Related papers: The Complexity of Boolean State Separation (Techni…
Connection-less, packet-switched quantum network architectures distribute entanglement across multi-hop paths through sequential entanglement swapping, in which each node acts on purely local state information. The architectural advantages…
We introduce a new family of separability criteria that are based on the existence of extensions of a bipartite quantum state $\rho$ to a larger number of parties satisfying certain symmetry properties. It can be easily shown that all…
Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…
This paper considers the liveness enforcement problem in a class of Petri nets (PNs) modeling distributed systems called Synchronized Sequential Processes (SSP). This class of PNs is defined as a set of mono-marked state machines…
Given a conjunctive Boolean network (CBN) with $n$ state-variables, we consider the problem of finding a minimal set of state-variables to directly affect with an input so that the resulting conjunctive Boolean control network (CBCN) is…
We show theoretically that in the superconducting nanostructures the gapped states of different topology are not always protected by separating gapped states. Depending on the structure design parameters, they can be either protected or…
Entanglement is a fundamental feature of quantum mechanics, playing a crucial role in quantum information processing. However, classifying entangled states, particularly in the mixed-state regime, remains a challenging problem, especially…
We investigate a two-parametric family of one-dimensional non-Hermitian complex potentials with parity-time ($\mathcal{PT}$) symmetry. We find that there exist two distinct types of phase transitions, from an unbroken phase (characterized…
In this paper, we focus on the study of quotients of Boolean control networks (BCNs) with the motivation that they might serve as smaller models that still carry enough information about the original network. Given a BCN and an equivalence…
The degree of a CSP instance is the maximum number of times that any variable appears in the scopes of constraints. We consider the approximate counting problem for Boolean CSP with bounded-degree instances, for constraint languages…
We investigate how classifiers for Boolean networks (BNs) can be constructed and modified under constraints. A typical constraint is to observe only states in attractors or even more specifically steady states of BNs. Steady states of BNs…
A new hierarchy of separability conditions for bipartite states is obtained. All the conditions in the hierarchy are necessary for separability. The conditions are expressed in terms of higher powers of the density operator of the bipartite…
We develop methods to probe the excitation spectrum of topological phases of matter in two spatial dimensions. Applying these to the Fibonacci string nets perturbed away from exact solvability, we analyze a topological phase transition…
Boolean networks are conventionally used to represent and simulate gene regulatory networks. In the analysis of the dynamic of a Boolean network, the attractors are the objects of a special attention. In this work, we propose a novel…
Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase…
We introduce a sequence of numerical tests that can determine the entanglement or separability of a state even when there is not enough information to completely determine its density matrix. Given partial information about the state in the…
Topological insulators and topological superconductors display various topological phases that are characterized by different Chern numbers or by gapless edge states. In this work we show that various quantum information methods such as the…
We study a single two-level atom interacting with a reservoir of modes defined by a reservoir structure function with a frequency gap. Using the pseudomodes technique, we derive the main features of a trapping state formed in the weak…
An extension to computational mechanics complexity measure is proposed in order to tackle quantum states complexity quantification. The method is applicable to any $n-$partite state of qudits through some simple modifications. A Werner…
Entanglement is one of the physical properties of quantum systems responsible for the computational hardness of simulating quantum systems. But while the runtime of specific algorithms, notably tensor network algorithms, explicitly depends…