Related papers: Factorization Law for Two Lower Bounds of Concurre…

We consider unitary transformations on a bipartite system A x B. To what extent entails the ability to transmit information from A to B the ability to transfer information in the converse direction? We prove a dimension-dependent lower…

Recently, Boehm and Stefan constructed duplicial (paracyclic) objects from distributive laws between (co)monads. Here we define the category of factorisations of a distributive law, show that it acts on this construction, and give some…

We introduce an intuitive measure of genuine multipartite entanglement which is based on the well-known concurrence. We show how lower bounds on this measure can be derived that also meet important characteristics of an entanglement…

The detection and estimation of quantum entanglement are the essential issues in the theory of quantum entanglement. We construct matrices based on the realignment of density matrices and the vectorization of the reduced density matrices,…

Gradient descent for matrix factorization exhibits an implicit bias toward approximately low-rank solutions. While existing theories often assume the boundedness of iterates, empirically the bias persists even with unbounded sequences. This…

We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion,…

Quantum entanglement is a crucial resource in quantum information processing, advancing quantum technologies. The greater the uncertainty in subsystems' pure states, the stronger the quantum entanglement between them. From the dual form of…

We study the law of the minimum of a Brownian bridge, conditioned to take specific values at specific points, and the law of the location of the minimum. They are used to compare some non-adaptive optimisation algorithms for black-box…

Recently, our group quantitatively defined two quantities, "competition ability" and "uniqueness" (Chin. Phys. Lett. 26 (2009) 058901) for a kind of cooperation-competition bipartite networks, where "producers" produce some "products" and…

A bi-disperse granular gas in a compartmentalized system is experimentally found to cluster competitively: Depending on the shaking strength, the clustering can be directed either towards the compartment initially containing mainly small…

In unitary property testing a quantum algorithm, also known as a tester, is given query access to a black-box unitary and has to decide whether it satisfies some property. We propose a new technique for proving lower bounds on the quantum…

The one-dimensional nearest-neighbor totally asymmetric simple exclusion process can be constructed in the same space as a last-passage percolation model in Z^2. We show that the trajectory of a second class particle in the exclusion…

Inspired by the `computable cross norm' or `realignment' criterion, we propose a new point of view about the characterization of the states of bipartite quantum systems. We consider a Schmidt decomposition of a bipartite density operator.…

Quantum dots are nanometer-scale semiconductor particles that exhibit size-dependent quantum mechanical properties. In this work, we investigate the dynamics of quantum correlations, quantified by the concurrence and the quantum coherence,…

We study conditions under which a partial differential operator of arbitrary order $n$ in two variables or ordinary linear differential operator admits a factorization with a first-order factor on the left. The factorization process…

Consider a finite system of Brownian particles on the real line. Each particle has drift and diffusion coefficients depending on its current rank relative to other particles, as in Karatzas, Pal and Shkolnikov (2012). We prove some…

In this paper, we consider the existence of a factorization of a monic, bounded motion polynomial. We prove existence of factorizations, possibly after multiplication with a real polynomial and provide algorithms for computing polynomial…

For a bipartite quantum system consisting of subsystems A and B it was shown by Zhang et al. (Physics Letters A 376 (2012) 3588-3592) that the amount of classical correlations, which is used to define the quantum discord, is known to be…

We provide a general description of the phenomenon of entanglement in bipartite systems, as it manifests in micro and macro physical systems, as well as in human cognitive processes. We do so by observing that when genuine coincidence…

We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled…