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Identical, independent quantum weak measurements violate objective realism

Tomasz Rybotycki, Tomasz Białecki, Josep Batle, Bartłomiej Zglinicki, Adam Szereszewski, Wolfgang Belzig, Adam Bednorz

Abstract

We demonstrate violation of objective realism in quantum world using unconstrained weak measurements. Instead of limited Leggett-Garg approach with artificial bounds on the observed values, we assume two identical and indepenent weak detectors and final conditioning. The experimental verification has been performed on public quantum computers, IBM and IonQ. Thanks to sufficiently large statistics, the violation is observed at the level of 10 standard deviations. The tests confirmed also high quality of parametric two-qubit gates offered by main quantum hardware providers.

Identical, independent quantum weak measurements violate objective realism

Abstract

We demonstrate violation of objective realism in quantum world using unconstrained weak measurements. Instead of limited Leggett-Garg approach with artificial bounds on the observed values, we assume two identical and indepenent weak detectors and final conditioning. The experimental verification has been performed on public quantum computers, IBM and IonQ. Thanks to sufficiently large statistics, the violation is observed at the level of 10 standard deviations. The tests confirmed also high quality of parametric two-qubit gates offered by main quantum hardware providers.
Paper Structure (7 sections, 2 theorems, 121 equations, 12 figures, 2 tables)

This paper contains 7 sections, 2 theorems, 121 equations, 12 figures, 2 tables.

Table of Contents

  1. Measurable condition for informative measurements
  2. Weak measurement by a two-level detector
  3. Classical weak measurements
  4. Violation with position and momentum
  5. IBM Quantum circuits
  6. Imperfect detection scheme
  7. Additional data

Key Result

Theorem 1

Let two systems $A$ and $B$ be prepared in states $\bar{P}_{A/B}$, measured by $\bar{M}_{A/B}$. One can apply a weak measurement for an arbitrary $H$, by $\check{\mathcal{U}}^\lambda=\exp\lambda \tilde{\mathcal{H}}$. The averages and the correlation read Let these measurements be unbiased, i.e. $\langle a\rangle_0=\langle b\rangle_0=0$. Suppose $\lim_{\lambda\to 0}\langle b\rangle_\lambda/\lambda

Figures (12)

  • Figure 1: The detection scheme to test objective realism. Two weak detectors of $A$ and $B$ measure the state $\rho$ before the final measurement $C$. The time order of the measurement is from the left to the right: $A\to B\to C$ in the upper and $B\to A\to C$ in the lower case.
  • Figure 2: Protocol of weak measurement of $Z$ on the upper qubits with a $(ZZ)_\theta$ gate by the lower (meter) qubit with the strength of the measurement defined by $\sin\theta$. The $(ZZ)_\theta$ gate is depicted as a link between the qubits. The sign of the gate $Y_\pm$ is equivalent to switching of the strength $\pm\theta$.
  • Figure 3: The complete circuit testing objective realism. The system $C$ is measured weakly by meters $A$ and $B$ before the final direct measurement.
  • Figure 4: The dependence of the ratio $\langle a+b|c\rangle^2/4\langle ab|c\rangle$ on the angle $\psi$ between the initial and final state and the measurement strength $\lambda$ which enters by the dependence of $p(c=1)=\langle C\rangle_\lambda$ as in (\ref{['ccc']}), (\ref{['axx']}), and (\ref{['lca']}). The solid line is the threshold $1$. Note that the point $\lambda=0$, $\psi=\pi/2$ is indeterminate, $0/0$.
  • Figure 5: The violation of (\ref{['lgg2']}) for fractional $RZZ$ gate on ibm_pittsburgh for each qubits set with the system qubit $C$ index denoted on the horizontal axis. The values correspond to the combination of correlations taken from the left hand side of Eq. (\ref{['lgg2']}), while $AB$ and $BA$ correspond to the order $A\to B$ and $B\to A$. The solid line is the perfect value $4/3$ while the yellow region is classical.
  • ...and 7 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2