Atul Singh Arora

• May 2016. Obtained a Bachelor's and Master's in Science (Physics major) from the Indian Institute of Science Education and Research (IISER), Mohali. The Master's thesis was supervised by Prof Arvind.
• October 2016. Started a PhD at l'Université libre de Bruxelles (ULB) under the supervision of Prof Jérémie Roland.

For details, see my curriculum vitae.

• Summer, 2015. Spent at the University of Siegen, Germany, working on a natural extension of Bell's inequality which uses position and momentum measurements instead of the usual two-level systems. [1]

• Academic year 2015-16. For the Master's thesis found out that the statement about contextuality can only be made under a rather reasonable condition, known as functional consistency, which is not quite obeyed under Bohm like theories. [2]

Motivation for the master's thesis:
In Siegen, I took a course in the foundations of quantum mechanics where I was introduced to the notion of contextuality which, roughly stated, means that the value assigned to an observable must necessarily depend on the set of compatible observables it is measured with. This was already rather unsettling for me at that time (still is). There was a guest lecture on Bohm's completion of quantum mechanics, often called Bohmian mechanics, which essentially said that the hidden variables needed to complete quantum mechanics were the particles' positions. Once these are known one can predict with certainty the outcome of each experiment. These two notions were at odds, at least on the face of it. I couldn't find a satisfactory explanation for these and decided to explored this apparent contradiction.

I started with working on what is called the quantum “Weak Coin Flipping” problem. Here's what Mochon, the person who made a breakthrough in this problem, had to say about it [1].

“God does not play dice. He flips coins instead.” And though for some reason He has denied us quantum bit commitment. And though for some reason he has even denied us strong coin flipping. He has, in His infinite mercy, granted us quantum weak coin flipping so that we too may flip coins.
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. 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.

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. Found analytic expressions for the unitaries corresponding to Mochon's constructions which yield arbitrarily small bias.

I hope to be able to switch gears soon and study communication/query complexity.

1. Participant. (Physics) Lindau Nobel Laureate Meeting (LiNo), 2019.
2. Speaker. Quantum Weak Coin Flipping. Phoenix, Arizona, USA. Symposium on Theory of Computing (STOC) 2019. [ pptx ]
3. Speaker. Quantum Weak Coin Flipping, where weakness is a virtue. Boulder, Colorado, USA. Quantum Information Processing (QIP) 2019. [ video, pdf, pptx ]

1. Explicit quantum weak coin flipping protocols with arbitrarily small bias. A.S.A., J. Roland, C. Vlachou (2019).
   arXiv:1911.13283. (Submitted.)
2. A simple proof of uniqueness of the KCBS inequality. K. Bharti, A.S.A., L. C. Kwek, J. Roland (2018).
   arXiv:1811.05294. (Submitted.)
3. Quantum Weak Coin Flipping. A.S.A., J. Roland, S. Weis (2018, conference version 2019).
   arXiv:1811.02984. 51st ACM Symposium on Theory of Computing (STOC'19), pages 205-216, 2019. Web.
4. Revisiting the admissibility of non-contextual hidden variable models in quantum mechanics. A.S.A., K. Bharti, Arvind (2016, revised 2018).
   arXiv:1607.03498. Physics Letters A (Nov 2018).
5. Proposal for a macroscopic test of local realism with phase-space measurements. A.S.A., A. Asadian (2015).
   arXiv:1508.04588. Phys. Rev. A 92, 062107

1. Quantum weak coin flipping with arbitrarily small bias. C. Mochon (2007). arXiv:0711.4114
2. A large family of quantum weak coin-flipping protocols. C. Mochon (2005). DOI:10.1103/PhysRevA.72.022341