Entanglement criterion via general symmetric informationally complete measurement

We propose entanglement criteria for multipartite systems via symmetric informationally complete (SIC) measurement and general symmetric informationally complete (GSIC) measurement. We apply these criteria to detect entanglement of multipartite states, such as the convex of Bell states, entangled states mixed with white noise. It is shown that these criteria are stronger than some existing ones.

Emergent classicality in general multipartite states and channels

In a quantum measurement process, classical information about the measured system spreads throughout the environment. Meanwhile, quantum information about the system becomes inaccessible to local observers. Here we prove a result about quantum channels indicating that an aspect of this phenomenon is completely general. We show that for any evolution of the system and environment, for everywhere in the environment excluding an O(1)-sized region we call the "quantum Markov blanket," any locally accessible information about the system must be approximately classical, i.e. obtainable from some fixed measurement. The result strengthens the earlier result of Brandão et al. (Nat. comm. 6:7908) in which the excluded region was allowed to grow with total environment size. It may also be seen as a new consequence of the principles of no-cloning or monogamy of entanglement. Our proof offers a constructive optimization procedure for determining the "quantum Markov blanket" region, as well as the effective measurement induced by the evolution. Alternatively, under channel-state duality, our result characterizes the marginals of multipartite states.

Local transformations of multiple multipartite states

Understanding multipartite entanglement is vital, as it underpins a wide range of phenomena across physics. The study of transformations of states via Local Operations assisted by Classical Communication (LOCC) allows one to quantitatively analyse entanglement, as it induces a partial order in the Hilbert space. However, it has been shown that, for systems with fixed local dimensions, this order is generically trivial, which prevents relating multipartite states to each other with respect to any entanglement measure. In order to obtain a non-trivial partial ordering, we study a physically motivated extension of LOCC: multi-state LOCC. Here, one considers simultaneous LOCC transformations acting on a finite number of entangled pure states. We study both multipartite and bipartite multi-state transformations. In the multipartite case, we demonstrate that one can change the stochastic LOCC (SLOCC) class of the individual initial states by only applying Local Unitaries (LUs). We show that, by transferring entanglement from one state to the other, one can perform state conversions not possible in the single copy case; provide examples of multipartite entanglement catalysis; and demonstrate improved probabilistic protocols. In the bipartite case, we identify numerous non-trivial LU transformations and show that the source entanglement is not additive. These results demonstrate that multi-state LOCC has a much richer landscape than single-state LOCC.

A link between symmetries of critical states and the structure of SLOCC classes in multipartite systems

Central in entanglement theory is the characterization of local transformations among pure multipartite states. As a first step towards such a characterization, one needs to identify those states which can be transformed into each other via local operations with a non-vanishing probability. The classes obtained in this way are called SLOCC classes. They can be categorized into three disjoint types: the null-cone, the polystable states and strictly semistable states. Whereas the former two are well characterized, not much is known about strictly semistable states. We derive a criterion for the existence of the latter. In particular, we show that there exists a strictly semistable state if and only if there exist two polystable states whose orbits have different dimensions. We illustrate the usefulness of this criterion by applying it to tripartite states where one of the systems is a qubit. Moreover, we scrutinize all SLOCC classes of these systems and derive a complete characterization of the corresponding orbit types. We present representatives of strictly semistable classes and show to which polystable state they converge via local regular operators.

Geometrical analysis and entanglement measure of symmetric multiqubit states

We geometrically examine the entanglement in symmetric multiquibt states using the spin coherent states properties. We employ the Majorana representation to examine how coherent (polarized) and unpolarized states can be represented in the Bloch sphere and subsequently to quantify entanglement in multipartite systems. Entanglement can be viewed as a distance separate two points in Bloch sphere and how this notion can be extended for multipartite states in W class. This provides us with an entanglement measure for [Formula: see text]-states analogue to the notion of Concurrence.

k-uniform maximally mixed states from multi-qudit phase states

This paper concerns the construction of k-uniform maximally mixed multipartite states by using the formalism of phase states for finite dimensional systems (qudits). The k-uniform states are a special kind of entangled (n)-qudits states, such that after tracing out arbitrary (n[Formula: see text]k) subsystems, the remaining (k) subsystems are maximally mixed. We recall some basic elements about unitary phase operators of a multi-qudit system and we give the corresponding separable density matrices. Evolved density matrices arise when qudits of the multipartite system are allowed to interact via an Hamiltonian of Heisenberg type. The expressions of maximally mixed states are explicitly derived from multipartite evolved phase states and their properties are discussed.