Related papers: Construct SLOCC invariants via square matrix
Quantum coherence has received significant attention in recent years, but its study is mostly conducted in single party settings. In this paper, we generalize important results in multipartite entanglement theory to their counterparts in…
In this note we define a polynomial invariant for colored links by a skein relation. It specializes to the Jones polynomial for classical links.
We show that in principle, $N$-partite unitary transformations can be perfectly discriminated under local measurement and classical communication (LOCC) despite of their nonlocal properties. Based on this result, some related topics,…
In this paper we define and give examples of a family of polynomial invariants of virtual knots and links. They arise by considering certain 2$\times$2 matrices with entries in a possibly non-commutative ring, for example the quaternions.…
Recently, a novel GHZ/W graphical calculus has been established to study and reason more intuitively about interacting quantum systems. The compositional structure of this calculus was shown to be well-equipped to sufficiently express…
In a recent paper \cite{mySEPvsLOCC}, we showed how to construct a quantum protocol for implementing a bipartite, separable quantum measurement using only local operations on subsystems and classical communication between parties (LOCC)…
We construct the protocols to achieve probabilistic and deterministic entanglement transformations for bipartite pure states by means of local operations and classical communication. A new condition on pure contraction transformations is…
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 new skein invariants of links based on a procedure where we first apply the skein relation only to crossings of distinct components, so as to produce collections of unlinked knots. We then evaluate the resulting knots using a…
We consider one single copy of a mixed state of two qubits and investigate how its entanglement changes under local quantum operations and classical communications (LQCC) of the type $\rho'\sim (A\otimes B)\rho(A\otimes B)^{\dagger}$. We…
We present two different constructions of invariants for Legendrian knots in the standard contact space $\R^3$. These invariants are defined combinatorially, in terms of certain planar projections, and are useful in distinguishing…
We show that every three-dimensional subspace of qutrit-qudit complex or real systems has a distinguishable basis under one-way local operations and classical communication (LOCC). In particular this solves an open problem proposed in [J.…
We present a method of determining important properties of a shared bipartite quantum state, within the ``distant labs'' paradigm, using \emph{only} local operations and classical communication (LOCC). We apply this procedure to spectrum…
In this paper, we study the number of rounds of communication needed to implement certain tasks by local quantum operations and classical communication (LOCC). We find that the class of LOCC operations becomes strictly more powerful as more…
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
We use planar 4-valent graphs and a graphical calculus involving such graphs to construct an invariant for balanced-oriented, knotted 4-valent graphs. Our invariant is an extension of the $sl(n)$ polynomial for classical knots and links. We…
We develop a simple method for constructing polynomial invariants of degree 4 for even-$n$ qubits and give explicit expressions for these polynomial invariants. We demonstrate the invariance of the polynomials under stochastic local…
In this paper, we study pure state entanglement in systems of dimension $2\otimes m\otimes n$. Two states are considered equivalent if they can be reversibly converted from one to the other with a nonzero probability using only local…
We construct exactly solvable models for four particles moving on a real line or on a circle with translation invariant two- and four-particle interactions.
Simple semitoric systems were classified about ten years ago in terms of a collection of invariants, essentially given by a convex polygon with some marked points corresponding to focus-focus singularities. Each marked point is endowed with…