[Paper Review] Experimental detection of microscopic environments using thermodynamic observables

Ivan Henao, Raam Uzdin+1 more|arXiv (Cornell University)|Aug 23, 2019

Quantum Information and Cryptography4 references4 citations

TL;DR

This paper proposes an experimental method to detect hidden microscopic environments in quantum systems using thermodynamic observables, leveraging violations of thermodynamic constraints such as the Clausius inequality and global passivity. By measuring mean values of specific observables on IBM quantum processors, the authors demonstrate that non-unitary dynamics—indicating environmental coupling—can be diagnosed without full state tomography, with scalability shown for systems up to four qubits.

ABSTRACT

Modern thermodynamic theories can be used to study highly complex quantum dynamics. Here, we experimentally demonstrate that the violation of thermodynamic constraints allows to detect the coupling of a quantum system to a hidden environment. By using the IBM quantum superconducting processors, we perform thermodynamic tests to detect a qubit environment interacting with a system composed of up to four qubits. The experiments are complemented by theoretical findings that show efficient scalability of the tests with respect to system size. Hence, they may be useful to detect an open system dynamics in situations where other methods (e.g. quantum state tomography) are practically infeasible.

Motivation & Objective

• To develop a scalable, experimentally feasible method to detect microscopic environmental couplings in open quantum systems.
• To overcome the limitations of quantum state tomography in large-scale quantum devices by using thermodynamic observables instead.
• To demonstrate that violations of thermodynamic constraints (e.g., Clausius inequality) serve as reliable indicators of non-unitary, environmentally driven dynamics.
• To validate the method experimentally on superconducting qubits using the IBM Quantum Experience platform.
• To show that thermodynamic tests based on mean observable values are more practical than trajectory-based methods like fluctuation relations.

Proposed method

• Use the observable $\mathcal{B} = -\ln(\rho_s)$, where $\rho_s$ is the initial thermal state, to define a thermodynamic constraint based on the Clausius inequality: $\Delta\langle\mathcal{B}\rangle \geq 0$ for unital evolutions.
• Measure the change in mean value $\Delta\langle\mathcal{B}\rangle$ of $\mathcal{B}$ after system evolution to detect violations indicating non-unital (non-unitary) dynamics.
• Apply global passivity constraints using passive observables $\mathcal{F}_\alpha$ to detect heat leaks, with $\Delta\langle\mathcal{F}_\alpha\rangle < 0$ indicating environmental coupling.
• Implement the tests on IBM's 5-qubit superconducting processors (Melbourne and Essex) using quantum circuits that prepare initial thermal states and evolve the system under controlled operations.
• Leverage theoretical results (Huang et al., 2020) to ensure that the number of required measurements scales polynomially with system size, enabling scalability.
• Compare results with thermodynamic resource theory constraints, showing that global passivity tests detect environments even when resource theory inequalities remain unviolated.

Experimental results

Research questions

• RQ1 Can thermodynamic constraints be used to detect microscopic environmental couplings in quantum systems without full state reconstruction?
• RQ2 How do violations of the Clausius inequality and global passivity constraints signal the presence of a hidden environment in a quantum system?
• RQ3 In what scenarios do thermodynamic tests based on mean observable values outperform standard resource theory inequalities in detecting environmental coupling?
• RQ4 Can these tests be experimentally realized on near-term quantum processors with limited qubit count and coherence?
• RQ5 What is the scalability of such thermodynamic diagnostics in terms of system size and measurement cost?

Key findings

• Violation of the Clausius inequality $\Delta\langle\mathcal{B}\rangle \geq 0$ was experimentally observed on IBM's 5-qubit processors, indicating non-unitary dynamics due to environmental coupling.
• The heat leak test based on global passivity constraints detected environmental coupling for $2.3 \lesssim \delta \lesssim 3.8$, even when thermodynamic resource theory inequalities remained unviolated.
• The method achieved accurate diagnostics with a number of measurements scaling polynomially with system size, enabling scalability to larger systems.
• The tests are self-contained and require only system measurements, avoiding the need for classical simulation or full tomography, which is infeasible for large devices.
• In cases where resource theory constraints failed to detect the environment (e.g., due to symmetric state exchanges), the global passivity test successfully identified the heat leak.
• The results confirm that thermodynamic observables provide a robust, low-cost alternative to trajectory-based methods like fluctuation relations for error diagnostics in quantum devices.