Distilling momentum-space entanglement in Luttinger liquids at finite temperature

While much is known about the entanglement characteristics of ground states, the properties of reduced thermal density matrices have received significantly less attention. Here we investigate the entanglement content of reduced thermal density matrices for momentum-space bipartitioning in Luttinger liquids using analytical and numerical methods. The low lying part of its spectrum contains an "entanglement gap", which persists up to temperatures comparable to the level spacing. With increasing temperature, the low energy modes acquire dispersion and resemble to those in the physical Hamiltonian with an enhanced effective temperature. The momentum-space entanglement is carried by high energy modes (compared to temperature), featuring a completely flat spectrum. The von-Neumann entropy increases with temperature with a universal Sommerfeld coefficient. The momentum-space entanglement Hamiltonian turns out to be as universal as the physical Hamiltonian.Comment: 6 pages, 2 figure

Robust engineering of maximally entangled states by identical particle interferometry

We propose a procedure for the robust preparation of maximally entangled states of identical fermionic qubits, studying the role played by particle statistics in the process. The protocol exploits externally activated noisy channels to reset the system to a known state. The subsequent interference effects generated at a beam splitter result in a mixture of maximally entangled Bell states and NOON states. We also discuss how every maximally entangled state of two fermionic qubits distributed over two spatial modes can be obtained from one another by fermionic passive optical transformations. Using a pseudospin-insensitive, non-absorbing, parity check detector, the proposed technique is thus shown to deterministically prepare any arbitrary maximally entangled state of two identical fermions. These results extend recent findings related to bosonic qubits. Finally, we analyze the performance of the protocol for both bosons and fermions when the externally activated noisy channels are not used and the two qubits undergo standard types of noise. The results supply further insights towards viable strategies for noise-protected entanglement exploitable in quantum-enhanced technologies.Comment: 9 pages, 6 figure

Bound entanglement in the XY model

We study the multi-spin entanglement for the 1D anisotropic XY model concentrating on the simplest case of three-spin entanglement. As compared to the pairwise entanglement, three-party quantum correlations have a longer range and they are more robust on increasing the temperature. We find regions of the phase diagram of the system where bound entanglement occurs, both at zero and finite temperature. Bound entanglement in the ground state can be obtained by tuning the magnetic field. Thermal bound entanglement emerges naturally due to the effect of temperature on the free ground state entanglement.Comment: 7 pages, 3 figures; some typos corrected, references adde

Entanglement crossover close to a quantum critical point

We discuss the thermal entanglement close to a quantum phase transition by analyzing the concurrence for one dimensional models in the quantum Ising universality class. We demonstrate that the entanglement sensitivity to thermal and to quantum fluctuations obeys universal $T\neq 0$--scaling behaviour. We show that the entanglement, together with its criticality, exhibits a peculiar universal crossover behaviour.Comment: 12 pages; 5 figures (eps). References added; to be published in Europhysics Letter