Related papers: Complexity of fermionic states
The spatial character of territorial systems plays a crucial role in the emergence of their complexities. This contribution aims at illustrating to what extent different types of complexities can be exhibited in models of such systems. We…
Using a generalization of Cayley's hyperdeterminant as a new measure of tripartite fermionic entanglement we obtain the SLOCC classification of three-fermion systems with six single particle states. A special subclass of such three-fermion…
We analyze tight informationally complete measurements for arbitrarily large multipartite systems and study their configurations of entanglement. We demonstrate that tight measurements cannot be exclusively composed neither of fully…
Many experiments in quantum information aim at creating multi-partite entangled states. Quantifying the amount of entanglement that was actually generated can, in principle, be accomplished using full-state tomography. This method requires…
Descriptional complexity is the study of the conciseness of the various models representing formal languages. The state complexity of a regular language is the size, measured by the number of states of the smallest, either deterministic or…
There are at least a number of ways to formally define complexity. Most of them relate to some kind of minimal description of the studied object. Being this one in form of minimal resources of minimal effort needed to generate the object…
We analyze many-body entanglement in interacting fermionic systems by using the $M$-body reduced density matrix. We demonstrate that if a particle number conserving fermionic Hamiltonian contains only up to $M$-body interaction terms, then…
The local field potential (LFP) is as a measure of the combined activity of neurons within a region of brain tissue. While biophysical modeling schemes for LFP in cortical circuits are well established, there is a paramount lack of…
We introduce a general bipartite-like representation and Schmidt decomposition of an arbitrary pure state of $N$ indistinguishable fermions, based on states of $M<N$ and $(N-M)$ fermions. It is directly connected with the reduced $M$- and…
We study quantum information aspects of the fermionic entanglement negativity recently introduced in [Phys. Rev. B 95, 165101 (2017)] based on the fermionic partial transpose. In particular, we show that it is an entanglement monotone under…
We present a novel, non-parametric form for compactly representing entangled many-body quantum states, which we call a `Gaussian Process State'. In contrast to other approaches, we define this state explicitly in terms of a configurational…
In quantum mechanics, outcomes of measurements on a state have a probabilistic interpretation while the evolution of the state is treated deterministically. Here we show that one can also treat the evolution as being probabilistic in nature…
Complexity of two-level systems, e.g. spins, qubits, magnetic moments etc, are analysed based on the so-called correlational entropy in the case of pure quantum systems and the thermal entropy in case of thermal equilibrium that are…
The mechanism of collectivity coexisting with chaos in a finite system of strongly interacting fermions is investigated. The complex spectra are represented in the basis of two-particle two-hole states describing the nuclear double-charge…
Learning physical properties of high-dimensional states is crucial for developing quantum technologies but usually consumes an exceedingly large number of samples which are difficult to afford in practice. In this Letter, we use the…
Entanglement depth characterizes the minimal number of particles in a system that are mutually entangled. For symmetric states, we show that there is a dichotomy for entanglement depth: an $N$-particle symmetric state is either fully…
Electron pairing at low temperatures leads to superconductivity. A fundamental question is whether more complex states - characterized by order in four-electron composite objects, termed electron quadrupling or composite order - can exist…
Kolmogorov complexity is a measure of the information contained in a binary string. We investigate here the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any…
The position and momentum spreading of the electron distribution of the two-dimensional confined hydrogenic atom, which is a basic prototype of the general multidimensional confined quantum systems, is numerically studied in terms of the…
The completeness of quantum state space, is usually expressed as \sum_{m=0}^{\infty}|m><m|=1, where {|m>} is selected set of quantum states (basis). Density matrix |m><m| describes a pure quantum state. In this paper, by virtue of the…