Leggett-Garg inequalities with deformed Pegg-Barnett phase observables

Abstract

We investigate the Leggett-Garg inequalities (LGIs) for a boson system whose observables are given by deforming the Pegg-Barnett phase operators. We consider two observables and show that the quantum Fourier transform is useful in the realization of the required measurements. Deriving explicit forms for the LGIs using the coherent state $|\alpha ⟩$ as the initial state, we explore the regimes where they are violated when the time difference between observations of the phase operators is varied. We show that the system remains nonclassical in the large amplitude limit without dissipation, however with dissipation, our violation diminishes rapidly.

arXiv comment20 pages, 10 eps figures, latex2e; v2: minor clarifications, 10 references added, figures improved

References in corpus (19)

• Leggett-Garg Inequalities
• Experimental violation of a Bell's inequality in time with weak measurement
• Violation of the Leggett-Garg inequality with weak measurements of photons
• Weak values and the Leggett-Garg inequality in solid-state qubits
• Violation of a Leggett-Garg inequality with ideal non-invasive measurements
• Classical world arising out of quantum physics under the restriction of coarse-grained measurements
• Approximate Quantum Fourier Transform and Decoherence
• The conditions for quantum violation of macroscopic realism
• A strict experimental test of macroscopic realism in a superconducting flux qubit
• Temporal quantum correlations and Leggett-Garg inequalities in multi-level systems
• Measuring a photonic qubit without destroying it
• No Fine theorem for macrorealism: Limitations of the Leggett-Garg inequality
• Experimental violation of the Leggett-Garg inequality under decoherence
• A macro-realism inequality for opto-electro-mechanical systems
• Experimental violation of the Leggett-Garg inequality in a 3-level system
• Optimal experimental demonstration of error-tolerant quantum witnesses
• Assessing the quantumness of a damped two-level system
• Modeling Leggett-Garg-inequality violation
• Violations of the Leggett-Garg inequality for coherent and cat states