Hierarchy of continuous-variable quantum resource theories. G. Gianfelici, H. Kampermann and D. Bruß in New J. Phys. 23:113008 (2021). What the paper says!?
The paper aims to extend results of quantum resource theories to the infinite-dimensional space, which is structurally different:
They use finite constraints, and also restrictions to Gaussian states. They also «establish a connection between non-uniformity, coherence, quantum discord and entanglement, by identifying a hierarchy between them». As such, the work is a generalization of Ref. [1] and a follow-up to Refs. [2][3].
The relevance and application to the optical field is discussed in a footnote:
The formalism is developed on states that depend on both frequency and position, the necessity for that is unclear.
They restrict to Gaussian states:
for which they give, however, a nice description of Gaussian states (Eqs. (6-8)).
Even basic extensions beyond Gaussian states are beyond the scope of their analysis (in another footnote):
Their hierarchy is the most important (and original) result. In the quantum-optical context, it is, however, unclear. It seems to say that a pure state with superpositions of the incoherent basis (as is the case of Glauber's coherent state) always has entanglement, which is not true. This is probably explained by their footnote (reproduced above). To make sure, one should study the papers which they extend,[1] in particular Ref. [4] to make sure what is meant in this community by entanglement in infinite-dimensional Hilbert space.
Despite such confusions, it has a nice introduction:
References
- ↑ 1.0 1.1 Maximal coherence and the resource theory of purity. A. Streltsov, H. Kampermann, S. Wölk, M. Gessner and D. Bruß in New J. Phys. 20:053058 (2018).
- ↑ Quantifying coherence in infinite-dimensional systems. Y. Zhang, L. Shao, Y. Li and H. Fan in Phys. Rev. A 93:012334 (2016).
- ↑ Quantifying coherence of Gaussian states. J. Xu in Phys. Rev. A 93:032111 (2016).
- ↑ On the quantification of entanglement in infinite-dimensional quantum systems. J. Eisert, C. Simon and M. B. Plenio in J. Phys. A.: Math. Gen. 35:3911 (2002).