⚛️ quantum physics

Wave--particle transition and quantum Zeno effect in which-way experiments with a superconducting quantum processor

This study utilizes a superconducting quantum processor to experimentally demonstrate the wave-particle transition and quantum Zeno effect in Mach-Zehnder interferometry, quantitatively characterizing how which-way measurements break coherence, induce information leakage, and establish complementarity relations between entropy and fringe visibility.

Original authors: Shiyu Wang, Zhiguang Yan, Clemens Gneiting, Rui Li, Franco Nori, Yasunobu Nakamura

Published 2026-04-22

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Shiyu Wang, Zhiguang Yan, Clemens Gneiting, Rui Li, Franco Nori, Yasunobu Nakamura

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are watching a magical show where a single photon (a tiny particle of light) is the star. This photon has a secret superpower: it can act like a wave (spreading out and interfering with itself) or like a particle (taking a single, definite path), but never both at the same time. This is the famous "wave-particle duality" of quantum mechanics.

This paper describes a team of scientists who built a high-tech "magic stage" using a superconducting quantum processor (a chip with 16 tiny artificial atoms called qubits) to watch this photon make the switch from wave to particle. They also discovered what happens when you stare at the photon too closely.

Here is the story of their experiment, broken down into simple concepts:

1. The Setup: A Quantum Highway

Think of the quantum processor as a miniature highway system.

The Photon: They create a single "microwave photon" (like a tiny packet of energy) at the start of the road.
The Split: The photon hits a "beam splitter" (a quantum traffic light) that sends it down two parallel roads at the same time.
The Goal: At the end, the two roads merge back together. If the photon acted like a wave, the two paths would interfere, creating a pattern of bright and dark spots (like ripples in a pond). If it acted like a particle, it would just pick one road, and the pattern would disappear.

2. The Experiment: The "Peeking" Game

The scientists wanted to see what happens if they try to "peek" at which road the photon is taking. This is called a "which-way" measurement.

The Weak Peek (The Wave): First, they peeked very gently. It was like looking at the photon through a foggy window. The photon still acted mostly like a wave, and the interference pattern remained strong.
The Strong Peek (The Particle): Then, they turned up the "brightness" of their peek. They looked harder and harder. As they looked more intensely, the interference pattern started to fade.
The Result: When they looked very hard (a "projective" measurement), the photon was forced to choose a single path. The wave behavior vanished, and it acted purely like a particle. The interference pattern disappeared completely.

The Analogy: Imagine a dancer spinning in a circle (the wave). If you watch from far away, you see the blur of the spin. If you zoom in with a super-magnifying glass to see exactly which foot is moving, the dancer gets confused, stops spinning, and stands still on one foot (the particle).

3. The Secret Cost: Information Leakage

The scientists didn't just watch the pattern; they also checked the "health" of the quantum system. They found that when you peek at the photon, you aren't just observing it; you are stealing its secrets.

Entanglement: Before the peek, the two paths were "entangled" (like two dancers perfectly synchronized).
The Breakup: As the scientists peeked harder, this synchronization broke. The paths became independent.
Leakage: The information about which path the photon took didn't just stay in the machine; it "leaked" into the measurement device (the environment). The more they peeked, the more information leaked out, and the more the quantum magic (coherence) disappeared.

They created a mathematical rule (a "complementarity relation") that proves: The more you know about the path (particle nature), the less you see the interference (wave nature).

4. The Quantum Zeno Effect: The "Freeze" Button

In a second, more advanced experiment, they didn't just peek once; they kept their eyes glued to the photon the entire time it was traveling.

The Paradox: In the quantum world, if you watch something constantly, you can actually stop it from moving. This is called the Quantum Zeno Effect.
What Happened: As they increased the strength of their continuous staring, the photon in the "watched" path got frozen. It couldn't move forward. It was like a car trying to drive through a tunnel while a guard keeps checking its license plate every millisecond; the car eventually stops moving because it's too busy being checked.
The Surprise: The photon didn't just stop; it started to bounce back! The stronger the measurement, the more the photon was "reflected" away from that path. This created a weird, non-straight line in the data: first, the system got messier (more entropy), but then, as the "freezing" took over, it actually got cleaner again because the photon was forced to stay in its starting spot.

Why Does This Matter?

This experiment is a big deal for a few reasons:

It's a Perfect Playground: Unlike real light experiments where you often have to destroy the photon to see it, this superconducting chip lets them watch the photon without killing it. They can see the whole journey.
Connecting Physics and Information: It proves that "wave vs. particle" isn't just about physics; it's about information. If information leaks out, the wave disappears.
Future Tech: This helps us understand how to build better quantum computers. If we want a quantum computer to work, we need to know exactly how much "peeking" (measurement) we can do before we accidentally break the magic.

In a nutshell: The scientists built a tiny quantum highway, watched a photon switch from a wave to a particle by peeking at it, and discovered that staring too hard can actually freeze the photon in place. It's a beautiful demonstration of how the act of observing the universe changes the universe itself.

1. Problem Statement

The paper addresses the fundamental quantum mechanical principle of Bohr's complementarity, which posits that quantum objects exhibit either wave-like or particle-like behavior depending on the measurement scheme, but not both simultaneously. While this has been demonstrated in various systems (photonic, atomic, electronic), there is a need for:

High-precision control over the strength of "which-way" (path) measurements to observe the continuous transition from wave to particle behavior.
Non-destructive detection to track the full propagation path of a quantum excitation without absorbing it (a limitation in optical systems).
Quantitative characterization of the relationship between wave-particle duality, quantum information leakage (decoherence), and entropy.
Investigation of the Quantum Zeno Effect (QZE) in the context of interferometry, specifically how continuous measurement affects path blocking and information leakage.

