A Brief Summary of the Most Significant Scientific Contributions of Dipankar Home having conceptual, empirical, and practical implications

PREAMBLE

Dipankar Home is the earliest Indian researcher who did his doctoral work on Foundations of Quantum Mechanics in the beginning of 1980s at Presidency College, Kolkata, followed by post-doctoral works in UK (Queen’s University, Belfast; University of Manchester; Birkbeck College, University of London), and subsequently joined Bose Institute, Kolkata as a faculty member in 1987.

He has been steadily contributing to this area over the last four decades resulting in 151 peer-reviewed publications and 2 Research-level books: (a) “Conceptual Foundations of Quantum Physics” (Plenum, 1997), and (b) “Einstein’s Struggles with Quantum Theory: A Reappraisal” with A. Whitaker (Springer, 2007), with the respective Forewords by 2 Nobel laureates Anthony Leggett and Roger Penrose. Both these books have been appreciatively reviewed in “Physics Today”, the flagship magazine of American Institute of Physics.

During the last few decades, this line of research, earlier not accepted as part of mainstream research pursuits, has remarkably evolved, leading to fundamentally important experiments, and has laid the basis for a frontier area of science, viz. Quantum Information Theory, alongside varied applications in Quantum Communication and Quantum Computation, thereby providing a cornerstone for the 21st Century Quantum Technologies. In fact, while announcing the Nobel Prizes in Physics 2022 for pioneering works in this area, this research area has been acclaimed by the Nobel Committee as a “vibrant and rapidly developing field” which has ushered in the “Second Quantum Revolution.”

Central Themes of the Most Significant Research Works of Home with his Collaborators

(A) Investigations on the interplay between foundational issues of Quantum Mechanics and their experimental realizations, exploring novel features of Quantum Mechanics.

(B) Studies on fundamental topics concerning the interplay between Quantum Foundations, Quantum Information Theory, and Quantum Entanglement enabled applications in secure information transfer/processing protocols.

HIGHLIGHTS

 As has been elaborated in the following, 3 of the proposed experiments by Home and his collaborators have been implemented revealing earlier unexplored quantum features, while 3 other proposed ideas are being pursued for experimental studies. Moreover, Home has contributed to a Theory-Experiment collaboration work which has been experimentally realized, and another such work is underway.

(I) Blending of two fundamental Quantum Features, Indistinguishability and Entanglement, with consequent applications

(a) An earlier unnoticed remarkable property of Entanglement arising from Indistinguishability of any two identical particles was uncovered by us, calling it ‘Duality in Entanglement’ [Physical Review Letters 110, 140404 (2013)].

Using photons, our predicted ‘Duality in Entanglement’ was experimentally verified at Tsinghua University, Beijing [New Journal of Physics 16, 083011 (2014)], followed by another photonic experimental study of this property at INRIM, Torino [Physical Review A 91, 062117 (2015)]. An interesting application of this property was also pointed out by others for performing entanglement sorting of photons [Physical Review A 91, 062303 (2015)].

(b) A novel scheme towards harnessing Quantum Indistinguishability for an arbitrarily efficient entanglement generation was formulated by us for any two identical Bosons/Fermions originating from two independent sources [Physical Review Letters 88, 050401 (2002)]. Such a scheme is of considerable significance since Entanglement lies at the core of Quantum Technology of the 21st Century.

While the ideas conceived in this work have been used by others, for example, in the studies concerning Free-electron Quantum Computation [Physical Review Letters 93, 020501 (2004)], the prospect of its experimental realization has now brightened and is being investigated taking advantage of the recent notable technological developments concerning molecular two-particle interferometry and non-absorptive path detectors, the two key ingredients of our scheme.

(II) Formulation of a novel testable scheme for evidencing Quantumness and testing violation of Macrorealism for oscillating objects having large mass

Using the currently available state-of-the-art technology, our work [Physical Review Letters 120, 210402 (2018)] has been successful in formulating a feasible way of testing Quantumness as well as the violation of the basic everyday notion of Macrorealism for optically trapped and harmonically oscillating nano-objects having masses 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 mechanics in the macroscopic domain. To be more specific, our scheme provides the means for testing the archetypal signature of classicality given by the Leggett-Garg macrorealist inequality (temporal counterpart of Bell-type inequality), currently attracting extensive studies. The implementation of our proposal is being pursued by H. Ulbricht and his group at University of Southampton UK. Apart from the fundamental importance of such an experiment in providing empirical constraints on the various suggested models of wave function collapse beyond standard Quantum Mechanics, the macroscopic quantumness so demonstrated can also have applications like in the area of Quantum Sensing.

(III) Introducing the notion of ‘Single Particle (intraparticle) Entanglement’ and formulating Bell-type inequality for testing Quantum Contextuality, with consequent applications

(a) This work by us was the earliest to come up with the notion of entanglement between two different dynamical variables of a single particle, formulating a general framework for a Bell-type inequality pertaining to such entanglement [Physics Letters A 102, 159 (1984)] based on the notion of Noncontextuality (assuming that the measured value of a dynamical variable does not depend on which other dynamical variable is measured alongside).

