Equilibration and the Eigenstate Thermalization Hypothesis as Limits to Observing Macroscopic Quantum Superpositions

Macroscopic quantum superpositions are widely believed to be unobservable because large systems cannot be perfectly isolated from their environments. Here, we show that even under perfect isolation, intrinsic unitary dynamics with the eigenstate thermalization hypothesis suppress the observable signatures of macroscopic coherence. Using the GHZ state as a representative example, we demonstrate that while fully correlated measurements can initially distinguish a macroscopic superposition from its corresponding classical mixture, generic many-body evolution renders them operationally indistinguishable for most times during the evolution. By analyzing both distinguishability measures and established quantifiers of macroscopic quantumness, we find that equilibration not only hides coherence from accessible observables but also suppresses macroscopic superpositions themselves. These results identify unitary thermalization, independent of environmental decoherence, as a fundamental mechanism that limits the emergence of macroscopic quantum effects.

💡 Research Summary

This paper investigates the fundamental limits to observing macroscopic quantum superpositions, arguing that the challenge extends beyond environmental decoherence to include intrinsic unitary dynamics governed by the Eigenstate Thermalization Hypothesis (ETH). The authors posit that even under perfect isolation, generic many-body evolution can suppress the observable signatures of macroscopic coherence, rendering superpositions operationally indistinguishable from classical mixtures for most times.

The study uses the Greenberger-Horne-Zeilinger (GHZ) state, (|0⟩^⊗N + |1⟩^⊗N)/√2, as a canonical example of a macroscopic superposition, and compares it to its corresponding classical mixture, an equal statistical mix of |0⟩^⊗N and |1⟩^⊗N. The analysis proceeds in two key stages. First, the paper examines the distinguishability of these states via different observables. It is shown that local, additive observables like total magnetization fail to distinguish the states at any time, as their expectation values are identical. In contrast, a fully correlated, non-local observable (e.g., σ_n^⊗N) can provide a finite distinguishing signal at time t=0. However, this signal is exponentially sensitive to precise alignment of the measurement direction.

The core theoretical contribution lies in the second stage, which analyzes the dynamical evolution under a generic, non-integrable many-body Hamiltonian. The authors invoke the theory of equilibration in isolated quantum systems and the ETH. Under ETH, energy eigenstates in chaotic systems behave thermally, and the off-diagonal matrix elements of observables between different energy eigenstates are exponentially small in system size. Employing this framework, the authors demonstrate analytically that for any observable whose operator norm grows at most polynomially with N—encompassing both local and highly non-local operators—the time-averaged difference in expectation values between the GHZ state and the mixture, Δ⟨A⟩, vanishes exponentially with N. Furthermore, the temporal fluctuations around this average also become negligible. This implies that after a short transient period, the system equilibrates to a state where no experimentally feasible observable can reliably tell the superposition apart from the mixture for the vast majority of time.

To substantiate the analytical claims, the authors perform numerical simulations on a chaotic spin chain described by an extended Heisenberg-XYZ Hamiltonian with next-nearest neighbor interactions and magnetic fields. The numerical results confirm that both the GHZ state and the mixture equilibrate under this dynamics (evidenced by low purity of their time-averaged states). Crucially, the plots show that the time-averaged distinguishability signal, Δ⟨A⟩, for both a local magnetization operator and the fully correlated operator, decays rapidly as the system size N increases, aligning with the theoretical predictions.

In conclusion, the paper identifies unitary equilibration and thermalization, independent of any environmental coupling, as a fundamental intrinsic mechanism that limits the emergence and detectability of macroscopic quantum effects. It challenges the notion that perfect isolation alone could preserve macroscopic coherence and provides a new perspective on the quantum-to-classical transition by linking it to the generic dynamical properties of complex, isolated quantum systems.