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Our goal is to clarify the relation between entanglement and correlation energy in a bipartite system with infinite dimensional Hilbert space. To this aim we consider the completely solvable Moshinskys model of two linearly coupled harmonic oscillators. Also for small values of the couplings the entanglement of the ground state is nonlinearly related to the correlation energy, involving logarithmic or algebraic corrections. Then, looking for witness observables of the entanglement, we show how to give a physical interpretation of the correlation energy. In particular, we have proven that there exists a set of separable states, continuously connected with the Hartree-Fock state, which may have a larger overlap with the exact ground state, but also a larger energy expectation value. In this sense, the correlation energy provides an entanglement gap, i.e. an energy scale, under which measurements performed on the 1-particle harmonic sub-system can discriminate the ground state from any other separated state of the system. However, in order to verify the generality of the procedure, we have compared the energy distribution cumulants for the 1-particle harmonic sub-system of the Moshinskys model with the case of a coupling with a damping Ohmic bath at 0 temperature.
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The concept of correlation is central to all approaches that attempt the description of many-body effects in electronic systems. Multipartite correlation is a quantum information theoretical property that is attributed to quantum states independent of the underlying physics. In quantum chemistry, however, the correlation energy (the energy not seized by the Hartree-Fock ansatz) plays a more prominent role. We show that these two different viewpoints on electron correlation are closely related. The key ingredient turns out to be the energy gap within the symmetry-adapted subspace. We then use a few-site Hubbard model and the stretched H$_2$ to illustrate this connection and to show how the corresponding measures of correlation compare.
We provide an analytical tripartite-study from the generalized $R$-matrix. It provides the upper bound of the maximum violation of Mermins inequality. For a generic 2-qubit pure state, the concurrence or $R$-matrix characterizes the maximum violation of Bells inequality. Therefore, people expect that the maximum violation should be proper to quantify Quantum Entanglement. The $R$-matrix gives the maximum violation of Bells inequality. For a general 3-qubit state, we have five invariant entanglement quantities up to local unitary transformations. We show that the five invariant quantities describe the correlation in the generalized $R$-matrix. The violation of Mermins inequality is not a proper diagnosis due to the non-monotonic behavior. We then classify 3-qubit quantum states. Each classification quantifies Quantum Entanglement by the total concurrence. In the end, we relate the experiment correlators to Quantum Entanglement.
Entanglement is one of the most fascinating features arising from quantum-mechanics and of great importance for quantum information science. Of particular interest are so-called hybrid-entangled states which have the intriguing property that they contain entanglement between different degrees of freedom (DOFs). However, most of the current continuous variable systems only exploit one DOF and therefore do not involve such highly complex states. We break this barrier and demonstrate that one can exploit squeezed cylindrically polarized optical modes to generate continuous variable states exhibiting entanglement between the spatial and polarization DOF. We show an experimental realization of these novel kind of states by quantum squeezing an azimuthally polarized mode with the help of a specially tailored photonic crystal fiber.
Recently, a framework was established to systematically construct novel universal resource states for measurement-based quantum computation using techniques involving finitely correlated states. With these methods, universal states were found which are in certain ways much less entangled than the original cluster state model, and it was hence believed that with this approach many of the extremal entanglement features of the cluster states could be relaxed. The new resources were constructed as computationally universal states--i.e. they allow one to efficiently reproduce the classical output of each quantum computation--whereas the cluster states are universal in a stronger sense since they are universal state preparators. Here we show that the new resources are universal state preparators after all, and must therefore exhibit a whole class of extremal entanglement features, similar to the cluster states.
Entanglement between two quantum systems is a resource in quantum information, but dissipation usually destroys it. In this article we consider two qubits without direct interaction and we show that, even in cases where the open system dynamics destroys any initial entanglement, the mere monitoring of the environment can preserve or create the entanglement, by filtering the state of the qubits. While the systems we study are very simple, we can show examples with entanglement protection or entanglement birth, death, rebirth due to monitoring.
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