Related papers: One-body entanglement as a quantum resource in fer…
We present the Schmidt decomposition for arbitrary wavefunctions of two indistinguishable bosons, extending the recent studies of entanglement or quantum correlations for two fermion systems [J. Schliemann et al., Phys. Rev. B {\bf 63},…
Fermions, as a major class of quantum particles, provide platforms for quantum information processing beyond the possibilities of spins or bosons which have been studied more extensively. One particularly interesting model to study, in view…
The existence of fundamentally identical particles represents a foundational distinction between classical and quantum mechanics. Due to their exchange symmetry, identical particles can appear to be entangled -- another uniquely quantum…
This paper deals with the asymptotic behaviour of a widely used correlation characteristic in large quantum systems. The correlations are known as quantum entanglement, the characteristic is called entanglement entropy, and the system is an…
Local unitary operations allow for a unifying approach to the quantification of quantum correlations among the constituents of a bipartite quantum system. For pure states, the distance between a given state and its image under…
The entanglement between occupation-numbers of different single particle basis states depends on coupling between different single particle basis states in the second-quantized Hamiltonian. Thus in principle, interaction is not necessary…
In systems undergoing localization-delocalization quantum phase transitions due to disorder or monitoring, there is a crucial need for robust methods capable of distinguishing phases and uncovering their intrinsic properties. In this work,…
We consider spinless fermions on a finite one-dimensional lattice, interacting via nearest-neighbor repulsion and subject to a strong electric field. In the non-interacting case, due to Wannier-Stark localization, the single-particle wave…
Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification…
Quantum mechanical entanglement is a resource for quantum computation, quantum teleportation, and quantum cryptography. The ability to quantify this resource correctly has thus become of great interest to those working in the field of…
In this research, the entanglement within two entangled n-qubit systems is analyzed using the one-tangle, two-tangle, and {\pi}-tangle. The findings indicate that for certain quantum states, such as the generalized W state, where the…
A system of fermions forming a Fermi surface exhibits a large degree of quantum entanglement, even in the absence of interactions. In particular, the usual case of a codimension one Fermi surface leads to a logarithmic violation of the area…
We develop an energy density matrix that parallels the one-body reduced density matrix (1RDM) for many-body quantum systems. Just as the density matrix gives access to the number density and occupation numbers, the energy density matrix…
In a quantum many-body system that possesses an additive conserved quantity, the entanglement entropy of a subsystem can be resolved into a sum of contributions from different sectors of the subsystem's reduced density matrix, each sector…
Entanglement is the key resource for quantum technologies and is at the root of exciting many-body phenomena. However, quantifying the entanglement between two parts of a real-world quantum system is challenging when it interacts with its…
I first give an overview of the thesis and Matrix Product States (MPS) representation of quantum spin chains with an improvement on the conventional notation. The rest of this thesis is divided into two parts. The first part is devoted to…
This thesis is a multidisciplinary contribution to the information theory of single-particle Coulomb systems in their relativistic and not relativistic description, to the theory of special functions of mathematical physics with the…
We analyze many body localization (MBL) in an interacting one-dimensional system with a deterministic aperiodic potential. Below the threshold value of the potential $h < h_c$, the non-interacting system has single particle mobility edges…
We identify a general criterion for detecting entanglement of pure bipartite quantum states describing a system of two identical particles. Such a criterion is based both on the consideration of the Slater-Schmidt number of the fermionic…
One of the most important questions in quantum information theory is the so-called separability problem. It involves characterizing the set of separable (or, equivalently entangled) states among mixed states of a multipartite quantum…