Measure of qubit-environment entanglement for pure dephasing evolutions

Abstract

We propose a qubit-environment entanglement measure which is tailored for evolutions that lead to pure dephasing of the qubit, such as are abundant in solid-state scenarios. The measure can be calculated directly form the density matrix without minimization of any kind. In fact, it does not require knowledge of the full density matrix and it is enough to know the initial qubit state and the states of the environment conditional on qubit pointer states. This yields a computational advantage over standard entanglement measures, which becomes large when there are no correlations between environmental components in the conditional environmental states. In contrast to all other measures of mixed-state entanglement, the measure has a straightforward physical interpretation directly linking the amount of information about the qubit state which is contained in the environment to the amount of qubit-environment entanglement. This allows for a direct extension of the pure-state interpretation of entanglement generated during pure dephasing to mixed states, even though pure-state conclusions about qubit decoherence are not transferable.

Convex-roof entanglement measures of density matrices block diagonal in disjoint subspaces for the study of thermal states

“…[57]. It has later been shown that the periodical emergence of such states is possible in qubit-environment evolutions driven by Hamiltonians that lead to pure dephasing of the qubit [19] and are important for the emergence of objectivity [58][59][60][61][62][63][64]. Here we have found that the emergence of such states is not limited to pure-dephasing evolutions and that they can manifest themselves in other classes of interactions.…”

“…The quest to find efficiently computable entanglement measures that have a clear physical interpretation continues [19][20][21], because entanglement remains an important factor which predetermines the possibility of very quantum and nonintuitive behavior of bipartite systems. One approach is to sacrifice generality in order to obtain solvable scenarios which allows for the study of entanglement present in density matrices generated by a certain class of Hamiltonians.…”

“…One approach is to sacrifice generality in order to obtain solvable scenarios which allows for the study of entanglement present in density matrices generated by a certain class of Hamiltonians. This has been done for qubits interacting with large environments via a Hamiltonian which leads to qubit pure decoherence [19,22,23] and then generalized to systems of any size [24]. The consequence here was that increased understanding of this type of entanglement allowed for schemes for its measurement to be devised [25][26][27], which have been experimentally tested [28].…”

Transfer and teleportation of system-environment entanglement

“…The qubit-environment entanglement measure tailored to pure dephasing evolutions, which was introduced in Ref. [35], can be used to quantify the amount of entanglement in the CE state in eq. (10).…”

“…respectively, while the condition of separability of qubit C and the environment pre-teleportation and decoherence ( 10) is R00 (τ) = R11 (τ). Hence, if there is no entanglement after the first part of teleportation then both states are either entangled or separable, and the amount of entanglement in the two states is also the same [35], as it is quantified by a function analogous to eq. ( 12),…”