Abstract
We investigate monogamy of correlations and entropy inequalities in the Bloch representation. Here, both can be understood as direct relations between different correlation tensor elements and thus appear intimately related. To that end we introduce the split Bloch basis, that is particularly useful for representing quantum states with low dimensional support and thus amenable to purification arguments. Furthermore, we find dimension dependent entropy inequalities for the Tsallis 2-entropy. In particular, we present an analogue of the strong subadditivity and a quadratic entropy inequality. These relations are shown to be stronger than subadditivity for finite dimensional cases.
Highlights
This articles covers two important themes of quantum information: entropy inequalities and monogamy relations
Note that if the subsystems of the bi-partition have the same dimension dΣ = dΩ the correlation tensors are defined as Definition 3 and the maximization is obsolete, if they have different dimension dΣ = dΩ the split Bloch basis will be used and the sum will be over TSvD 2 as defined in Definition 6
In the case of α = q = 2 we can use the simple representation of Tr ρ2 in form of correlation tensor norms to find simple forms of these entropies: Remark 6 Given n-partite quantum state ρΣ ∈ HdΣ = ⊗ni=1Hdi where Σ := {Σ1, Σ2, · · ·, Σn} is the set of all parties we find the Tsallis 2 or linear entropy as: SL(ρΣ) := 1 − Tr(ρ2Σ)
Summary
This articles covers two important themes of quantum information: entropy inequalities and monogamy relations. That the introduction of dimensional factors enlarges the applicability of monogamy and entropy relations is in itself a noteworthy observation already made in [24], in this article we are able to contribute entropy and (quasi-) monogamy relations Let us stress another important point: Even though both areas of research, entropy inequalities and monogamy relations, are usually considered as two distinct subfields, there exists an intimate connection, which becomes clear once we identify them as particular instances of the marginal problem. Since both entropy inequalities as well as monogamy relations depend on functions of the marginals, it is not surprising that a connection between them can be made This connection becomes obvious by using the correlation tensor of the generalized Bloch representation [27–30].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
