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--- members:atulsingharora [2019/02/13 16:19]
atulsingharora [Publications/preprints]
+++ members:atulsingharora [2019/10/21 22:53]
atulsingharora [Research]
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 >Instructions for the flipping of coins are contained herein. But be warned! Only those who have mastered Kitaev's formalism relating coin flipping and operator monotone functions may succeed. For those foolhardy enough to even try, a complete tutorial is included.
-Two distrustful players wish to remotely agree on a random bit and have opposite preferences (Alice wants 1 and Bob wants 0, for instance). The protocol must protect an honest player against a cheating player. The figure of merit of a protocol is called the bias of a protocol, denoted by ε. A protocol which provides complete immunity has ε=0 while a protocol which provides no protection has ε=1/2. What Mochon proved in the said article was that there exists a protocol for any ε>0. This was back in 2007. The catch is that the explicit protocol is still unknown. The currently best known explicit protocol is the one found by Mochon [2] in 2005 which yields ε tending to 1/6. My task is to find protocols with ε<1/6.
+Two distrustful players wish to remotely agree on a random bit and have opposite preferences (Alice wants 1 and Bob wants 0, for instance). The protocol must protect an honest player against a cheating player. The figure of merit of a protocol is called the bias of a protocol, denoted by ε. A protocol which provides complete immunity has ε=0 while a protocol which provides no protection has ε=1/2. What Mochon proved in the said article was that there exists a protocol for any ε>0. He used Kitaev's point game formalisms—a series of equivalent frameworks introduced to study coin flipping. This was back in 2007. The catch is that the explicit protocol is still unknown. The currently best known explicit protocol is the one found by Mochon [2] in 2005 which yields ε tending to 1/6. My task is to find protocols with ε<1/6.
-Towards the end of 2017 we found protocols with ε tending to 1/10. The technique we used was insufficient was for going beyond this limit. Only recently, i.e. the end of 2018, have we been able to formalise a method, which we call the Elliptic Monotone Align algorithm, that effectively allows us to construct protocols with arbitrarily small bias (in the absence of noise).
+//End of 2017.// Found protocols with ε tending to 1/10. The technique we used was insufficient was for going beyond this limit.\\
+//End of 2018.// Constructed a numerical algorithm which can provably find a numerical description of any protocol from its point game description. Effectively, this allows one to construct explicit (although numerical) protocols with arbitrarily small biases (in the absence of noise). \\
+//End of 2019.// We are now trying to find the analytic expressions for the unitaries corresponding to Mochon's constructions which yield arbitrarily small bias. This will hopefully yield the complete description of an explicit weak coin flipping protocol with ε tending to zero. \\
-I am now switching gears and studying communication complexity, the second theme of my PhD thesis.
+I hope to be able to switch gears soon and study communication/query complexity.
 \\
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    - A simple proof of uniqueness of the KCBS inequality. K. Bharti, A.S.A., L. C. Kwek, J. Roland (2018).\\ [[https://arxiv.org/abs/1811.05294|arXiv:1811.05294]]. (Submitted to PRL.)
-   - Quantum Weak Coin Flipping. A.S.A., J. Roland, S. Weis (2018).\\ [[https://arxiv.org/abs/1811.02984|arXiv:1811.02984]]. ([[http://jila.colorado.edu/qip2019/program.html|Accepted. QIP 2019]]; [[http://acm-stoc.org/stoc2019/STOC%202019%20accepted%20papers.html|Accepted. STOC, 2019]].)
+   - Quantum Weak Coin Flipping. A.S.A., J. Roland, S. Weis (2018).\\ [[https://arxiv.org/abs/1811.02984|arXiv:1811.02984]]. ([[http://jila.colorado.edu/qip2019/program.html|Accepted. QIP '19]]; [[http://acm-stoc.org/stoc2019/STOC%202019%20accepted%20papers.html|Accepted. STOC '19]].)
    - Revisiting the admissibility of non-contextual hidden variable models in quantum mechanics. A.S.A., K. Bharti, Arvind (2016, revised 2018).\\ [[https://arxiv.org/abs/1607.03498|arXiv:1607.03498]]; [[https://doi.org/10.1016/j.physleta.2018.11.049|Physics Letters A (Nov 2018)]].
    - Proposal for a macroscopic test of local realism with phase-space measurements. A.S.A., A. Asadian (2015).\\ [[https://arxiv.org/abs/1508.04588|arXiv:1508.04588]]; [[https://doi.org/10.1103/PhysRevA.92.062107|Phys. Rev. A 92, 062107]]