🔬 mesoscale physics

Detecting entanglement with transport measurement in weakly interacting and fluctuating systems

This paper proposes a feasible protocol to measure von Neumann entropy and mutual information in complex, interacting quantum transport systems by leveraging the persistent connection between entanglement and two-point correlation functions, even under realistic conditions like boundary interactions and quantum quenches.

Original authors: Zhenhua Zhu, Gu Zhang, Dong E. Liu

Published 2026-07-27

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CC BY 4.0

Original authors: Zhenhua Zhu, Gu Zhang, Dong E. Liu

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 the universe as a giant, invisible dance floor where tiny particles like electrons are the dancers. In the world of quantum physics, these dancers can do something magical called "entanglement." When two particles are entangled, they become so deeply connected that what happens to one instantly affects the other, no matter how far apart they are. It's like if you and your best friend shared a single brain; if you suddenly decided to wear a red hat, your friend would instantly know, even if they were on the other side of the galaxy. Scientists call this connection "entanglement," and it's the secret sauce behind future technologies like super-fast quantum computers.

However, measuring this invisible dance is incredibly hard. Usually, to see how much two dancers are entangled, you have to stop the music, freeze the dance, and look at every single step they've ever taken. But in the real world, these particles are constantly bumping into each other, pushing and pulling (interactions), and the dance floor is often crowded with other groups of dancers (multipartite systems). Traditional methods for measuring entanglement break down when things get messy, noisy, or when there are more than just two dancers involved. It's like trying to count the number of handshakes in a crowded room while everyone is shouting and running around.

This is where a team of physicists from Tsinghua University and Nanjing University steps in with a clever new idea. They have developed a "detective kit" to measure entanglement in these messy, crowded, and interactive quantum systems without having to freeze time. Instead of trying to stop the dance, they propose watching how the particles flow through a system, much like observing traffic on a busy highway.

The researchers discovered that even when particles are interacting and pushing against each other, the amount of entanglement (which they call "von Neumann entropy") is still secretly written in the patterns of how particles move and scatter. Think of it like listening to the sound of a crowd. Even if you can't see individual people, the way the noise rises and falls tells you exactly how many people are there and how they are interacting. By measuring the "traffic" of electrons—specifically how many electrons jump from one part of the system to another and how much their numbers fluctuate—the team found a way to calculate the entanglement.

Their work shows that this method works in two tricky scenarios that were previously thought to be too difficult. First, it works when the "messy" interactions happen right at the edges or boundaries of the system, like a quantum island surrounded by wires. Second, and perhaps more surprisingly, it works even when the interactions happen deep inside the system (the "bulk"), provided the system is jolted suddenly—like a sudden switch in the road conditions—between being fully open and fully closed.

The paper suggests that by using these transport measurements, scientists can finally quantify entanglement in complex, real-world quantum devices. They prove that the connection between the flow of particles and the hidden quantum links remains strong, even when the particles are interacting. This doesn't just solve a math puzzle; it offers a practical path to experimentally check if a quantum system is truly isolated or if it's leaking information to its environment. In short, they've found a way to hear the quantum whispers of a crowded, chaotic room, turning a previously impossible measurement into a feasible experiment for the future of quantum technology.

Technical Summary: Detecting Entanglement with Transport Measurement in Weakly Interacting and Fluctuating Systems

Problem Statement
Measuring entanglement entropy, specifically the von Neumann entropy (VNE) and mutual information, in interacting, multipartite quantum systems remains a significant experimental challenge. Existing protocols for measuring VNE are largely restricted to non-interacting bipartite systems or confined quasi-particle systems. These limitations hinder the application of entanglement quantification to realistic experimental setups characterized by many-body interactions and multiple subsystems (multipartite structures). Furthermore, distinguishing between system-environment coupling and isolated system dynamics in complex, interacting devices requires robust theoretical frameworks that bridge microscopic quantum scattering and macroscopic transport observables.

Methodology
The authors develop a generalized protocol to experimentally measure VNE and mutual information in quantum transport systems. The core methodology relies on establishing a rigorous connection between the VNE of a subsystem and the two-point correlation functions (specifically, the correlation matrix $M(R)$ ) derived from full counting statistics (FCS).

