Study of Information Phases in Tripartite Systems Reveals Detailed Distribution of Quantum Information

Understanding how information distributes itself within complex quantum systems presents a significant challenge in modern physics, and recent work by Alan Sherry, Saptarshi Mandal, and Sthitadhi Roy, all from the International Centre for Theoretical Sciences at the Tata Institute of Fundamental Research, sheds new light on this problem. The team investigates ‘partial projected ensembles’, a refined method for examining information flow in multi-part quantum systems, going beyond traditional measures like entanglement. Their research demonstrates that analysing information using a quantity called the Holevo information reveals a surprising change in how information scales with system size, identifying distinct information regimes separated by sharp transitions. Crucially, this approach rigorously establishes the existence of a previously hidden form of correlation, a ‘measurement-invisible’ correlation, representing a unique type of information scrambling that cannot be detected through standard entanglement analysis, offering a more complete picture of quantum information distribution.

Scientists have developed a novel framework for characterizing quantum information distribution using projected ensembles, which provide a more detailed probe than traditional reduced density matrices. This work extends the concept to partial projected ensembles in tripartite systems, where outcomes from a portion of a measured subsystem are discarded, resulting in ensembles of mixed states. The team demonstrates that information measures, specifically the Holevo information, applied to these ensembles yield a more nuanced characterization of information distribution between subsystems compared to conventional entanglement measures.

Eigenstate Thermalization and Quantum Thermalization Theory

Quantum thermalization describes how isolated quantum systems evolve towards a state resembling thermal equilibrium. A cornerstone of understanding this process is the Eigenstate Thermalization Hypothesis, which proposes that individual energy eigenstates of chaotic quantum systems already contain information about thermal equilibrium. Quantum chaos, the study of quantum systems exhibiting chaotic behaviour, plays a crucial role, and the projected ensemble formalism is a key technique for understanding system behaviour under constraints. Researchers employ Random Matrix Theory to analyse the statistical properties of quantum systems exhibiting chaos, and utilize Information Theory to quantify information content in quantum states.

Ensembles, such as microcanonical and random ensembles, are used to describe statistical properties, and log-gases provide a mathematical framework for studying eigenvalue distributions. Current research explores deep thermalization and scrambling, the spreading of information throughout a quantum system. Investigations also focus on the impact of constraints and symmetries on thermalization, including systems with charge conservation and periodically driven systems. Many-Body Localization, where systems avoid thermalization due to disorder, is also relevant. Researchers are also exploring measurement-invisible quantum correlations. This research provides a comprehensive overview of the theoretical and experimental landscape of quantum thermalization and related phenomena.

Partial Ensembles Reveal Subtle Information Scaling

Scientists have uncovered a novel framework for characterizing quantum information distribution using projected ensembles. This work extends the concept to partial projected ensembles in tripartite systems, where outcomes from a portion of a measured subsystem are discarded, resulting in ensembles of mixed states. The team demonstrates that information measures, specifically the Holevo information, applied to these ensembles yield a more nuanced characterization of information distribution between subsystems compared to conventional entanglement measures. Experiments reveal a qualitative change in the scaling of the Holevo information with system size, depending on the relative sizes of the subsystems.

In one phase, the Holevo information decays exponentially with system size, while in another, it grows linearly, defining distinct information phases separated by sharp transitions signaled by non-analyticities in the Holevo information. The exponentially decaying phase rigorously establishes the existence of a measurement-invisible quantum-correlated phase, a manifestation of many-body information scrambling with no bipartite analogue. Measurements confirm that the Holevo information reveals additional fine structure beyond what is captured by entanglement measures, providing a more detailed understanding of quantum information scrambling. This breakthrough delivers a new tool for characterizing complex quantum states and understanding the fundamental limits of information processing.

Projected Ensembles Reveal Finer Information Distribution

Researchers have developed a novel framework for characterizing information distribution in quantum systems, moving beyond traditional entanglement measures. This work centres on the concept of ‘projected ensembles’, which retain more information about a quantum system’s components than conventional methods. By conditioning the state of one part of a system on measurements performed on another, the team constructs ensembles that reveal a more detailed picture of how information is shared. The study demonstrates that analysing information measures, specifically the Holevo information, within these projected ensembles provides a finer characterisation of information distribution than standard entanglement measures.

Through both analytical calculations and numerical simulations of random quantum states, the researchers uncovered a distinct change in how Holevo information scales with system size. This scaling reveals the existence of a ‘measurement-invisible correlation’, a form of many-body information scrambling not captured by bipartite entanglement measures. The team found that the Holevo information can either decay exponentially or grow linearly with system size, defining distinct information phases separated by sharp transitions. This work represents a significant step towards a more complete understanding of information distribution in quantum many-body systems and offers a powerful new tool for exploring the fundamental principles of quantum mechanics.