2019/07/05 by H. S. Karthik, Akshata Shenoy H., Akshata Shenoy Hejamadi +1
Mathematics · Physics and Astronomy · #Algebraic number #Hamiltonian (control theory) #Mathematical analysis #Mathematics #Observable #Physics #Quantum #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Qubit #Weak measurement #quant-ph
paper · pdf · doi:10.1103/physreva.103.032420
published as Phys. Rev. A 103, 032420 (2021) · 5 pages, 4 figures, RevTex; Comments welcome
arxiv created 2019/07/05 · openalex created_date 2019/07/12 · openalex publication_date 2021/03/17 · arxiv updated 2021/03/24 · openalex updated_date 2026/08/05
Macrorealistic description governing the classical realm is known to get uprooted in the quantum domain. The Leggett-Garg inequality [A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985)] proposes to probe the macrorealistic limit emerging from the quantum scenario. It places a bound on the linear combinations of temporal correlations of observables measured sequentially at different time intervals. Violation of the Leggett-Garg inequality, up to the so-called temporal Tsirelson bound (TTB), has been realized in the quantum domain. It is important to understand whether quantum theory permits larger violation beyond the TTB and up to the algebraic maximum value of the Leggett-Garg inequality. To this end, it has been shown [C. Budroni and C. Emary, Phys. Rev. Lett. 113, 050401 (2014)] that a three-term Leggett-Garg inequality can be violated beyond the TTB 3/2 in the time evolution of N>2 level quantum systems by choosing suitable measurement schemes and state-update rules. Furthermore, it is revealed that the algebraic maximum value 3 can be realized in the limit N\ensuremath→\ensuremath∞. Their measurement scheme rules out violation of the Leggett-Garg inequality beyond the TTB by a qubit. Being genuinely quantum in nature, we ask whether such enhanced violation of the Leggett-Garg inequality could be witnessed in a qubit itself. Here, we show that a qubit undergoing time evolution generated by a non-Hermitian PT-symmetric Hamiltonian indeed violates the three-term Leggett-Garg inequality beyond the TTB and up to its algebraic maximum value 3.