We examine the entanglement of cyclic spin 1/2 chains with anisotropic XY Z Heisenberg couplings of arbitrary range at transverse factorizing magnetic fields. At these fields the system exhibits a degenerate symmetry-breaking separable ground state (GS). It is shown, however, that the side limits of the GS pairwise entanglement at these fields are actually non-zero in finite chains, corresponding such fields to a GS spin-parity transition. These limits exhibit universal properties like being independent of the pair separation and interaction range, and are directly related to the magnetization jump. Illustrative exact results are shown for chains with I) full range and II) nearest neighbor couplings. Global entanglement properties at such points are also discussed.Comment: 5 pages, 4 figure

Control at the interface between the classical and the quantum world is fundamental in quantum physics. In particular, how classical control is enhanced by coherence effects is an important question both from a theoretical as well as from a technological point of view. In this work, we establish a resource theory describing this setting and explore relations to the theory of coherence, entanglement and information processing. Specifically, for the coherent control of quantum systems the relevant resources of entanglement and coherence are found to be equivalent and closely related to a measure of discord. The results are then applied to the DQC1 protocol and the precision of the final measurement is expressed in terms of the available resources.Keywords: Resource Theories, Coherence, Entanglement, Discord, Quantumness, Quantum Computation Introduction -Coherent superposition is a defining characteristic of the quantum world. Coherence indicates the fundamental misalignment, or noncommutativity, between quantum states and the interactions or observables which we may use to probe them. Due to its intimate connection with quantum superposition, coherence is also important in a large number of quantum information protocols. In fact, coherence can be seen as a type of resource, allowing one to perform tasks which would be more difficult or not possible otherwise. Indeed, coherence has recently been developed into a formal quantum resource theory [1][2][3][4][5][6][7][8][9][10][11][12][13][14] 1 , similar to that for entanglement [20,21].In the macroscopic classical world, where states and observables commute, superposition effects are suppressed and physical systems can be described without coherence, using classical probability distributions. Yet some special systems, often found at mesoscopic scales, can exist in the murky borderlands between the classical and quantum worlds. In fact, systems which bridge between these worlds are very important in modern experiments. Operationally, it is common to employ intermediary physical systems, such as lasers, magnetic fields, or photodiodes, to interface with a separate "target" quantum system. By coupling to the target system, these mediator systems can function as state preparation, control, and measurement devices.In order to interact meaningfully with the controlled system, the mediator systems must themselves be able to exert a nonclassical effect on their targets. At the same time, they must also interface with the classical world in order to communicate human-or machine-readable instructions and measurement outcomes. Through this, they are inevitably exposed to classical noise and decoherence effects which makes the creation and the conservation of coherence a costly task. Recognising that co- * These authors contributed equally to this work 1 Another possible approach to coherence theory [15,16] is based on the theory of reference frames [17,18], which proved useful in quantum thermodynamics [19].herence is a potential resource, we might ask: what value might be gai...

We determine the conditions for the existence of a pair of degenerate parity breaking separable eigenstates in general arrays of arbitrary spins connected through XY Z couplings of arbitrary range and placed in a transverse field, not necessarily uniform. Sufficient conditions under which they are ground states are also provided. It is then shown that in finite chains, the associated definite parity states, which represent the actual ground state in the immediate vicinity of separability, can exhibit entanglement between any two spins regardless of the coupling range or separation, with the reduced state of any two subsystems equivalent to that of pair of qubits in an entangled mixed state. The corresponding concurrences and negativities are exactly determined. The same properties persist in the mixture of both definite parity states. These effects become specially relevant in systems close to the XXZ limit. The possibility of field induced alternating separable solutions with controllable entanglement side limits is also discussed. Illustrative numerical results for the negativity between the first and the j th spin in an open spin s chain for different values of s and j are as well provided.

We determine the conditions under which general dimer-type spin chains with XY Z couplings of arbitrary range in a general transverse field will exhibit an exactly separable parity-breaking eigenstate. We also provide sufficient conditions which ensure that it will be a ground state. We then examine the exact side limits at separability of the entanglement between any two spins in a finite chain, showing that in the vicinity of separability, the system will loose all signatures of dimerization, with pairwise entanglement approaching infinite range and becoming independent of separation and interaction range. The possibility of a non-uniform exactly separable ground state induced by an alternating field is also shown. As illustration, we examine the behavior of the pairwise entanglement in a finite XY dimer chain under a uniform as well as alternating field. Related aspects of the magnetization are also discussed.

We discuss a general treatment based on the mean field plus random phase approximation (RPA) for the evaluation of subsystem entropies and negativities in ground states of spin systems. The approach leads to a tractable general method, becoming straightforward in translationally invariant arrays. The method is examined in arrays of arbitrary spin with XY Z couplings of general range in a uniform transverse field, where the RPA around both the normal and parity breaking mean field state, together with parity restoration effects, are discussed in detail. In the case of a uniformly connected XY Z array of arbitrary size, the method is shown to provide simple analytic expressions for the entanglement entropy of any global bipartition, as well as for the negativity between any two subsystems, which become exact for large spin. The limit case of a spin s pair is also discussed.