Entanglement Detection by Macroscopic Quantities
- Detection of entanglement in magnetic solids, modelled by the xxx Heisenberg spin-1/2 (a, top) and spin 1 (b, bottom) chains. The black solid curves are temperature dependences of the zero-field magnetic susceptibilities per particle and the red curves are “entanglement witnesses”. All points below left of intersection points (below the critical temperatures) indicate the existence of entanglement in the solids.
It is commonly believed that for the understanding of the behaviour of large, macroscopic, objects there is no need to invoke any genuine quantum entanglement - Einstein's ”spooky action at a distance”. This is because decoherence effects arising from many particles interaction with the environment would destroy all quantum correlations. Our research, however, shows that this belief is fundamentally mistaken and that entanglement is crucial to correctly describe some macroscopic properties of solids.
We demonstrated that macroscopic thermodynamical properties, such as internal energy, heat capacity or magnetic susceptibility - can reveal the existence of entanglement within solids in the thermodynamical limit even at moderately high temperatures. We found the critical values of physical parameters (e.g. the high-temperature limit and the maximal strength of magnetic field) below which entanglement exists in solids. In a different work we investigated entanglement between two or more macroscopic samples - such as blocks of harmonic oscillators in a linear harmonic chain or sets of spins in a long spin chain - which can be revealed by measuring only collective observables of the oscillators or spins, respectively. In the case of oscillators we found that such entanglement can be demonstrated even in the cases when neither of the oscillators from one block is entangled with the oscillator from the other block (i.e. it cannot be understood as a cumulative effect of entanglement between pairs of oscillators.)
C. Brukner and V. Vedral,
Macroscopic Thermodynamical Witnesses of Quantum Entanglement
e-print
M. Wiesniak. V. Vedral & C. Brukner,
Magnetic Susceptibility as Macroscopic Entanglement Witness
J. Kofler, V. Vedral, M. S. Kim & C. Brukner,
Entanglement between Collective Operators in a Linear Harmonic Chain
Phys. Rev. A 73, 052107 (2006) / e-print
J. Kofler and C. Brukner,
Entanglement Distribution Revealed by Macroscopic Observations
Phys. Rev. A 74, 050304(R) (2006) / e-print
