Dr Shash Virmani
Senior Lecturer

Research Interests

My research concerns quantum information theory and all things related to the complexity of quantum systems. Preprints to all my publications can be found on the quant-ph arXiv (here) or on Brunel's research archives.

Here are short summaries of my research work, loosely organised into various themes:

Entanglement theory and entanglement measures

I started out my scientific career as a graduate student at Imperial College under the supervision of Martin Plenio (now at Ulm) and Peter Knight, working on entanglement theory. Results include statements about the relative ordering of entanglement measures, bounds on the relative entropy of entanglement, and computation of an asymptotic entanglement measure (a paper for which most credit goes to coauthor Koenraad Audenaert for his quite heroic contribution). Since my PhD I have often revisited the topic of entanglement measures with the fortunate assistance of many insightful coauthors, e.g. here and here.

Quantum Computation with Triplet/Singlet measurements

In a collaboration with Terry Rudolph that seems to become active with approximately the same period as a typical species of cicada, I established the "STP=BQP" conjecture of Michael Freedman, Matt Hastings, and Modjtaba Shokrian-Zini. We did this by building upon the insights of their paper which proposed and evidenced the conjecture, and our own other work on a related question from many years ago. The published proof of the conjecture is available at this link. Loosely speaking, the work demonstrates that using only measurements of two qubit total angular momentum, one can perform quantum computation given almost any initial state that is not completely symmetric. This brings natural robustness to a certain form of error, and has interesting fundamental connections to the study of quantum reference frames. It is also perhaps surprising that quantum computation is possible with a single combined dynamical/measurement operation of such a simple and physically natural form, in a way that is almost completely agnostic about the initialisation of the qubits.

LOCC discrimination of quantum states

I had an early interest in the LOCC discrimination of quantum states (loosely speaking - how to distinguish quantum states of many quantum subsystems when you can only measure the subsystems in a distributed way). In collaboration with various colleagues I showed that two pure states can be optimally discriminated even in the LOCC setting, and obtained bounds on when discrimination is possible given more states, and obtained optimal LOCC protocols in some settings with high symmetry.

Correlated error quantum information

I was introduced to this topic while I was a postdoc with Chiara Macchiavello at Pavia. We investigated the effect of correlations on the information carrying capacity of two correlated quantum channels. Motivated by some intriguing non-analyticity in that example, together with Martin Plenio I developed connections between correlated error quantum channel capacities and many-body physics, see here and here for details.

Classical simulation of quantum systems

Motivated by the ever increasing buzz concerning quantum computing, I became interested in how well classical computers can efficiently simulate quantum systems. Together with various coauthors I've developed bounds (e.g. here and here) on the noise that quantum computers can tolerate before losing their advantage over classical computers. In more recent work have shown how ideas from the foundations of physics can be used to develop efficient simulations of some complex quantum systems, even without noise. Perhaps the most surprising example of this arises in certain pure entangled modifications of cluster state quantum computing, which we have shown can be efficiently simulated classically (see also here for more explicit examples). Some of this work was supported by an EPSRC "Bright Ideas" grant and an EPSRC DTP.