Quantifying entanglement with scattering experiments

Modern Physics Letters B, 2011

In order to quantify entanglement between two parts of a quantum system, one of the most used estimator is the Von Neumann entropy. Unfortunately, computing this quantity for large interacting quantum spin systems remains an open issue. Faced with this difficulty, other estimators have been proposed to measure entanglement efficiently, mostly by using simulations in the valence-bond basis. We review the different proposals and try to clarify the connections between their geometric definitions and proper observables. We illustrate this analysis with new results of entanglement properties of spin 1 chains.

Physical Review Letters, 2004

We study entanglement in Valence-Bond-Solid state, which describes the ground state of an AKLT quantum spin chain, consisting of bulk spin-1's and two spin-1/2's at the ends. We characterize entanglement between various subsystems of the ground state by mostly calculating the entropy of one of the subsystems; when appropriate, we evaluate concurrences as well. We show that the reduced density matrix of a continuous block of bulk spins is independent of the size of the chain and the location of the block relative to the ends. Moreover, we show that the entanglement of the block with the rest of the sites approaches a constant value exponentially fast, as the size of the block increases. We also calculate the entanglement of (i) any two bulk spins with the rest, and (ii) the end spin-1/2's (together and separately) with the rest of the ground state. For example, we show that (i) any two bulk spins become maximally entangled with the rest of the ground state exponentially fast in their separation distance, (ii) the two end spin-1/2's share no entanglement, and (iii) each end spin-1/2 is maximally entangled with the rest.

2011

We show how entanglement may be quantified in spin and cold atom many-body systems using standard experimental techniques only. The scheme requires no assumptions on the state in the laboratory and a lower bound to the entanglement can be read off directly from the scattering cross section of Neutrons deflected from solid state samples or the time-of-flight distribution of cold atoms in optical lattices, respectively. This removes a major obstacle which so far has prevented the direct and quantitative experimental study of genuine quantum correlations in many-body systems: The need for a full characterization of the state to quantify the entanglement contained in it. Instead, the scheme presented here relies solely on global measurements that are routinely performed and is versatile enough to accommodate systems and measurements different from the ones we exemplify in this work.

Proceedings of the National Academy of Sciences, 2007

Physica Scripta, 2020

We compute concurrence, a measure of bipartite entanglement, of the first excited state of the 1-D Heisenberg frustrated J 1-J 2 spin-chain and observe a sudden change in the entanglement of the eigen state near the coupling strength α = J 2/J 1 ≈ 0.241, where a quantum phase transition from spin-fluid phase to dimer phase has been previously reported. We numerically observe this phenomena for spin-chain with 8 sites to 16 sites, and the value of α at which the change in entanglement is observed, asymptotically tends to a value α c ≈ 0.24116. We have calculated the finite-size scaling exponents for spin chains with even and odd spins. It may be noted that bipartite as well as multipartite entanglement measures applied on the ground state of the system, fail to detect any quantum phase transition from the gapless to the gapped phase in the 1-D Heisenberg frustrated J 1-J 2 spin-chain. Furthermore, we measure bipartite entanglement of first excited states for other spin models like 2...

2008

We study entanglement in Valence-Bond-Solid state, which describes the ground state of an AKLT quantum spin chain, consisting of bulk spin-1’s and two spin-1/2’s at the ends. We characterize entanglement between various subsystems of the ground state by mostly calculating the entropy of one of the subsystems; when appropriate, we evaluate concurrences as well. We show that the reduced density matrix of a continuous block of bulk spins is independent of the size of the chain and the location of the block relative to the ends. Moreover, we show that the entanglement of the block with the rest of the sites approaches a constant value exponentially fast, as the size of the block increases. We also calculate the entanglement of (i) any two bulk spins with the rest, and (ii) the end spin-1/2’s (together and separately) with the rest of the ground state. For example, we show that (i) any two bulk spins become maximally entangled with the rest of the ground state exponentially fast in their...

2009

We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and, more generally, on the concept of area law. We also briefly describe the relation between entanglement and the presence of impurities, the idea of particle entanglement, the evolution of entanglement along renormalization group trajectories, the dynamical evolution of entanglement and the fate of entanglement along a quantum computation.

Physical Review A, 2004

The phase diagram of spins 1/2 embedded in a magnetic field mutually interacting antiferromagnetically is determined. Contrary to the ferromagnetic case where a second order quantum phase transition occurs, a first order transition is obtained at zero field. The spectrum is computed for a large number of spins and allows one to study the ground state entanglement properties which displays a jump of its concurrence at the critical point.

Recent Progress in Many-Body Theories - Proceedings of the 14th International Conference, 2008

We investigate a class of one-dimensional, exactly solvable anisotropic XY spin-1/2 models in an alternating transverse magnetic field from an entanglement perspective. We find that a physically motivated Lie-algebraic generalized entanglement measure faithfully portraits the static phase diagram -including second-and fourth-order quantum phase transitions belonging to distinct universality classes. In the simplest time-dependent scenario of a slow quench across a quantum critical point, we identify parameter regimes where entanglement exhibits universal dynamical scaling relative to the static limit.

Physical Review B, 2007

We investigate the entanglement properties of the valence-bond-solid states with generic integer spin S. Using the Schwinger boson representation of the valence-bond-solid states, the entanglement entropy, the von Neumann entropy of a subsystem, is obtained exactly and its relationship with the usual correlation function is clarified. The saturation value of the entanglement entropy, 2 log 2 ͑S +1͒, is derived explicitly and is interpreted in terms of the edge-state picture. The validity of our analytical results and the edge-state picture is numerically confirmed. We also propose an application of the edge state as a qubit for quantum computation.