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My broad areas of research are quantum information theory and quantum chaos. 

Classical chaos leads to large fluctuations in the evolution of a system due to small perturbations in the system. Quantum-classical
correspondence in chaotic systems, particularly in the deep quantum regime, has been a long-standing open question. Chaotic behavior at the quantum level can be an obstacle in the building of large scale quantum computers due to the presence of a large number of inter-qubit couplings, though small in strength. Thus, an understanding of quantum chaos is of paramount importance. On the other hand, quantum chaotic systems have been shown to generate entanglement, which makes them a potential resource for quantum computation. One of the major goals of my Ph.D. has been to develop an understanding of quantum chaos from a quantum information-theoretic perspective. Here is a brief description of my research contributions so far: 

  1. We developed a method to quantify the Bohr correspondence principle by giving a set of criteria to calculate the magnitude of quantum numbers for which quantum-classical correspondence will be observed in periodically driven systems. Using this method, we explained the reason for the breakdown of quantum-classical correspondence in chaotic systems, which has been a long-standing open question. We also identified a new quantum signature of classical bifurcations in the survival probability of quantum states. These results can be found in the publication PRE 97, 052209 (2018).

  2. How does classical chaos affect the generation of quantum entanglement? Can regular systems also produce large entanglement? Is quantum entanglement a signature of chaos? How does the quantumness of the system affect the answers to the aforementioned questions? These questions have puzzled physicists for a couple of decades now. We have unravelled these questions in the publication "Untangling entanglement and chaos", PRA 99, 042311 (2019). We have analytically shown how the extent of delocalization of a quantum state affects the amount of entanglement in a quantum state. For technical readers, we do this using the Fannes-Audenaert inequality for von Neumann entropy. Irrespective of the quantumness of the system, quantum systems whose underlying classical dynamics are chaotic always leads to greater delocalization, thus producing more entanglement. On the other hand, quantum systems whose underlying classical dynamics are regular may produce large delocalization in a deep quantum regime unlike in a semiclassical regime. Thus, our research clarifies the relationship between classical chaos and quantum entanglement and explains previous numerical results.

In addition to my research focused on quantum chaos, I have also pursued a few fundamental quantum information questions: 

  1. Given a 2-qudit quantum state, how can we tell if there exists a 3-qudit quantum state whose two of the 2-qudit reduced states are the same? This question has various applications such as entanglement detection, quantum key distribution and in characterizing anti-degradable channels. Using the monogamy property of Bell CHSH inequality, we gave a sufficient condition for the nonexistence of symmetric extension of a 2-qubit quantum state. Given any monogamous Bell inequality for qudit states, this condition extends simply to yield a sufficient condition for the nonexistence of symmetric extension of a 2-qudit quantum state. Further, we conjectured using numerical evidence that the Bell CGLMP inequality for qutrits is monogamous. These results are in PRA  96, 012128 (2017).

  2. The fidelity of a quantum system usually decays significantly upon any perturbation to its Hamiltonian. One of the perturbations can be an error in the value of classical control parameters of the system, such as strength of the magnetic field in an experiment. We have engineered a method to lower bound the fidelity decay (by a non-zero value) of a quantum system with respect to such perturbations of the classical control parameter. This has been done by quantizing the classical control parameter itself. This method is applicable to any quantum system. These results are in arXiv:1711.07906.

I have become interested in more research topics recently such as coherence theory in quantum information, quantum speed limits, out-of-time-order correlators as a quantum analog of classical Lyapunov exponents, indefinite causal order and causal inequalities, apart from the research topics I have already worked on which include Bell inequalities, entanglement, quantum discord, symmetric extension of quantum states, classical and quantum chaos. Stay tuned for more of my research contributions!