(b) We later developed this work by devising an empirically realizable scheme involving specifically path-spin entanglement for a single particle, thereby providing the basis for an experimental demonstration of Quantum Contextuality for the first time by adapting an appropriate form of Bell-type inequality in this context [Physics Letters A 279, 281 (2001)]. The proposed experiment was subsequently performed by the Neutron Interferometric group at Atominstitut, Vienna [Nature 425, 45 (2003)]. This was followed by theoretical and experimental studies by various groups concerning such single particle (intraparticle) entanglement and its applications in quantum information transfer protocols, including our further contributions in this area [Reviewed by S. Azzini et al. in Advanced Quantum Technology, Vol. 3, No. 10 (2020)].

(IV) DNA Molecular scheme for probing the “Schrödinger-Cat” or the Quantum Measurement Problem

DNA molecular analogue of the much-discussed Schrödinger’s Cat example was formulated by us for the first time in the context of the Quantum Measurement Problem in the mesoscopic domain, using the biochemical property of photolyase enzyme attachment to uv-absorbed DNA molecules acting as detectors of uv photons [Physical Review Letters 76, 2836 (1996)]. The way such an example can provide empirically relevant constraints on the wave function collapse models proposed for addressing this central riddle of Quantum Mechanics was analysed by us which played a key role in opening up an earlier uncharted area of study using such systems.

The futuristic significance of this intriguing work was commented upon in “Encyclopaedia Britannica Book of the Year 1996” (edited by G. M. Edwards), pp. 242-243, as well as in the Review article by the Nobel laureate A. J. Leggett, J. Phys. Condens. Matter 14, R415 (2002). In view of the recent advances in studies towards using biomolecular systems for investigating fundamental quantum issues, further development of our original proposal for empirically probing deeper the much-debated aspects of the Quantum Measurement Problem is acquiring more topical significance. 

(V) Revealing an earlier unexplored facet of wave-particle duality of single photons

A testable experiment was proposed by us predicting wave-like optical tunneling as well as particle-like anticoincidences of single photons in the same setup for a double-prism device [Physics Letters A 153, 403 (1991); 168, 95 (1992)], subsequently implemented at the Hamamatsu Photonics Central Research Laboratory, Japan [Physics Letters A 168, 1 (1992)] demonstrating a novel aspect of wave-particle duality. This provided a stimulating twist to the Bohrian principle of wave-particle complementarity by going beyond the usual domain of its application concerning the single particle interference vis-à-vis which-path determination. Conceptual implications of this work had evoked considerable discussions in a number of papers/books. Furthermore, the double-prism device for single photonic experiment developed for this purpose at the Hamamatsu Laboratory, Japan had interesting applications.

(VI) 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 developed by providing the required theoretical inputs, in collaboration with U. Sinha’s experimental quantum optics group at Raman Research Institute, Bangalore, resulted in an unambiguous demonstration of the empirical violation of the Leggett-Garg inequality, thereby decisively repudiating the notion of realism for single photons, by closing all the relevant loopholes (including the most important ones, detection efficiency and clumsiness loopholes) for the first time by using appropriately devised strategies [Physical Review X Quantum 3, 010307 (2022)].

Thus, this 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.

(VII) Exploring novel uses and fundamental implications of the temporal counterpart of Bell inequality, viz. the Leggett-Garg macrorealist inequality

(a) In the case of arbitrarily large spins, even under the coarsening of measurement times, coupled with the coarsening of measurement outcomes, the persistence of quantum mechanical violation of the Leggett-Garg inequality implying incompatibility with the notion of macrorealism was shown in our work for the first time [Physical Review A 94, 052110 (2016); Physical Review A 100, 042114 (2019)]. This striking feature revealed that classicality for large spin does not emerge from quantum mechanics, whatever be the form and degree of ‘unsharpness’ or coarse graining of the measurements outcomes. Such finding has fundamental implications concerning the much debated issue of the Classical Limit of Quantum Mechanics.

(b) Our 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. 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 underway, including trying to unravel the deeper ramifications of this experiment, in conjunction with the implications of our earlier initiating work on this topic.

(VIII) Generalising Wigner’s approach for detecting Multipartite Nonlocality

(a) 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 work opened up an earlier unexplored direction for studying multipartite nonlocality, a topic which is of much contemporary interest.

(b) Recently, we followed up our preceding work by showing that Wigner’s approach can be further developed by deriving a suitable set of local realist multipartite inequalities having the following important feature. Their quantum mechanical violation can not only rigorously certify multipartite nonlocality for any multipartite entanglement by considering all its different bipartitions, but can 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 the 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.

(IX) Formulating novel approaches for studying Quantification and Uses of Quantum Entanglement as Resource

 (a) Using Pearson Correlators for Quantifying Higher Dimensional Entanglement

In view of considerable advantages provided by the high dimensional entangled states for ensuring efficient and robust applications in Quantum Communication, the quantification of high dimensional entanglement is of much topical importance for enabling judicious assessment of the usefulness of a given entangled state for its efficient applications.  In this context, our work [Physical Review A 101, 022112 (2020)] initiated a novel direction of study in terms of the empirically measurable statistical correlator known as the Pearson Correlator, which we analytically related with a suitable entanglement measure like Negativity for a range of bipartite pure and mixed qutrit states using only a pair of complementary observables in each wing of the bipartite system. This approach, therefore, opens up unique empirical means for exactly quantifying such higher dimensional entanglement measure. 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.

 

(b) 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 bipartite 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 this novel approach should be of considerable significance.

(c) Identifying the appropriate Quantitative Measure of effectiveness of any Resource State for Quantum Steering

Besides its 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 bipartite 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 a promising line of studies towards further developing this approach and exploring its potential applications by harnessing Quantum Steering in areas like Quantum Communication.