NDLI: A Simpler Proof of the Existence of Quantum Weak Coin Flipping with Arbitrarily Small Bias

Please wait, while we are loading the content...

A Simpler Proof of the Existence of Quantum Weak Coin Flipping with Arbitrarily Small Bias

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Ganz, Maor Kerenidis, Iordanis Chailloux, André Magnin, Loïck Aharonov, Dorit
Copyright Year	2016
Abstract	Mochon's proof [Quantum Weak Coin Flipping with Arbitrarily Small Bias, preprint, arXiv:0711.4114, 2007] of the existence of quantum weak coin flipping with arbitrarily small bias is a fundamental result in quantum cryptography, but at the same time one of the least understood. Though used several times as a black box in important follow-up results [M. Ganz, Quantum Leader Election, preprint, arXiv:0910.4952, 2009; A. Chailloux and I. Kerenidis, in Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Los Alamitos, CA, 2009, pp. 527--533; N. Aharon and J. Silman, New J. Phys., 12 (2010), 033027; A. Chailloux and I. Kerenidis, in Proceedings of the 52nd Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Los Alamitos, CA, 2011; I. Kerenidis and S. Zhang, in Theory of Quantum Computation, Communication, and Cryptography, Lecture Notes in Computer Science 7582, Springer, Berlin, 2013, pp. 13--28], the result has not been peer reviewed, its novel techniques (and, in particular, Kitaev's point game formalism) have not been applied anywhere else, and an explicit protocol is missing. We believe that truly understanding the existence proof and the novel techniques it relies on would constitute a major step in quantum information theory, leading to deeper understanding of entanglement and of quantum protocols in general. In this work, we make a first step in this direction. We simplify parts of Mochon's construction considerably, making about $20$ pages of analysis in the original proof superfluous, clarifying some other parts of the proof on the way, and presenting the proof in a way which is conceptually easier to grasp. We believe the resulting proof of existence is easier to understand, more readable, and certainly verifiable. Moreover, we analyze the resources neededto achieve a bias $\varepsilon$ and show that the number of qubits is $O(\log \frac{1}{\varepsilon})$, while the number of rounds is $(\frac{1}{\varepsilon})^{O(\frac{1}{\varepsilon})}$. A true understanding of the proof, including Kitaev's point-game techniques and their applicability, as well as completing the task of constructing an explicit (and also simpler and more efficient) protocol, are left to future work.
Starting Page	633
Ending Page	679
Page Count	47
File Format	PDF
ISSN	00975397
DOI	10.1137/14096387X
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	3 (Special Section on the Fifty-Fourth Annual IEEE Symposium on Foundations of Computer Science (FOCS 2013))
Volume Number	45
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2016-05-10
Access Restriction	Subscribed
Subject Keyword	security Quantum computation quantum cryptography Quantum algorithms and complexity quantum protocols quantum weak coin flipping Quantum cryptography theory
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

A simpler proof of existence of quantum weak coin flipping with arbitrarily small bias

A simpler proof of existence of quantum weak coin flipping with arbitrarily small bias

Quantum weak coin flipping with arbitrarily small bias

Analytic quantum weak coin flipping protocols with arbitrarily small bias

Quantum weak coin flipping with arbitrarily small bias

Quantum weak coin flipping with arbitrarily small bias

Coin Flipping with Constant Bias Implies One-Way Functions

Coin Flipping with Constant Bias Implies One-Way Functions

Weak coin flipping with small bias

A Simpler Proof of the Existence of Quantum Weak Coin Flipping with Arbitrarily Small Bias

Similar Documents

A simpler proof of existence of quantum weak coin flipping with arbitrarily small bias

A simpler proof of existence of quantum weak coin flipping with arbitrarily small bias

Quantum weak coin flipping with arbitrarily small bias

Analytic quantum weak coin flipping protocols with arbitrarily small bias

Quantum weak coin flipping with arbitrarily small bias

Quantum weak coin flipping with arbitrarily small bias

Coin Flipping with Constant Bias Implies One-Way Functions

Coin Flipping with Constant Bias Implies One-Way Functions

Weak coin flipping with small bias

A Simpler Proof of the Existence of Quantum Weak Coin Flipping with Arbitrarily Small Bias