Related papers: The Complexity of Boolean State Separation (Techni…
Detectability describes the property of an system whose current and the subsequent states can be uniquely determined after a finite number of observations. In this paper, we relax detectability to C-detectability that only requires a given…
We construct parametrized isometric tensor network states -- referred to as skeletons -- that allow us to explore phases of abelian topological order and can be efficiently implemented on quantum processors. We obtain stable finite…
Boolean networks is a well-established formalism for modelling biological systems. A vital challenge for analysing a Boolean network is to identify all the attractors. This becomes more challenging for large asynchronous Boolean networks,…
We introduce a novel class of phase transitions separating quantum states with different entanglement features. An example of such an "entanglement phase transition" is provided by the many-body localization transition in disordered quantum…
With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (non-trivial only for mixed states) which captures the localisation of entanglement of the state. Particular…
A Boolean network (BN) is a transformation of the set of Boolean configurations of a given length. A trapspace of a BN is a subcube invariant by the BN; a principal trapspace is the smallest trapspace containing a given configuration; a…
We analyze exact ground state (GS) separability in general $N$ particle systems with two-site couplings. General necessary and sufficient conditions for full separability, in the form of one and two-site eigenvalue equations, are first…
One of the fundamental concepts of quantum information theory is that of entanglement purification; that is, the transformation of a partially entangled state into a smaller-dimensional, more completely entangled state. Of particular…
The degree of a CSP instance is the maximum number of times that a variable may appear in the scope of constraints. We consider the approximate counting problem for Boolean CSPs with bounded-degree instances, for constraint languages…
Boolean control networks (BCNs) are discrete-time dynamical systems with Boolean state-variables and inputs that are interconnected via Boolean functions. BCNs are recently attracting considerable interest as computational models for…
A remarkable feature of quantum entanglement is that an entangled state of two parties, Alice (A) and Bob (B), may be more disordered locally than globally. That is, S(A) > S(A,B), where S(.) is the von Neumann entropy. It is known that…
We study separability properties in a 5-dimensional set of states of quantum systems composed of three subsystems of equal but arbitrary finite Hilbert space dimension d. These are the states, which can be written as linear combinations of…
Topological boundary states exhibit distinctive properties, including unidirectional propagation and noise robustness, which hold significant potential for advancing the performance of quantum science and technology. Here, we demonstrate…
Using new results on the separability properties of bosonic systems, we provide a new complete criterion for separability. This criterion aims at characterizing the set of separable states from the inside by means of a sequence of…
We present a new set of inseparabilty inequalities to detect entanglement in $N$-spin states. These are based on negative partial transposition and involve collective spin-spin correlations of any two partitions of the entire system. They…
In conformal field theories, in contrast to \emph{adding} some auxiliary states into the bipartite mixed state $\rho_{AB}$ as the usual purifications do, we show a pure entangled state $\psi_{AB}$ can be constructed by \emph{subtracting}…
In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. For this purpose, its randomness is estimated using three measures, of which…
We consider from a microscopic perspective large deviation properties of several stochastic interacting particle systems, using their mapping to integrable quantum spin systems. A brief review of recent work is given and several new results…
The present paper proves that a Sleptsov net (SN) is Turing-complete, that considerably improves, with a brief construct, the previous result that a strong SN is Turing-complete. Remind that, unlike Petri nets, an SN always fires enabled…
Number partitioning is an NP-complete problem of combinatorial optimization. A statistical mechanics analysis reveals the existence of a phase transition that separates the easy from the hard to solve instances and that reflects the…