Dimensionally sharp inequalities for the linear entropy

Abstract

We derive an inequality for the linear entropy, that gives sharp bounds for all finite dimensional systems. The derivation is based on generalised Bloch decompositions and provides a strict improvement for the possible distribution of purities for all finite dimensional quantum states. It thus extends the widely used concept of entropy inequalities from the asymptotic to the finite regime, and should also find applications in entanglement detection and efficient experimental characterisations of quantum states.

Monogamy of correlations and entropy inequalities in the Bloch picture

“…The key technique in all our theorems is the relation of the purity r Tr 2 ( )to correlation tensor norms Typically we employ purity here, however a sharper bound may lead to better results. Indeed, after the submission of our manuscript [44] proves a dimensionally sharp subadditivity, building upon and generalising our Bloch based derivation. Further possible candidates could be found in either [45] or [46], where more involved relations for r Tr 2 ( )are given.…”

“…Using the purity bound we are able to turn the equality in equation (44) into an inequality and thus managed to also cover entangled or correlated composite systems r AB instead of the product state appearing on the left hand side of equation (44). This turns the pseudo-additivity into a general non-linear inequality for linear entropy that is applicable to all states.…”

Wetland degradation of a ramsar site: A study of East Kolkata wetlands of West Bengal, India

“…We can study a variety of states in this regard. For multipartite states, the entropy of the subsystems follows several types of inequalities like the triangle inequality [23] or Araki-Lieb inequality [24]. This limits how entangled can one particle be with another particle if it is already entangled to a third.…”

Linear entropy fails to predict entanglement behavior in low-density fermionic systems

“…Thus entropy measures which are simpler to be calculated, as the linear entropy 15,16,[18][19][20] − associated to the purity of the reduced system − are extremely valuable from the computational point of view. Another advantage of the linear entropy is to allow analytical approaches 21,22 .…”