Essential role of quantum speed limit in violation of Leggett-Garg inequality across a PT-transition

Abstract

We study Leggett-Garg inequality (LGI) of a two level system (TLS) undergoing non-Hermitian dynamics governed by a non-linear Bloch equation (derived in J. Phys. A: Math. Theor. 54, 115301 (2021)) across a PT-transition. We present an algebraic identification of the parameter space for the maximum violation of LGI (in particular $K_3$). In the PT-symmetric regime the maximum allowed value for $K_3$ is always found to be greater than the quantum bound (Lüders bound) of $3/2$ but it does not reach the algebraic maximum of $K_3=3$ in general. However, in the limit where PT-symmetry breaking parameter approaches the exceptional point from the PT-symmetric side, $K_3$ is found to asymptotically approach its algebraic maximum of 3. In contrast, the maximum value of $K_3$ always reaches its algebraic maximum in the PT-broken phase $i.e.$ $K_3\to 3$. We find that (i) the speed of evolution (SOE) must reach its maximum value (in the parameter space of initial state and the time interval between successive measurements) to facilitate the value of $K_3\to 3$, (ii) together with the constraint that its minimum value must run into SOE equals to zero during the evolution of the state. In fact we show that the minimum speed of evolution can serve as an order parameter which is finite on the PT-symmetric side and identically zero on the PT-broken side. Finally, we discuss a possible experimental realization of this dynamics by quantum measurement followed by post-selection procedure in a three level atom coupled to cavity mode undergoing a Lindbladian dynamics.

9 pages, 5 figures

References in corpus (10)

• The Fidelity and Trace Norm Distances for Quantifying Coherence
• Mixed-state evolution in the presence of gain and loss
• Necessary and sufficient conditions for macroscopic realism from quantum mechanics
• Exceptional points of any order in a single, lossy, waveguide beamsplitter by photon-number-resolved detection
• Interference experiment, anomalous weak value and Leggett-Garg test of macrorealism
• Loophole free interferometric test of macrorealism using heralded single photons
• Floquet exceptional contours in Lindblad dynamics with time-periodic drive and dissipation
• $\mathcal{P}\mathcal{T}$ symmetric evolution, coherence and violation of Leggett-Garg inequalities
• Strict experimental test of macroscopic realism in a light-matter-interfaced system
• Leggett-Garg inequality in Markovian quantum dynamics: role of temporal sequencing of coupling to bath

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• Enhanced non-macrorealism: Extreme violations of Leggett-Garg inequalities for a system evolving under superposition of unitaries
• Fractional Conformal Map, Qubit Dynamics and the Leggett-Garg Inequality
• Chaos-Mediated Quantum State Discrimination Near Unit Fidelity