Localizable multipartite entanglement
Abstract: The localizable entanglement (LE) is the maximal amount of entanglement that can be concentrated, on average, onto part of a multipartite system via local projective measurements on its complement. The LE has found bountiful applications in the study of quantum phase transitions and entanglement in spin systems. Traditionally, the LE has been defined with respect to bipartite entanglement measures, such as the entanglement entropy or the two-qubit concurrence. More recent work has analyzed specific quantum states using the LE defined by multipartite entanglement measures. Motivated by a GHZ state extraction problem, we study the LE given by multipartite entanglement measures known as the n-tangle, the GME-concurrence, and the concentratable entanglement (CE). For generic states, we derive a set of easily computable and experimentally accessible upper and lower bounds on the LE given by these measures in terms of either spin correlation functions or explicit functions of marginal states. Continuing along this line, we also derive a set of uniform continuity bounds on the LE. Using this collection of bounds, we study concentration phenomena of the LE, revealing the typical behavior of the LE in large Hilbert spaces. To illustrate the utility of our bounds, we apply them to analyze allowable state transformations on graph states for a variety of examples. We also supplement our analytical results with numerical simulations for random states to investigate the tightness of our bounds. Finally, we numerically show how the LE may reveal critical behavior in spin-half systems by computing the LE and its bounds for ground states of the transverse-field Ising model. (Joint work with Samihr Hermes and Felix Leditzky)
