Enhanced non-macrorealism: Extreme violations of Leggett-Garg inequalities for a system evolving under superposition of unitaries

Quantum theory contravenes classical macrorealism by allowing a system to be in a superposition of two or more physically distinct states, producing physical consequences radically different from that of classical physics. We show that a system, upon subjecting to transform under superposition of unitary operators, exhibits enhanced non-macrorealistic feature - as quantified by violation of the Leggett-Garg inequality (LGI) beyond the temporal Tsirelson bound. Moreover, this superposition of unitaries also provides robustness against decoherence by allowing the system to violate LGI and thereby retain its non-macrorealistic behavior for a strikingly longer duration. Using an NMR register, we experimentally demonstrate the superposition of unitaries with the help of an ancillary qubit and verify these theoretical predictions.

💡 Research Summary

The paper investigates how quantum systems can exhibit stronger violations of macrorealism than previously thought by employing a novel dynamical scheme called “superposition of unitaries.” Classical macrorealism assumes that a system possessing two or more distinguishable states is always in one definite state. Quantum mechanics violates this assumption, and the Leggett‑Garg inequality (LGI) provides a quantitative test: for a dichotomic observable Q measured at three times t₁, t₂, t₃, the combination K₃ = C₁₂ + C₂₃ – C₁₃ (with Cᵢⱼ = ⟨Q(tᵢ)Q(tⱼ)⟩) must satisfy –3 ≤ K₃ ≤ 1 in any macrorealistic theory. In quantum two‑level systems (TLS) evolving under a single unitary, the maximum quantum value is limited by the temporal Tsirelson bound (TTB), also known as Lüder’s bound, K₃ ≤ 1.

The authors propose to go beyond this bound by letting the system evolve under a superposition of two distinct unitary rotations. They define two rotations U₀(δ)=exp(–i σₙ ωδ/2) and U₁(δ)=exp(–i σₘ ωδ/2), where the rotation axes n̂ and m̂ differ (–1 < n̂·m̂ ≤ 1). A superposition parameter α∈