Markov property of Gaussian states of canonical commutation relation algebras

Abstract

tF wthF hysF 50D IIQSIU @PHHWA Markov property of Gaussian states of canonical commutation relation algebras D enes Petz 1;3;4 and J ozsef Pitrik 2;4 3 elfr ed enyi snstitute of wthemtisD rEIQTR fudpestD yf IPUD rungry 4 heprtment for wthemtil enlysisD fudpest niversity of ehnology nd ionomis rEISPI fudpest sFD rungry

Quantum versus Classical Correlations in Gaussian States

“…Therefore, the Gaussian states with CM σ AB that have zero Gaussian quantum discord are the ones such that strong subadditivity is saturated on Gaussian extensions σ ABC = σ AB ⊕ σ C . In the general case of tripartite Gaussian states where each subsystem A, B, and C contains an arbitrary number of modes, Petz and Pitrik have recently characterized the subset of Gaussian states (tagged as Markov states) saturating the strong subadditivity [20]. For a tripartite n-mode CM for some j, 0 ≤ j ≤ m − l. In our setting, the block B is made of a single mode only, hence the only possibilities are j = 0, 1.…”

“…In any dimension (including infinite dimensions under the constraint of finite mean energy), the states AB with zero discord are the ones that saturate the strong subadditivity inequality for the Von Neumann entropy on a tripartite state ABC where C is an ancillary system realizing the measurements on B [14,19]. From the characterization of such states in the Gaussian scenario [20] (see Supplementary Appendix A [21] for more details), it follows that the only two-mode Gaussian states with zero Gaussian quantum discord are product states σ AB = α ⊕ β, i.e., states with no correlations at all, that constitute a zero measure set. Quite remarkably, then, all correlated two-mode Gaussian states have non-classical correlations certified by a nonzero quantum discord.…”

Gaussian Geometric Discord

“…This set can be characterised following the results of Ref. 31 (see also the Supplemental Material in 10 ). The quantity Q G in Eq.…”

A Survey on Quantum Channel Capacities

“…For the properties of Holevo information and on the capacity of quantum channels see the works of Holevo [231], [233], Schumacher and Westmoreland [464,465,466,467,468,469], Horodecki [237], Datta [127], Arimoto [18]. On the geometrical interpretation of the maps of a quantum channel see the works of Cortese [114], Petz [427][428][429][430][431][432][433], [435], Hiai [229].…”