Entanglement in Disordered Systems at Criticality

Abstract

Entanglement is a physical resource of a quantum system just like mass, charge or energy. Moreover it is an essential tool for many purposes of nowadays quantum information processing, e.g. quantum teleportation, quantum cryptography or quantum computation. In this work we investigate an extended system of N qubits. In our system a qubit is the absence or presence of an electron at a site of a tight-binding system. Several measures of entanglement between a given qubit and the rest of the system and also the entanglement between two qubits and the rest of the system is calculated in a one-electron picture in the presence of disorder. We invoke the power law band random matrix model which even in one dimension is able to produce multifractal states that fluctuate at all length scales. The concurrence, the tangle and the entanglement entropy all show interesting scaling properties.

4 pages, 5 figures, TIDS12 proceedings

References in corpus (8)

• Entanglement of a Pair of Quantum Bits
• Global entanglement in multiparticle systems
• Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
• Entanglement sharing in one-particle states
• Replacing energy by von Neumann entropy in quantum phase transitions
• Virial expansion for almost diagonal random matrices
• Supersymmetry Approach to Almost Diagonal Random Matrices
• Bipartite entanglement and localization of one-particle states

Cited by in corpus (3)

• Signatures of metal-insulator and topological phase transitions in the entanglement of one-dimensional disordered fermions
• Entropy of entanglement and multifractal exponents for random states
• Directional Localization in Disordered 2D Tight-Binding Systems: Insights from Single Particle Entanglement Measures