# Berlin 2005 – wissenschaftliches Programm

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# Q: Quantenoptik und Photonik

## Q 42: Quanteninformation II

### Q 42.5: Vortrag

### Dienstag, 8. März 2005, 15:00–15:15, HU Audimax

**Localizable Entanglement** — •Markus Popp^{1}, Frank Verstraete^{1}, Ignacio Cirac^{1}, and Miguel-Angel Martín-Delgado^{2} — ^{1}Max-Planck-Institut für Quantenoptik, 85748 Garching — ^{2}Departamento de Física Teórica I, Universidad Complutense de Madrid, E-28040, Spain

We consider systems of interacting spins and study the entanglement that
can be *localized*, on average, between two separated spins by performing
local measurements on the remaining spins. This concept of *Localizable
Entanglement* (LE) [1] leads naturally to notions like
entanglement length and entanglement fluctuations. For both spin-1/2 and spin-1
systems we prove that the LE of a pure quantum state can be lower bounded by
classical correlation functions. We further propose a scheme, based on
matrix-product states and the Monte Carlo method, to efficiently calculate the LE
for quantum states of a large number of spins. The virtues of LE are
illustrated for various spin models. In particular,
characteristic features of a quantum phase transition such as a diverging
entanglement length can be observed. We also give examples for pure quantum states
exhibiting a diverging entanglement length but finite correlation length [2]. We have numerical evidence that the ground state of
the antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum
channel. Furthermore we apply the numerical method to mixed states and study the entanglement as a function of temperature.

References:
[1] F. Verstraete, M. Popp, and J.I. Cirac,
Phys. Rev. Lett. **92**, 027901 (2004).
[2] F. Verstraete, M.A. Martin-Delgado, and J.I. Cirac,
Phys. Rev. Lett. **92**, 087201 (2004).