Quantum Physics
[Submitted on 26 Nov 2018 (v1), last revised 25 Feb 2021 (this version, v2)]
Title:Nonnegativity for hafnians of certain matrices
View PDFAbstract:We show that a complex symmetric matrix of the form $A(Y,B) = \begin{bmatrix}Y & B\\ B^\top & \overline{Y} \end{bmatrix},$ where $B$ is Hermitian positive semidefinite, has a nonnegative hafnian. These are positive scalar multiples of matrices $A(Y,B)$ that are encodable in a Gaussian boson sampler. Further, the hafnian of this matrix is non-decreasing in $B$ in the sense that $\mathrm{haf}A(Y,L) \ge \mathrm{haf}A(Y,B)$ if $L \succeq B$.
Submission history
From: Kamil Bradler [view email][v1] Mon, 26 Nov 2018 13:01:48 UTC (7 KB)
[v2] Thu, 25 Feb 2021 15:44:45 UTC (8 KB)
Current browse context:
quant-ph
References & Citations
Bookmark
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.