No-Go Theorems and Quantum Exceptional Points in Non-Hermitian Quantum Mechanics

Non-Hermitian quantum mechanics has garnered growing interest since the groundbreaking papers by Carl Bender et al. in the late 1990s. 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, perfect discrimination of nonorthogonal states, and the increase of quantum entanglement by local operations have been reported. As a result, Bender's 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 the formalism is properly applied. 

I will also discuss our proposal for defining quantum exceptional points. First, I will recall the popular Hamiltonian exceptional points (HEPs), which are spectral degeneracies of non-Hermitian Hamiltonians describing classical and semiclassical open systems with gain and/or loss. A multitude of intriguing properties associated with systems at HEPs have been predicted in the literature, including stimulated emission, spontaneous emission, chirality, unidirectional invisibility, control of whispering-gallery microcavities, exceptional Kerr effect, and related exceptional photon blockade, as well as the generation of higher-order HEPs. However, the Hamiltonian-based definition of exceptional points neglects quantum jumpsin the evolution of quantum systems. The effects of quantum jumps can be accounted for by considering Liouvillians and their quantum exceptional points (LEPs), which we first introduced in 2019. These quantum exceptional points have garnered increasing interest in both theoretical and experimental domains. Notably, recent experiments with a single superconducting qubit and a single trapped ion have been conducted. I will report on our recent experiment (performed on an IBMQ processor), demonstrating that standard quantum process tomography, which reveals the dynamics of a quantum system, can be readily applied to reveal and characterize LEPs in non-Hermitian systems.

Full author list

Adam Miranowicz (1,2), Fabrizio Minganti (3), Karol Bartkiewicz (1), Shilan Abo (1), Patrycja Tulewicz (1), Ievgen I. Arkhipov (4), Sahin K. Ozdemir (5), and Franco Nori (2,6) 

1. Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, 61-614 PoznaÒ, Poland 

2. Quantum Information Physics Theory Research Team, Quantum Computing Center, RIKEN, Wakoshi, Saitama 351-0198, Japan 

3. Institute of Physics, Ecole Polytechnique FÈdÈrale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland 

4. Joint Laboratory of Optics of Palack藵 University and Institute of Physics of CAS, Faculty of Science, Palack藵 University, 771 46 Olomouc, Czech Republic 

5. Department of Engineering Science and Mechanics, and Materials Research Institute (MRI), The Pennsylvania State University, Pennsylvania 16802, USA 

6. Physics Department, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA