A Brief Summary of the Research works during last 10 years (2013 – 2022)
PREAMBLE
Dipankar Home is the earliest Indian researcher to have done Ph. D. doctoral work on Foundations of Quantum Mechanics in the beginning of 1980s. Over the last four decades, this line of research has remarkably evolved, providing the basis for a frontier area of science, viz. Quantum Information Theory, alongside its applications in Quantum Communication and Quantum Computation, acclaimed by the Nobel Committee as ushering in the “Second Quantum Revolution” while announcing the Nobel Prizes in Physics 2022 awarded for pioneering works in this area. During all these years, Home’s research works along this line have resulted in 148 peer-reviewed publications and 2 Research-level books: (a) “Conceptual Foundations of Quantum Physics” (Plenum, 1997). (b) “Einstein’s Struggles with Quantum Theory: A Reappraisal” with A. Whitaker (Springer, 2007), with the respective Forewords by 2 Nobel laureates Sir Anthony Leggett and Sir Roger Penrose.
Central Theme of the Research works during 2013 – 2022
Exploring novel fundamental features of Quantum Mechanics, their experimental realisations, and their interplay with Quantum Information, alongside applications in Quantum Communication protocols
This Theme of Research works is in consonance with the main objectives of the National Quantum Mission of the Govt. of India.
Highlights of Research Works during 2013 – 2022
(i) Total Number of Research Papers published during 2013 – 2022 in peer reviewed high impact level International Journals = 30.
This includes 2 papers published in Physical Review Letters, 11 papers published in Physical Review A, 5 papers published in Physics Letters A, apart from papers published in reputed Journals like Physical Review X Quantum, Journal of Optical Society America, Quantum Information Processing, Annals of Physics, Classical and Quantum Gravity.
Further, 3 papers accepted for publication during January – June, 2023, in the respective high impact-level Journals Communications Physics (Nature), Physical Review Research, and Physical Review A.
(ii) During this period, 2 of the proposed experiments by Home and his collaborators have been implemented, and a Theory-Experiment collaborative work has been empirically realised, whose relevant specifics have all been mentioned in the following writeup.
(iii) Key Features of the Most Significant Research Works with his Collaborators during 2013 – 2022
(a) Blending of two fundamental Quantum Mechanical Features, Indistinguishability and Entanglement, with consequent applications
An earlier unnoticed remarkable property of Entanglement arising from Indistinguishability of any two identical particles was uncovered by us, which we had named ‘Duality in Entanglement’ [Physical Review Letters 110, 140404 (2013)].
Using photons, our predicted feature of ‘Duality in Entanglement’ was experimentally verified at Tsinghua University, Beijing [New Journal of Physics 16, 083011 (2014)], followed by another photonic experimental study of our predicted property at INRIM, Torino [Physical Review A 91, 062117 (2015)]. Further, an interesting application of this property was pointed out by G. S. Agarwal et al. for performing entanglement sorting of photons [Physical Review A, 91, 062303 (2015)]
(b) Formulation of a novel testable scheme for evidencing Macroscopic Quantumness and testing violation of Macrorealism for large mass oscillating objects having large mass.
Using the currently available state-of-the-art technology, our work [Physical Review Letters 120, 210402 (2018)] has delineated a feasible way of testing Quantumness and violation of Macrorealism for optically trapped and harmonically oscillating nano-objects having mass around 106 – 109 amu (about million to billion times heavier than hydrogen atom), much greater than that possible by other methods realised so far. This would, therefore, contribute significantly to the contemporary frontier research enterprise of testing the limits of validity of quantum mechanical principles in the macroscopic domain by using the Leggett-Garg macrorealist inequality (temporal counterpart of Bell-type inequality) which is currently attracting intense explorations. Such studies are also motivated towards harnessing macroscopic quantumness for the potential practical applications like in quantum sensing, as well as for the foundational purpose of testing wave function collapse models. The implementation of our proposal is being pursued by H. Ulbricht and his group at University of Southampton UK.
(c) Theory-Experiment Collaboration Work: Single photon based interferometric loophole-free test of the temporal counterpart of Bell inequality, viz. the Leggett-Garg macrorealist inequality
This work was developed by providing the required theoretical inputs, in collaboration with U. Sinha’s experimental quantum optics group at Raman Research Institute, Bangalore, resulting in an unambiguous demonstration of the empirical violation of Leggett-Garg inequality, thereby providing the most conclusive evidence of quantumness of single photons by decisively repudiating the pivotal classical notion of realism for single photons. This was achieved for the first time by closing all the relevant loopholes (including the most important ones, detection efficiency and clumsiness loopholes) using appropriately devised strategies [Physical Review X Quantum 3, 010307 (2022)].
Thus, this ingeniously designed experimental platform provides a powerful means for certifying inherent nonclassicality of single photons which can be reliably and efficiently harnessed towards Quantum Communication based applications for which the single photon is a ubiquitous workhorse.
(d) Exploring novel applications of the Leggett-Garg macrorealist inequality having fundamental implications
(i) Our this work [Physical Review A 88, 022115 (2013)] was the first to probe implications of the quantum mechanical violation of the Leggett-Garg inequality in the context of weak interaction induced two state oscillations of neutral kaons and neutrinos. A remarkable result was obtained that this violation for the kaon oscillation is enhanced due to CP noninvariance, while, for the neutrino oscillation, such violation is sensitively dependent on the value of the mixing parameter. Thus, this work opened up a potentially rich area, inspiring other studies, including an important experiment [Physical Review Letters 117, 050402 (2016)] which demonstrated quantum mechanically predicted violation of the Leggett-Garg inequality for neutrino oscillation over a length scale of nearly 700 km. Further studies are under way, trying to unravel the deeper implications of this experiment, in conjunction with that of our work.
(ii) Persistence of quantum mechanical violation of the temporal counterpart of Bell inequality, viz. the Leggett-Garg inequality implying incompatibility with the notion of macrorealism was demonstrated for the first time for arbitrarily large spins under the coarsening of measurement times, as well as under the coarsening of measurement outcomes [Physical Review A 94, 052110 (2016) Physical Review A 100, 042114 (2019)]. The striking feature, thus, revealed entailing that classicality for large spin does not emerge from quantum mechanics, whatever be the form and degree of ‘unsharpness’ or course graining of the measurements, has deep-seated implications concerning the much investigated and debated issue of the classical limit of quantum mechanics.
(e) Generalising and Demonstrating the efficacy of Wigner’s approach for detecting Multipartite Nonlocality
Distinct from Bell’s approach, Wigner had suggested an elegant formulation of local realist inequality for showing quantum nonlocality. However, Wigner’s original scheme was restricted to only bipartite maximally entangled states, and hence was largely ignored. Our work [Physical Review A 91, 012102 (2015)] was the first to successfully generalise Wigner’s approach towards detecting nonlocality of an arbitrary multipartite entangled state by deriving appropriate local realist multipartite inequalities. Thus, this paper opened up an earlier unexplored direction for studying multipartite nonlocality, a topic which is of much contemporary interest.
Very recently, we followed up our earlier above mentioned work by showing that Wigner’s approach can be further developed by deriving a suitable set of local realist multipartite inequalities whose quantum mechanical violation would not only rigorously certify multipartite nonlocality for any multipartite entangled state, but would also enable detecting whether there is any particular bipartition of the multipartite system which is nonlocally correlated for cases where not all different bipartitions are nonlocally correlated [Physical Review A 106, 062203 (2022)]. This additional feature provides our formulated extension of Wigner’s scheme a significant advantage compared to other standard multipartite nonlocality detection scheme based on using the Svetlichny inequality. The efficacy of our scheme has been comprehensively illustrated for the tripartite and quadripartite states.
(f) Novel studies on Quantification and Uses of Quantum Entanglement as Resource
(i) Using Pearson Correlators for Certifying and Quantifying High Dimensional Entanglement
In view of considerable advantages provided by the high dimensional entangled states for ensuring efficient and robust applications in Quantum Communication, the certification and quantification of high dimensional entanglement is of much topical importance. In this context, our work [Physical Review A 101, 022112 (2020)] has initiated a novel direction of study in terms of the empirically measurable statistical correlator known as the Pearson Correlator, which we have analytically related with a suitable entanglement measure like Negativity for a range of bipartite qutrit states using only a pair of complementary observables. This approach, therefore, opens up unique empirical means for exactly quantifying such high dimensional entanglement. Extension of this scheme for a wider class of high dimensional bipartite entangled states using Pearson Correlator and other statistical correlators like Mutual Predictability and Mutual Information is a promising area of research with multifold applications in Quantum Information and Quantum Communication, and our research work along this direction is currently in progress.
(ii) Appropriate Quantification of the effectiveness of any resource state for implementing Remote State Preparation
In this work [Physical Review A 98, 062320 (2018)] we show that an appropriate measure of simultaneous correlations in mutually unbiased bases can serve as a powerful quantifier of the usefulness of a resource state for Remote State Preparation (RSP) based on entangled as well as separable states, even using zero-discord states. Given the importance of RSP as a key Quantum Information Processing task, further works harnessing the potentiality of our novel approach should be of considerable significance.
(iii) Identifying the appropriate quantitative measure of effectiveness of any resource state for Quantum Steering
Besides its profound fundamental implications, the phenomenon of Quantum Steering has wide-ranging useful Quantum Information Processing applications. However, an outstanding issue underlying such applications is the question concerning what aspect of Quantum Correlation can serve as the appropriate quantitative resource for Quantum Steering. This has, surprisingly, remained unaddressed. It is in this work [Physical Review A 98, 042306 (2018)] we have resolved this issue by analytically relating an appropriate measure of simultaneous correlations in mutually unbiased bases to the standard measure of Quantum Steering used for two-qubit states so that a higher value of the measure of such correlations implies a higher degree of Quantum Steering. This scheme, thus, opens up promising line of studies towards further developing this approach and exploring its potential applications by harnessing Quantum Steering in areas like Quantum Communication.
(iv) Latest Significant Work accepted for Publication
Going beyond Bohrian Wave-Particle Complementarity: Joint Detection of the spatially separated properties of a single photon in the respective two arms of an interferometer
Accepted for Publication: Communications Physics (Nature Group)
Principal authors: Dipankar Home with Urbasi Sinha (Raman Research Institute, Bangalore) and Alex Matzkin (Cergy Paris University)
Theory – Experimental Collaborative Work:
Combining theoretical expertise of Dipankar Home and Alex Matzkin with the photonic experimental group of Urbasi Sinha at Raman Research Institute where the experiment has been performed.
Significance of this Work
Bohr’s complementarity principle of wave-particle mutual exclusivity and the dictum that one cannot speak about the behavior of a particle within an interferometer lie at the heart of standard quantum interpretation of any interference experiment. In this context, our experiment provides an intriguing twist by not only jointly detecting the spatially separated different properties of a single photon within an interferometer, but also at the same time preserving the wave-like coherence between the superposed states of a single photon in the two arms. The wide-ranging ramifications of this curious effect, which has been called the Quantum Cheshire Cat effect, have both deep-seated foundational and practical implications, like in Quantum Sensing, which call for comprehensive studies.