Spin system entanglement

Entanglement in supramolecu-lar spin systems of two weakly coupled antiferromagnetic rings (Purple-Cr7Ni). Phys. Rev. Lett., 104, 037203. 

Recently, the concept of thermal entanglement was introduced and studied within one-dimensional spin systems [64-66]. The state of the system described by the Hamiltonian H at thermal equilibrium is p T) = exp —H/kT)/Z, where Z = Tr[exp(—7//feT)] is the partition function and k is Boltzmann s constant. As p T) represents a thermal state, the entanglement in the state is called the thermal entanglement [64]. 

In this section, we investigate the dynamics of entanglement in one-dimensional spin systems with a time-dependent magnetic field. The Hamiltonian for such a system is given by [98]... 

In spite of impressive experimental demonstrations of basic quantum information effects in a number of different mesoscopic solid state systems, such as quantum dots in semiconductor microcavities, cold ions in traps, nuclear spin systems, Josephson junctions, etc., their concrete implementation is still at the proof-of-principle stage [1]. The development of materials that may host quantum coherent states with long coherence lifetimes is a critical research problem for the nearest future. There is a need for the fabrication of quantum bits (qubits) with coherence lifetimes at least three-four orders of magnitude longer than it takes to perform a bit flip. This would involve entangling operations, followed by the nearest neighbor interaction over short distances and quantum information transfer over longer distances. 

Because the temperature of a realistic nuclear spin system is not at zero degrees absolute, the internal interaction Hamiltonians always contain two parts one is stationary or coherent, the other fluctuating or incoherent, or random. The former part usually determines the positions of the peaks in a spectrum, the latter part governs the dynamics of the system. However, they may become entangled under certain conditions. For spin-1/2 systems, r.f. interactions can be made larger than the internal interactions in most cases, thus the manipulation of the interactions with r.f. pulses is realizable. This is an advantage of NMR over many other spectroscopies. In fact, most experimental methods in NMR spectroscopy correspond to certain manipulations of the internal interactions. For quadrupolar spin systems, the internal... 

Very large micelles may also form in binary surfactant systems. These are long wormlike micelles that become entangled at higher concentrations, giving rise to rheological properties similar to those in polymer solutions. Such systems have been examined by H band shape analysis [52,53]. The protons of the surfactant hydrocarbon chain form a very large dipolar coupled spin system with an essentially continuous distribution of transverse relaxation rates. The distribution of relaxation rates is related to the distribution of order... 

In this case, we will refer to pe as a pseudo-cat state. Generally, if p represents an entangled state, we say that Pe is pseudo-entangled. Now, if pi is a cat-state, the question is whether P( is entangled or not. We have to keep in mind that the density matrix of the whole spin system is Pe, and not p, but remember that NMR signals are proportional to pi, and not Pe. 

This section presents results of the space-time analysis of the above-mentioned motional processes as obtained by the neutron spin echo technique. First, the entropically determined relaxation processes, as described by the Rouse model, will be discussed. We will then examine how topological restrictions are noticed if the chain length is increased. Subsequently, we address the dynamics of highly entangled systems and, finally, we consider the origin of the entanglements. 

At the current time, there is no simple way to carry out the calculations with all these entanglement measures. Their properties, such as additivity, convexity, and continuity, and relationships are still under active investigation. Even for the best-understood entanglement of formation of the mixed states in bipartite systems AB, once the dimension or A or B is three or above, we don t know how to express it simply, although we have the general definitions given previously. However, for the case where both subsystems A and B are spin-i particles, there exists a simple formula from which the entanglement of formation can be calculated [42]. 

For simplicity, let us illustrate the calculations of entanglement for two spin- particles. The general Hamiltonian, in atomic units, for such a system is given by [57]... 

---