Nonclassicality of a Macroscopic Qubit-Ensemble via Parity Measurement Induced Disturbance

TL;DR

The work addresses testing nonclassicality in macroscopic spin systems by treating an $N$-qubit ensemble as a single spin with angular momentum $j=N/2$ and testing macrorealism via a two-time No Disturbance Condition using parity measurements in a common resonator. In the ideal limit the MR violation is independent of $N$ and maximally realized at $\phi=\pi/4$, while realistic noise from rotation errors, decoherence, and inhomogeneous couplings induces a quantum-to-classical transition quantified by $r_c=\gamma_c/\chi$, $r_s=\gamma_s/\chi$ and a spread $\sigma_g$ in couplings. The paper provides closed-form expressions for the measurement probabilities $P_1(\pm)$, $P_2(\pm)$ and the NDC violations $V_{\pm}$ for integer and half-integer $j$, and demonstrates that MR violation can be observed up to $N_{\text{NDC}} \sim 41$–$110$ qubits across superconducting, Rydberg, and spin-qubit platforms with current technology. This work offers a scalable, parity-based protocol to probe genuine nonclassicality in macroscopic spins, clarifying how decoherence and practical constraints shape the apparent quantum-to-classical transition and challenging the notion that Bohr's correspondence principle is fundamental.

Abstract

We propose an experimental scheme to test the nonclassicality of a macroscopic ensemble of qubits, through the violation of the classical notion of macrorealism (MR) via the fundamental measurement-induced disturbance of quantum systems. An electromagnetic resonator is used to probe the parity of the qubit-ensemble. The action of sequential measurements allows the nonclassicality of whole ensemble to manifest itself, in the ideal case, irrespective of its size. This enables to probe the macroscopic limits of quantum mechanics as the qubit-ensemble is, effectively, a single large spin of many $\hbar$ units. Even as $\hbar \rightarrow 0$ in comparison to the total angular momentum of the ensemble, a constant amount of violation of MR is found in the noiseless case. However, environmental decoherence and inhomogeneity of qubit-electromagnetic field couplings precipitate the quantum-to-classical transition. This implies that Bohr's correspondence principle is not fundamental, but a consequence of practical limitations. We outline an implementation with a variety of qubits (superconducting qubits, spins in semiconductors, and Rydberg atoms) coupled to a coplanar waveguide resonator, and - via the corresponding noise analysis - find that violation of MR is detectable up to $100$ qubits via current technology.

Figures (7)

• Figure 1: Husimi representations of even and odd CS of a large spin ($j=10$).
• Figure 2: Variation of the magnitude of violation of the NDC, denoted by $|V_{\pm}|$, versus $\phi$ for different $j$ in the ideal case.
• Figure 3: Violation of NDC as function of two rotation angles $\phi_1$, $\phi_2$ for of a spin $j=10$ with the analytically derived results for $\phi_1 = \phi_2$ being depicted in red and that for $\phi_1 = \pi/2 - \phi_2$ being presented in green.
• Figure 4: Violation of the NDC of a large spin (a) under spin decoherence as function of the decoherence rate $\gamma_s$ for different spin values $j$, and (b) with cavity leaking, as function of the cavity decay rate $\gamma_c$ with different cavity intensity $|\alpha_0|$. The $\gamma_s$ and $\gamma_c$ are in the entanglement coupling ($\chi$) units.
• Figure 5: Violation of the NDC of a qubit ensemble measured by a cavity field with inhomogeneous qubit-cavity couplings, extracted from a Gaussian distribution of standard deviation $\sigma_g$. Violation (a) as function of $r_\sigma =\sigma_g/\braket{g}$ with $j=12$; and as function of ensemble size at constant (b) $r_\sigma = 0.005$ and (c) $r_\sigma = 0.01$.