariant way. Special cases thereof are quantum NOT operations which transform…
Suppose several parties jointly possess a pure multipartite state, |\psi>. Using local operations on their respective systems and classical communication (i.e. LOCC) it may be possible for the parties to transform deterministically |\psi>…
We prove, in a multipartite setting, that it's always feasible to exactly transform a genuinely $m$-partite entangled state with sufficient many copies to any other $m$-partite state via local quantum operation and classical communication.…
From both theoretical and experimental points of view symmetric states constitute an important class of multipartite states. Still, entanglement properties of these states, in particular those with positive partial transposition (PPT), lack…
The tensor rank (also known as generalized Schmidt rank) of multipartite pure states plays an important role in the study of entanglement classifications and transformations. We employ powerful tools from the theory of homogeneous…
Let E' denote the set of non-normalized two-qutrit entangled states of rank four having positive partial transpose (PPT). We show that the set of SLOCC equivalence classes of states in E', equipped with the quotient topology, is…
Suppose that two distant parties Alice and Bob share an entangled state $\rho_{AB}$, and they want to exchange the subsystems of $\rho_{AB}$ by local operations and classical communication (LOCC). In general, this LOCC task (i.e. the LOCC…
A bipartite state which is secretly chosen from a finite set of known entangled pure states cannot be immediately useful in standard quantum information processing tasks. To effectively make use of the entanglement contained in this unknown…
An optimal local conversion strategy between any two pure states of a bipartite system is presented. It is optimal in that the probability of success is the largest achievable if the parties which share the system, and which can communicate…
We study the entanglement cost under quantum operations preserving the positivity of the partial transpose (PPT-operations). We demonstrate that this cost is directly related to the logarithmic negativity, thereby providing the operational…
We present a theory of entanglement transformations of Gaussian pure states with local Gaussian operations and classical communication. This is the experimentally accessible set of operations that can be realized with optical elements such…
The remarkable phenomenon of catalyst tells us that adding a catalyst could help state transformation. In this paper, we consider the problem of catalyst-assisted probabilistic coherence distillation for mixed states under strictly…
We demonstrate that local transformations on a composite quantum system can be enhanced in the presence of certain entangled states. These extra states act much like catalysts in a chemical reaction: they allow otherwise impossible local…
We develop the theory of local operations and classical communication (LOCC) for bipartite quantum systems represented by commuting von Neumann algebras. Our central result is the extension of Nielsen's Theorem, stating that the LOCC…
We study the general representations of positive partial transpose (PPT) states in ${\cal C}^K \otimes {\cal C}^M \otimes {\cal C}^N$. For the PPT states with rank-$N$ a canonical form is obtained, from which a sufficient separability…
Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single copy of the state. Accordingly, we say…
Suppose Alice and Bob jointly possess a pure state, $|\psi\ra$. Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform $|\psi\ra$ into another joint state $|\phi\ra$.…