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Atul Singh Arora

atulwebsitepicture.jpg

Email: Atul.Singh.Arora (at) ulb.ac.be
Phone: +32-2-650 29 72
Fax: +32-2-650 29 41
Address: QuIC - Ecole Polytechnique de Bruxelles
Université Libre de Bruxelles
50 av. F. D. Roosevelt - CP 165/59
B-1050 Bruxelles
Belgique

Education

  • 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.

Research

Master's

  • 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.


PhD (current)

I am currently 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. 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. 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).

I am now switching gears and studying communication complexity, the second theme of my PhD thesis.

Publications/preprints

  1. Proposal for a macroscopic test of local realism with phase-space measurements. A.S.A., A. Asadian (2015). DOI:10.1103/PhysRevA.92.062107
  2. Revisiting the admissibility of non-contextual hidden variable models in quantum mechanics. A.S.A., K. Bharti, Arvind (2016). arXiv:1607.03498
  3. Quantum Weak Coin Flipping. A.S.A., J. Roland, S. Weis (2018).
    arXiv:1811.02984


References

  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