Open Quantum Systems

I have been involved in studies in quantum statistical mechanics. In particular, **the major
theme of my work is to show how The theory of Open Quantum Systems provides a
common umbrella to understand quantum optics, quantum information processing, quantum
computing, quantum cryptography, relativistic quantum mechanics, particle physics and
the foundations of quantum mechanics.** The theory of open quantum systems addresses
the problems of damping and dephasing in quantum systems by its assertion that all real
systems of interest are in fact ‘open’ systems, each surrounded by its environment. The recent upsurge of interest in the problem of open quantum systems is because of the spectacular
progress in manipulation of quantum states of matter (atoms, or bosonic or fermionic gases
or molecules), encoding, transmission and processing of quantum information, for all of
which understanding and control of the environmental impact are essential. The Nobel
Prize for 2012 was awarded to D. J. Wineland and S. Haroche for experimental justifications
of quantum coherence and its decay in realistic scenarios. In a number of my works involving
the application of open system ideas to quantum information and quantum optics, I have
made use of the experimental results of Wineland and Haroche. Recently, I have started systematic application of Open System Ideas to foundational issues in relativistic systems,
as well as sub-atomic systems, such as mesons and neutrinos. Our work on Quantum Correlations in neutrinos, where we established that **quantum correlations imply
neutrino oscillations and vice versa**, is very timely as the 2015 Nobel Prize in Physics has been awarded for establishing neutrino mass.

A unifed, information theoretic interpretation of the number-phase complementarity
that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems has been developed, in the context of Open Quntum Systems. Over the last few years I have been developing a graphical representation
of quantum mechanics. I have become interested recently in Flavor Physics that explores the deviations of predictions
from the Standard Model. A major thrust in this direction is the probing of the
foundations of physics at the subatomic level. This can yield a number of surprises. Thus,
on one hand, a study of quantum correlations in neutral mesons reveals features not seen
in stable quantum systems and on the other hand, the **use of open system ideas on these
systems leads to predictions that suggest a rethinking of the interpretation of important
observables in particle physics and also suggests background effects which could be possible
signatures of quantum gravity. **

I have developed, over the last decade, a consistent approach to the application of ideas from Open Quantum Systems to various facets of Quantum Information. I have also worked on the interface between Quantum Optics and Quantun Information.

I have been involved in studies ranging from the fundamental aspects of quantum statistical mechanics to the mathematical physics aspects of canonical transformations of Bosonic quantum fields in Fock space. My work on the Open System Study of non-linear Quantum Brownian Motion, starting from correlated initial conditions, involved the adaptation of field theoretic techniques to Quantum Statistical Mechanics.

- Quantum Correlations imply neutrino oscillations and vice versa. This is very timely as the 2015 Nobel Prize in Physics has been awarded for establishing neutrino mass.
- Use of open system ideas on sub-atomic systems leads to predictions that suggest a rethinking of the interpretation of important observables in particle physics and also suggests background effects which could be possible signatures of quantum gravity.
- Characterization of the Unru Channel, for a Dirac mode, by obtaining its Kraus representation.
- Introduced a method of quantum error correction based characterization of dynamics (QECCD) and also ambiguous stabilizer code (ASC), which can be useful for the characterization of quantum dynamics (CQD).
- Method to disambiguate different non-Markovian sources in a complex evolution developed.

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