Physics – Quantum Physics
Scientific paper
2010-08-25
Phys. Rev. A 82, 052341 (2010)
Physics
Quantum Physics
22 pages, 13 figures, comments welcome. v2: typos corrected and references added. v3: minor corrections (more similar to publi
Scientific paper
We address the quantification of non-Gaussianity of states and operations in continuous-variable systems and its use in quantum information. We start by illustrating in details the properties and the relationships of two recently proposed measures of non-Gaussianity based on the Hilbert-Schmidt (HS) distance and the quantum relative entropy (QRE) between the state under examination and a reference Gaussian state. We then evaluate the non-Gaussianities of several families of non-Gaussian quantum states and show that the two measures have the same basic properties and also share the same qualitative behaviour on most of the examples taken into account. However, we also show that they introduce a different relation of order, i.e. they are not strictly monotone each other. We exploit the non-Gaussianity measures for states in order to introduce a measure of non-Gaussianity for quantum operations, to assess Gaussification and de-Gaussification protocols, and to investigate in details the role played by non-Gaussianity in entanglement distillation protocols. Besides, we exploit the QRE-based non-Gaussianity measure to provide new insight on the extremality of Gaussian states for some entropic quantities such as conditional entropy, mutual information and the Holevo bound. We also deal with parameter estimation and present a theorem connecting the QRE nonG to the quantum Fisher information. Finally, since evaluation of the QRE nonG measure requires the knowledge of the full density matrix, we derive some {\em experimentally friendly} lower bounds to nonG for some class of states and by considering the possibility to perform on the states only certain efficient or inefficient measurements.
Genoni Marco G.
Paris Matteo G. A.
No associations
LandOfFree
Quantifying non-Gaussianity for quantum information does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantifying non-Gaussianity for quantum information, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantifying non-Gaussianity for quantum information will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-525177