Related papers: The split and approximate split property in 2D sys…
The efficient generation of random quantum states is a long-standing challenge, motivated by their diverse applications in quantum information processing tasks. In this work, we identify entanglement as the key resource that enables local…
Entanglement is the resource to overcome the natural limitations of spatially separated parties restricted to Local Operations assisted by Classical Communications (LOCC). Recently two new classes of operational entanglement measures, the…
Absolutely maximally entangled (AME) pure states of a system composed of $N$ parties are distinguished by the property that for any splitting at least one partial trace is maximally mixed. Due to maximal possible correlations between any…
We introduce a new entanglement measure based on optimal entanglement witness. First of all, we show that the entanglement measure satisfies some necessary properties, including zero entanglements for all separable states, convexity,…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where…
Anyons are exotic quasiparticles living in two dimensions that do not fit into the usual categories of fermions and bosons, but obey a new form of fractional statistics. Following a recent proposal [Phys. Rev. Lett. 98, 150404 (2007)], we…
We characterize the boundary of the convex compact set of absolutely separable states, referred as {\bf AS}, that cannot be transformed to entangled states by global unitary operators, in $2\otimes d$ Hilbert space. However, we show that…
It is shown that local distinguishability of orthogonal mixed states can be completely characterized by local distinguishability of their supports irrespective of entanglement and mixedness of the states. This leads to two kinds of upper…
In the companion paper of the authors, a general synchronization framework was developed in the paradigmatic context of the 2D Navier-Stokes equations that allows one to precisely study the relation between the determining modes property of…
Until recently, a careful derivation of the fusion structure of anyons from some underlying physical principles has been lacking. In [Shi et al., Ann. Phys., 418 (2020)], the authors achieved this goal by starting from a conjectured form of…
The existence of a maximally entangled pure state is a cornerstone result of entanglement theory that has paramount consequences in quantum information theory. A natural generalization of this property is to consider whether a notion of…
Long-range entangled states are vital for quantum information processing and quantum metrology. Preparing such states by combining measurements with unitary gates opened new possibilities for efficient protocols with finite-depth quantum…
Quantum states are the key mathematical objects in quantum mechanics, and entanglement lies at the heart of the nascent fields of quantum information processing and computation. However, there has not been a general, necessary and…
Laughlin states have recently been constructed on fractal lattices and have been shown to be topological in such systems. Some of their properties are, however, quite different from the two-dimensional case. On the Sierpinski triangle, for…
Decomposition of state spaces into dynamically different components is helpful for the understanding of dynamical behaviors of complex systems. A Conley type decomposition theorem is proved for nonautonomous dynamical systems defined on a…
We study the superselection sectors of two quantum lattice systems stacked onto each other in the operator algebraic framework. We show in particular that all irreducible sectors of a stacked system are unitarily equivalent to a product of…
We review aspects of classical and quantum mechanics of many anyons confined in an oscillator potential. The quantum mechanics of many anyons is complicated due to the occurrence of multivalued wavefunctions. Nevertheless there exists, for…
Motivated to understand how entanglement resources can be distributed in quantum networks, we introduce threshold entanglement (TE) states. These are multipartite quantum states whose entanglement across bipartitions forces all marginals of…
We provide a powerful machinery to prove fully smooth one shot multipartite covering, aka convex split, type results for quantum states. In the important case of smooth multipartite convex split for classical quantum states, aka smooth…