Research Projects

The second quantum revolution focuses on controlling quantum systems to store, process, and transmit information [1]. A key task in this context is the discrimination of quantum states, especially when the states are shared between distant parties. Remarkably, not all orthogonal quantum states can be perfectly distinguished using Local Operations and Classical Communication (LOCC) [2]. In a seminal paper [3] Bennett et al., showed that orthogonal product states in (C³)*² and (C²)*³ are locally indistinguishable and introduced the concept of ``quantum nonlocality without entanglement." This project explores the structural gaps in local state discrimination, focusing on both limitations of LOCC and broader operational classes like separable and PPT operations. While multiple copies of states significantly enhance distinguishability [4], some ensembles remain indistinguishable even with more resources. Notably, Banik et al., [5] recently showed that certain two-qubit ensembles require at least three copies for perfect discrimination under LOCC—establishing a genuine copy gap in local discrimination. However, for ensembles of three orthogonal states in two-qubit, such a gap has not been observed. We aim to investigate whether a hierarchy in nonlocality can still exist in such cases by considering PPT-preserving operations and entanglement-assisted strategies. One goal is to compare different sets of orthogonal states based on the amount of entanglement assistance required optimally to distinguish them perfectly. Further, the project studies the activation of nonlocality-transforming a locally distinguishable set into a locally indistinguishable one using only LOCC. This reveals a notion of hidden nonlocality [6], which serves as a resource for quantum data hiding and cryptographic protocols [7]. We develop a quantitative measure of hidden nonlocality via optimal error probabilities under one-way LOCC. For a state ensemble, we define the LOCC error as a weighted average of Helstrom errors [8] after Alice’s local measurement. If one ensemble consistently has a higher minimum error probability across measurements, it is deemed to have greater hidden nonlocality. In conclusion, this project uncovers deeper layers of nonlocality by analyzing distinguishability gaps, the role of entanglement, and probabilistic LOCC strategies. These insights contribute to a refined classification of quantum ensembles based on their cryptographic and operational power.\\ References:\\ 1. Dowling et al., Phil. Trans. R. Soc. A 361, 1655 (2003).\\ 2. Walgate et al., Phys. Rev. Lett. 85, 4972 (2000).\\ 3. Bennett et al., Phys. Rev. A 59, 1070 (1999).\\ 4. S. Bandyopadhyay, Phys. Rev. Lett.106, 210402 (2011).\\ 5. Banik et al., Phys. Rev. Lett. 126, 210505 (2021).\\ 6. Bandyopadhyay et al., Phys. Rev. A 104, L050201 (2021).\\ 7. Bera et al., Phys. Rev. A 110, 042424 (2024).\\ 8. C. W. Helstrom, J. Stat. Phys. 1, 231-252 (1969).\\