Related papers: Complexity of fermionic states
There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or…
Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…
We analyze the problem of quantifying entanglement in pure and mixed states of fermionic systems with fixed number parity yet not necessarily fixed particle number. The "mode entanglement" between one single-particle level and its…
We analyze fermionic modes as fundamental entities for quantum information processing. To this end we construct a density operator formalism on the underlying Fock space and demonstrate how it can be naturally and unambiguously equipped…
In recent years, the entanglement spectra of quantum states have been identified to be highly valuable for improving our understanding on many problems in quantum physics, such as classification of topological phases, symmetry-breaking…
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its…
Entanglement between the constituents of a quantum system is an essential resource in the implementation of many quantum processes and algorithms. Indeed, universal quantum computation is possible by measuring individual qubits comprising…
In this paper we give a definition for the Kolmogorov complexity of a pure quantum state. In classical information theory the algorithmic complexity of a string is a measure of the information needed by a universal machine to reproduce the…
The study of entanglement in systems composed of identical particles raises interesting challenges with far-reaching implications in both, our fundamental understanding of the physics of composite quantum systems, and our capability of…
We consider free fermion systems in arbitrary dimensions and represent the occupation pattern of each eigenstate as a classical binary string. We find that the Kolmogorov complexity of the string correctly captures the scaling behavior of…
The possible compatibility of density matrices for single-party subsystems is described by linear constraints on their respective spectra. Whenever some of those quantum marginal constraints are saturated, the total quantum state has a…
Entanglement entropy under a particle bipartition provides complementary information to mode entanglement as it is sensitive to interactions and particle statistics at leading order and does not depend on any externally imposed length…
We propose an entropic measure of non-classical correlations in general mixed states of fermion systems, based on the loss of information due to the unread measurement of the occupancy of single particle states of a given basis. When…
The Fock space of a system of indistinguishable particles is isomorphic (in a non-unique way) to the state-space of a composite i.e., many-modes, quantum system. One can then discuss quantum entanglement for fermionic as well as bosonic…
Unlike bosons, fermions always have a non-trivial entanglement. Intuitively, Slater determinantal states should be the least entangled states. To make this intuition precise we investigate entropy and entanglement of fermionic states and…
Fermionic Hamiltonians play a critical role in quantum chemistry, one of the most promising use cases for near-term quantum computers. However, since encoding nonlocal fermionic statistics using conventional qubits results in significant…
We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two…
A measure called Physical Complexity is established and calculated for a population of sequences, based on statistical physics, automata theory, and information theory. It is a measure of the quantity of information in an organism's genome.…
The emergence of a complex, large-scale organisation of cosmic matter into the Cosmic Web is a beautiful exemplification of how complexity can be produced by simple initial conditions and simple physical laws. In the epoch of Big Data in…
Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…