The theoretical framework proceeds through several key steps:

Multipartite Definition: The authors define $x$ -partite mutual information $I^{(x)}$ based on the VNEs of various subsystem subsets. They propose that the change in mutual information, $\Delta I^{(x)}$ , serves as a criterion for identifying system-environment coupling, particularly when the system is partitioned into an odd number of subsystems.
Correlation-Entropy Relation: The central theoretical tool is the relation $\Delta S(R) = \sum_{m>0} \frac{\alpha_m}{m!} C^{(R\bar{R})}_m$ , which links the production of VNE to the cumulants of particle number fluctuations (FCS) between a subset $R$ and its complement $\bar{R}$ .
Handling Interactions: The paper extends this relation to interacting systems through two distinct theoretical approaches:
- Weakly Interacting Regime (Perturbation Theory): The authors prove that for systems with conserved charges and sufficiently weak interactions, the reduced density matrix can be expanded around a fermionic Gaussian state. They demonstrate that the VNE retains the standard form dependent solely on the two-point correlation matrix $M(R)$ , even in the presence of weak quartic interactions.
- Weak Fluctuation Regime (Saddle-Point Approximation): For systems where interactions may be strong but fluctuations around a stable saddle point are small, the authors employ the Hubbard-Stratonovich transformation. By integrating out bosonic fields and retaining Gaussian fluctuations, they show that the effective density matrix remains quadratic, preserving the VNE-correlation relation.
Transport Feasibility: The authors analyze the experimental feasibility of measuring the correlation matrix $M(R)$ $M (R)$ via transport. They distinguish between two physical scenarios:
- Boundary Interactions: Where interactions are localized at the boundaries (e.g., an island coupled to leads). In this case, the correction to the generating function remains quadratic, allowing the standard extraction of the spectral density of $M(R)$ from transport data.
- Bulk Interactions: Where interactions exist throughout the leads. Here, the generating function acquires additional interaction-dependent terms. The authors show that the standard protocol remains valid to the leading order if the system is in a state where occupation numbers are either 0 or 1 (e.g., zero temperature or abrupt switching between transparent and disconnected limits).

Key Contributions

Generalization to Multipartite Systems: The work extends entanglement detection protocols beyond bipartite, non-interacting paradigms to general multipartite systems.
Robustness Against Interactions: The paper establishes that the fundamental connection between VNE and two-point correlation functions persists in both weakly interacting and weakly fluctuating regimes. This is formalized in Theorem 1 (perturbative limit) and Theorem 2 (saddle-point limit).
Experimental Protocol for Interacting Systems: The authors provide a concrete pathway to measure VNE and mutual information in interacting transport setups. They demonstrate that for boundary-interacting systems, the measurement is feasible without modification to the non-interacting protocol. For bulk-interacting systems, they identify specific conditions (low temperature or specific switching dynamics) under which the protocol remains applicable.
System-Environment Indicator: The work proposes the change in multipartite mutual information ( $\Delta I^{(x)}$ ) as an experimentally accessible indicator for system-environment entanglement, specifically noting its utility when $x$ is odd.

Results

Theoretical Validity: The authors prove that the VNE of a subset $R$ in a weakly interacting or weakly fluctuating system is given by $S(R) = -\text{Tr}[(1-M(R))\log(1-M(R)) + M(R)\log M(R)]$ , where $M(R)$ is the correlation matrix. This result holds up to the leading order of interaction strength or quantum fluctuations.
Transport Measurement: The spectral density of the correlation matrix $M(R)$ $M (R)$ , which determines the VNE, can be extracted from the generating function of full counting statistics, $\chi(\lambda)$ $χ (λ)$ .
- In boundary-interaction scenarios (e.g., Kondo systems, local electron-electron interactions at an island), the relation between VNE and FCS cumulants holds exactly as in non-interacting systems.
- In bulk-interaction scenarios, the relation requires modifications unless the system satisfies specific conditions (e.g., $M_{ii}^{(R),0} \to 0$ or $1$). Under these conditions, the protocol from Ref. [26] (originally for non-interacting systems) remains valid to the leading order of interaction.
Non-Equilibrium Extension: The results are shown to hold for non-equilibrium systems where the internal couplings undergo a quantum quench (abrupt switching), provided the initial state and interaction regimes satisfy the derived constraints.

Significance
The paper claims to provide a pathway to experimentally quantify entanglement in complex, realistic quantum systems that were previously inaccessible to such measurements due to the presence of interactions and multipartite structures. By establishing that VNE and mutual information are experimentally accessible via transport measurements in these regimes, the work broadens the applicability of entanglement quantification frameworks. It specifically furnishes a concrete indicator for system-environment entanglement, which is crucial for characterizing quantum devices and understanding decoherence in many-body systems. The work complements existing studies on many-body bulk systems by focusing specifically on quantum transport signatures in mesoscopic devices.

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