Seminarium Optyczne

I will discuss two topics of non-Hermitian quantum mechanics: No-go theorems in quantum information based on non-Hermitian systems:Recently, apparent nonphysical implications of Bender's non-Hermitian quantum mechanics have been discussed in the literature. In particular, the apparent violation of the no-signaling theorem, discrimination of nonorthogonal states, and the increase of quantum entanglement by local operations were reported, and therefore the Bender theory was not considered to be fundamental. I will show that these and other no-go principles (including the no-cloning and no-deleting theorems) of conventional quantum mechanics still hold in finite-dimensional non-Hermitian quantum systems, including parity-time symmetric and pseudo-Hermitian cases, if its formalism is properly applied. Quantum and semiclassical exceptional points (EPs): When a quantum system is isolated from its environment, it is described by a Hermitian Hamiltonian. Its eigenvalues characterize the resonances frequency, while its eigenvectors describe the form of those resonances. If, however, the system interacts with its environment, some particles will leak, while others will enter. For semiclassical systems, this loss and gain can be captured by a non-Hermitian Hamiltonian, whose eigenvalues represent both the resonance frequencies and lifetime. The presence of the environment can cause two different resonances to become the same, forcing the frequency and the lifetime to match. In this case, we speak of EPs, which are considered as the basis for enhanced sensing measures and are relevant to describe dynamical phase transitions and characterize topological phases of matter. Many exotic phenomena, such as parity-time symmetry breaking and unidirectional propagation, have been observed in the proximity of EPs. The vast majority of the studies on EPs, however, have focused on semiclassical models. To properly describe open quantum systems, quantum jumps, representing the instantaneous switching between the energy levels of the system, must be included. Using Liouvillian quantum jumps, we defined quantum EPs, and showed how, and if, they could correspond to semiclassical EPs. Recent experiments and numerous theoretical studies of various groups confirm the usefulness of the quantum EPs proposed by us. [1] I. I. Arkhipov, A. Miranowicz, F. Minganti, K. Özdemir, F. Nori, Nat. Comm. 14, 2076 (2023). [2] D.-G. Lai, C.-H. Wang, A. Miranowicz, and F. Nori, Optica 11, 485 (2024).[3] C.-Y. Ju, A. Miranowicz, Y.-N. Chen, G.-Y. Chen, F. Nori, Quantum 8, 1277 (2024). [4] A. Laha, A. Miranowicz, R. K. Varshney, and S. Ghosh, Phys. Rev. A 109, 033511 (2024). [5] I. I. Arkhipov, A. Miranowicz, F. Nori, S. K. Özdemir, F. Minganti, Phys. Rev. Res. 108, 033512 (2023). [6] J. Perina Jr., A. Miranowicz, J. K. Kalaga, W. Leonski, Phys. Rev. A 108, 033512 (2023). [7] C.-Y. Ju, A. Miranowicz, F. Minganti, C.-Ts. Chan, G.-Y. Chen, F. Nori, Phys. Rev. Res. 4, 023070 (2022). [8] C.-Y. Ju, A. Miranowicz, G.-Y. Chen, F. Nori, Phys. Rev. A 100, 062118 (2019). [9] F. Minganti, A. Miranowicz, R. Chhajlany, F. Nori, Phys. Rev. A 100, 062131 (2019). [10] S. Abo, P. Tulewicz, K. Bartkiewicz, S. K. Özdemir, and A. Miranowicz, e-print arXiv:2401.14993 (2024). [11] D.-G. Lai, A. Miranowicz, F. Nori, to appear in Phys. Rev. Lett. (2024).