Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Bohr's complementarity principle tested on a real quantum computer via interferometer experiments

Celia Álvarez Álvarez, Mariamo Mussa Juane

TL;DR

This work tests Bohr's Complementarity Principle using updated wave-particle trade-offs expressed as $C_{l_1}( ho)+P_{l_1}( ho)\leq d-1$ by implementing Biased Mach-Zehnder Interferometer (BMZI) and Partial Quantum Eraser (PQE) on real quantum hardware. The authors define $C_{l_1}$ and $P_{l_1}$ from the density-matrix elements and reconstruct final states via quantum-state tomography to evaluate the bound across one- and two-qubit circuits, with a detailed deconstruction of mean squared error into $\mathrm{MSE}(C_{l_1})$, $\mathrm{MSE}(P_{l_1})$, and a correlation term. They report qubit-dependent performance on the QMIO device, observe correlations that can mask pure-state behavior, and demonstrate that small MSE values do not guarantee fidelity to theory unless the correlation is also low. The work provides a concrete methodology for quantifying wave-particle duality on noisy quantum hardware and highlights the need for multi-faceted diagnostics when testing fundamental quantum principles, with implications for cross-platform benchmarking and interpretation debates.

Abstract

Bohr's Complementarity Principle is a core concept of quantum mechanics. In this article, an updated complementarity relation for the wave and ondulatory aspects of a quantum system is presented and discussed. Two interferometric experiments are implemented in one and two qubit circuits and executed on real hardware. The final state density matrices are reconstructed using quantum state tomography and the complementarity relation is tested via direct computation. Results of the executions are presented both graphically and with a mean squared error analysis for a better comprehension.

Bohr's complementarity principle tested on a real quantum computer via interferometer experiments

TL;DR

This work tests Bohr's Complementarity Principle using updated wave-particle trade-offs expressed as by implementing Biased Mach-Zehnder Interferometer (BMZI) and Partial Quantum Eraser (PQE) on real quantum hardware. The authors define and from the density-matrix elements and reconstruct final states via quantum-state tomography to evaluate the bound across one- and two-qubit circuits, with a detailed deconstruction of mean squared error into , , and a correlation term. They report qubit-dependent performance on the QMIO device, observe correlations that can mask pure-state behavior, and demonstrate that small MSE values do not guarantee fidelity to theory unless the correlation is also low. The work provides a concrete methodology for quantifying wave-particle duality on noisy quantum hardware and highlights the need for multi-faceted diagnostics when testing fundamental quantum principles, with implications for cross-platform benchmarking and interpretation debates.

Abstract

Bohr's Complementarity Principle is a core concept of quantum mechanics. In this article, an updated complementarity relation for the wave and ondulatory aspects of a quantum system is presented and discussed. Two interferometric experiments are implemented in one and two qubit circuits and executed on real hardware. The final state density matrices are reconstructed using quantum state tomography and the complementarity relation is tested via direct computation. Results of the executions are presented both graphically and with a mean squared error analysis for a better comprehension.
Paper Structure (12 sections, 14 equations, 6 figures)

This paper contains 12 sections, 14 equations, 6 figures.

Table of Contents

  1. INTRODUCTION.
  2. METHODS.
  3. Coherence, predictability and continuous complementarity.
  4. A note on incoherence and purity.
  5. A note on independence.
  6. Experiments to test Bohr's Complementarity Principle.
  7. Biased Mach-Zehnder Interferometer. 1 Qubit.
  8. Partial Quantum Eraser. 2 Qubits.
  9. Deconstructed mean squared error
  10. RESULTS.
  11. CODE.
  12. CONCLUSIONS.

Figures (6)

  • Figure 1: Implementation of the BMZI on a 1-qubit quantum circuit with qiskit. The angles $\phi$ and $-\beta$ will be fixed to 0 and $\pi$, respectively.
  • Figure 2: Implementation of the PQE on a 2-qubit quantum circuit with qiskit.
  • Figure 3: BCP curves
  • Figure 4: $MSE(\mathbf{C_{l_1}}+\mathbf{P_{l_1}})$ histogram
  • Figure 6: BCP curves
  • ...and 1 more figures