Distribution of G-concurrence of random pure states

Abstract

Average entanglement of random pure states of an N x N composite system is analyzed. We compute the average value of the determinant D of the reduced state, which forms an entanglement monotone. Calculating higher moments of the determinant we characterize the probability distribution P(D). Similar results are obtained for the rescaled N-th root of the determinant, called G-concurrence. We show that in the limit $N\to \infty$ this quantity becomes concentrated at a single point G=1/e. The position of the concentration point changes if one consider an arbitrary N x K bipartite system, in the joint limit $N,K\to \infty$, K/N fixed.

arXiv commentRevTeX4, 11 pages, 4 Encapsuled PostScript figures - Introduced new results, Section II and V have been significantly improved - To appear on PRA

References in corpus (10)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Entanglement Measures and Purification Procedures
• Entanglement monotones
• Induced measures in the space of mixed quantum states
• Aspects of generic entanglement
• Statistical properties of random density matrices
• Family of Concurrence Monotones and its Applications
• Hilbert--Schmidt volume of the set of mixed quantum states
• Bounds on entanglement in qudit subsystems
• Mixed State Entanglement of Assistance and the Generalized Concurrence

Cited by in corpus (24)

• Statistical distribution of quantum entanglement for a random bipartite state
• Symmetry-resolved Page curves
• Distinguishability of generic quantum states
• Optimal two-qubit gate for generation of random bipartite entanglement
• Entanglement in random pure states: Spectral density and average von Neumann entropy
• Parameters of Pseudo-Random Quantum Circuits
• Entanglement of three-qubit random pure states
• Bures-Hall Ensemble: Spectral Densities and Average Entropies
• Compact smallest eigenvalue expressions in Wishart-Laguerre ensembles with or without fixed-trace
• Entanglement of genuinely entangled subspaces and states: exact, approximate, and numerical results
• Purity distribution for generalized random Bures mixed states
• Moment-Based Evidence for Simple Rational-Valued Hilbert-Schmidt Generic 2 x 2 Separability Probabilities
• Entangled random pure states with orthogonal symmetry: exact results
• Quantumness Beyond Entanglement: The Case of Symmetric States
• Largest Schmidt eigenvalue of entangled random pure states and conductance distribution in chaotic cavities
• Distribution of interference in random quantum algorithms
• Characterizing and Quantifying Quantum Chaos with Quantum Tomography
• Typical Entanglement
• Polarized ensembles of random pure states
• Lower and upper bounds for entanglement of Rényi-$\alpha$ entropy
• Non-Abelian entanglement asymmetry in random states
• Bures and Hilbert-Schmidt 2 x 2 Determinantal Moments
• All possible permutational symmetries of a quantum system
• Integrals of Irreducible Representations of Classical Groups