2. Methodology

The researchers utilized a 16-qubit 2D superconducting quantum processor (composed of frequency-tunable transmon qubits) to implement Mach–Zehnder (MZ) interferometry. The system Hamiltonian was mapped to a hard-core boson model, equivalent to a spin-1/2 antiferromagnetic XY model.

Two distinct experimental configurations were employed:

A. 4-Qubit MZ Interferometer (Discrete Measurement)

Setup: A single microwave photon is generated by exciting qubit $Q_0$ . It propagates through two paths: Path 1 ( $Q_1$ ) and Path 2 ( $Q_2$ ), recombining at $Q_3$ .
Measurement Scheme: A "which-way" measurement is performed on $Q_2$ (Path 2) while the qubits are decoupled (frozen in time).
Control: The measurement strength is tuned by varying the amplitude of a dispersive readout pulse, controlling the measurement-induced dephasing rate ( $\Gamma_m$ ) from zero (no measurement) to the projective regime.
Analysis:
- Interference: Measured by varying the phase difference ( $\phi$ ) in Path 1 and observing the population of $Q_3$ to calculate fringe visibility ( $V$ ).
- Quantum State Tomography: Performed on the two-qubit system ( $Q_1, Q_2$ ) to reconstruct the density matrix.
- Metrics: Calculated Concurrence (entanglement), Purity ( $P_s$ ), and Von Neumann Entropy ( $S_s$ ) in the single-excitation subspace.

B. 12-Qubit MZ Interferometer (Continuous Measurement)

Setup: A larger interferometer using 12 qubits to form two distinct paths (Path 1: $Q_1, Q_4, Q_5, Q_7, Q_{13}$ ; Path 2: $Q_2, Q_8, Q_{10}, Q_{11}, Q_{14}$ ).
Measurement Scheme: A continuous which-way measurement is applied to $Q_2$ throughout the entire evolution of the photon.
Control: The measurement strength is swept from 0 to $\approx 18$ MHz. Stark shifts induced by the measurement are compensated via Z-bias pulses.
Analysis: Similar tomography and metric extraction were performed on qubits $Q_4$ and $Q_8$ (representing the two paths) to observe the dynamics of entanglement and entropy under continuous observation.

3. Key Contributions

Demonstration of Wave-Particle Transition: The first observation of a continuous transition from wave-like to particle-like behavior in a superconducting processor by precisely tuning the which-way measurement strength.
Quantitative Complementarity Relations: Derivation and experimental verification of inequalities linking fringe visibility ( $V$ ) with linear entropy and Von Neumann entropy:
- $2(1 - P_s) + V^2 \leq 1$
- $S_s \leq S_{sym}^s(V)$
  These relations mathematically formalize the trade-off between path information (entropy) and interference visibility.
Observation of Quantum Zeno Effect in Interferometry: Demonstrated that strong continuous measurement on one path effectively "blocks" that path, reflecting the photon and preventing it from entering the interferometer arm, thereby altering the interference dynamics.
Non-Monotonic Entropy Dynamics: Revealed a counter-intuitive behavior where, under strong continuous measurement (QZE regime), the system's purity increases (and entropy decreases) after an initial drop. This indicates that strong measurement suppresses information leakage by reflecting the photon before it can entangle with the environment.

4. Key Results

Visibility vs. Measurement Strength: As the measurement-induced dephasing rate ( $\Gamma_m$ ) increased in the 4-qubit system, the interference fringe visibility ( $V$ ) decreased monotonically from $\approx 1$ to $0$, confirming the transition from wave to particle behavior.
Entanglement Destruction: The concurrence between the two path qubits dropped from $\approx 0.717$ to nearly $0$ as measurement strength increased, proving that which-way measurements destroy inter-path entanglement.
Information Leakage: The Von Neumann entropy ( $S_s$ ) increased with measurement strength in the 4-qubit system, confirming that quantum information leaks from the system into the measurement apparatus.
Quantum Zeno Effect (12-qubit system):
- At low measurement strength, the photon propagates through both paths.
- As strength increases, the population in Path 2 decreases, and the photon is forced to Path 1.
- Non-monotonic Purity/Entropy: Unlike the 4-qubit case, the 12-qubit system showed that purity initially decreased (entropy rose) but then increased (entropy fell) at very high measurement strengths. This confirms that the QZE reflects the photon, reducing the time available for information leakage and effectively "freezing" the state in the initial path.
Theoretical Fit: The experimental data for entropy vs. visibility closely matched the theoretical bounds derived in the paper, validating the complementarity relations.

5. Significance

Fundamental Physics: The work provides a high-precision, controllable platform to test foundational quantum mechanics, specifically the interplay between measurement, decoherence, and complementarity.
Quantum Information: It establishes a direct quantitative link between wave-particle duality and quantum information metrics (entropy, purity, entanglement), showing that "which-way" information is synonymous with information leakage and loss of coherence.
Platform Capability: It demonstrates the capability of superconducting quantum processors to perform complex, multi-qubit interferometry with non-destructive, tunable measurements, surpassing the limitations of optical systems where photon absorption is often required for detection.
Future Applications: The setup paves the way for advanced experiments such as delayed-choice experiments, Franson Bell-CHSH tests, and multi-photon interference on programmable quantum hardware. The observation of non-monotonic entropy under QZE offers new insights into optimizing measurement strategies for time-of-arrival detection.