Subsystem Fidelity in Two-dimensional Conformal Field Theories Demonstrates Universal Contributions for Arbitrary 2D CFTs

Subsystem fidelity, a measure of how distinguishable quantum states are, presents a significant challenge in understanding complex quantum systems, and recent work by Bin Sui, Yihao Wang, and Jiaju Zhang from Tianjin University offers new insights into this problem within the framework of two-dimensional conformal field theories. The researchers investigate how this fidelity behaves when examining small regions within these theories, employing a powerful mathematical technique known as the operator product expansion. Their calculations reveal universal patterns applicable to a wide range of these theories, confirmed by existing analytical results and numerical simulations, and they successfully extend this approach to explore the connection between quantum information and gravity through holographic conformal field theories. This achievement establishes a unified method for quantifying state distinguishability, offering a valuable tool for investigating quantum systems ranging from condensed matter physics to the fundamental nature of black holes.

Analytical predictions demonstrate excellent agreement with established analytical results in field theories and numerical calculations in integrable models. Furthermore, the method extends to holographic conformal field theories, where subsystem fidelity serves to analyse the distinguishability of black hole microstates through the AdS/CFT correspondence. This work establishes a unified framework for quantifying quantum state distinguishability across various 2D conformal field theories, bridging quantum information techniques with applications in quantum gravity.

Entanglement Entropy, Thermalization and Holographic Duality

This research investigates the connection between entanglement entropy, the structure of quantum states, and holographic duality. Scientists explore how these concepts relate to the thermalization of quantum systems within the framework of conformal field theory (CFT) and the AdS/CFT correspondence. A central focus is developing tools to distinguish between different quantum states, particularly in the context of black hole microstates and the information paradox. Entanglement entropy, a measure of quantum entanglement, is a crucial quantity for understanding quantum information and the structure of quantum states.

The team focuses on Rényi entropy, a generalization of entanglement entropy. Conformal field theory provides a powerful framework for studying quantum field theories with conformal symmetry and is often used as the boundary theory in AdS/CFT. The AdS/CFT correspondence, a profound conjecture, relates a gravitational theory in Anti-de Sitter (AdS) space to a conformal field theory on its boundary, providing a powerful tool for studying strongly coupled quantum systems. The Eigenstate Thermalization Hypothesis (ETH) proposes that the eigenstates of a chaotic quantum system behave like thermal ensembles, implying randomness and describability by statistical mechanics.

The research develops methods to quantify how different two quantum states are, which is important for understanding the information content of quantum states and resolving the black hole information paradox. Scientists aim to understand how to distinguish between different microstates of a black hole, crucial for resolving the information paradox. Rényi entropy is extensively used as a tool to study entanglement and distinguishability. The team explores the universal properties of the spectrum of 2D CFTs in the large c limit. Trace distance, a measure of the distinguishability of two quantum states, is calculated between quantum states.

The research utilizes the short interval expansion of Rényi entropy to study entanglement at short distances and employs recursion formulas to compute conformal blocks. A truncation method is developed to compute trace distance between fermionic Gaussian states, and perturbative analysis is used to study the behavior of Rényi entropy and trace distance. The main contributions include new methods for computing Rényi entropy and trace distance, insights into the structure of black hole microstates, verification of the Eigenstate Thermalization Hypothesis, and a connection between CFT and holography. This research contributes to the understanding of the universal properties of 2D CFTs. In essence, this work is a technical contribution to quantum gravity and quantum information, using CFT, holography, and entanglement entropy to explore the fundamental nature of quantum states and the information paradox.

Subsystem Fidelity via Twist Operator Expansion

Scientists have achieved a significant breakthrough in quantifying the distinguishability of quantum states within two-dimensional conformal field theories (2D CFTs). The work centers on calculating subsystem fidelity, a measure of similarity between quantum states, using a refined replica trick and the operator product expansion (OPE) of twist operators. This approach allows for the evaluation of fidelity through the short-interval expansion of these operators, revealing contributions from various quasiprimary operators organized by their scaling dimensions. The team derived universal contributions applicable to all 2D CFTs from general quasiprimary operators, alongside specific contributions calculated for free massless boson and fermion theories.

These analytical predictions demonstrate excellent agreement with established analytical results and numerical calculations performed on integrable models, validating the accuracy of the method. Researchers successfully calculated subsystem fidelity between low-lying eigenstates in both the free massless boson and fermion theories, confirming the approach’s effectiveness in solvable models. Furthermore, the study extends this methodology to holographic CFTs, leveraging the AdS3/CFT2 correspondence to analyze the distinguishability of black hole microstates, offering new insights into quantum gravity. The results provide a unified framework for quantifying state distinguishability across diverse 2D CFTs, bridging techniques from quantum information theory with applications in gravity and offering a powerful tool for understanding the structure of the Hilbert space. This research establishes a robust method for evaluating the similarity of quantum states, with implications for quantum metrology, quantum computing, and the study of quantum thermalization.

Distinguishability of Quantum States via Twist Operators

This research establishes a comprehensive framework for quantifying the distinguishability of quantum states within two-dimensional conformal field theories (2D CFTs). By employing the operator product expansion of twist operators, scientists have calculated the short-interval expansion of subsystem fidelity, revealing contributions from quasiprimary operators organized by their scaling dimensions. These analytical predictions demonstrate strong agreement with established results obtained from both field theory and numerical calculations in integrable models, validating the approach across different theoretical frameworks. The team extended this method to holographic CFTs, successfully applying it to analyze the distinguishability of black hole microstates through the lens of the AdS/CFT correspondence, thereby connecting quantum information concepts with gravity. This work provides a unified approach applicable to a broad range of 2D CFTs, bridging techniques previously used in disparate areas of theoretical physics.