Violation of noninvasive macrorealism by a superconducting qubit: Implementation of a Leggett-Garg test that addresses the clumsiness loophole

The Leggett-Garg inequality holds for any macrorealistic system that is being measured noninvasively. A violation of the inequality can signal that a system does not conform to our primal intuition about the physical world. Alternatively, a violation can simply indicate that a “clumsy” experimental technique led to invasive measurements. Here, we consider a recent Leggett-Garg test designed to try to rule out the mundane second possibility. We tailor this Leggett-Garg test to the IBM 5Q Quantum Experience system and find compelling evidence that qubit $Q_2$ of the system cannot be described by noninvasive macrorealism.

Figure 1

Proposed Leggett-Garg experimental program. The symbols ${\sigma }_z$ and ${\sigma }_{\theta }$ should be ignored while deriving the Leggett-Garg inequality, which does not presume any quantum mechanics. The symbol ${\sigma }_z$ below, say, $O_3$ indicates that, in quantum theory, $O_3$ consists of a measurement along the qubit initialization direction $\widehat{z}$. The symbol ${\sigma }_{\theta }$ below, say, $O_1$ indicates that $O_1$ consists of manipulations and a measurement that are equivalent to a measurement along a direction $sin\theta \widehat{y}+cos\theta \widehat{z}$ oriented at an angle $\theta$ with respect to $\widehat{z}$.

Figure 2

Protocol (a) of the experiment implemented in a circuit acting on qubit $Q_2$.

Figure 3

Protocols (b) and (d) of the experimental program implemented in circuits.

Figure 4

Protocols (c) and (e) of the experiment program implemented in circuits.

Figure 5

Protocol (f) of the experiment program implemented in circuits.