Locc Equivalence to Thermal States Achieves Criteria for Multipartite Correlations

Scientists are increasingly focused on understanding the thermal behaviour of complex quantum systems. Toshihiro Yada, Nobuyuki Yoshioka, and Takahiro Sagawa from the University of Tokyo demonstrate a crucial distinction between how pure and thermal states behave when subjected to local operations and classical communication (LOCC). Their research establishes clear criteria for determining if a pure state is truly equivalent to a thermal state under LOCC, revealing that multipartite correlations , not just local indistinguishability , govern work extraction potential. This is significant because it moves beyond traditional understandings of thermal equivalence, offering a refined operational definition vital as experimental quantum operations become more sophisticated and allow access to classically accessible correlations.

Multipartite correlations define pure-thermal state equivalence classes

Scientists have demonstrated a refined understanding of thermal equivalence in quantum many-body systems, establishing criteria to determine when pure states behave similarly to thermal states even under local operations with classical communication (LOCC). The research, published recently, addresses a fundamental question in quantum thermodynamics: does the equivalence between pure and thermal states persist when classically accessible correlations are exploited for work extraction? Researchers established that the thermal equivalence of many-body pure states is governed by their multipartite correlation structure, revealing a nuanced relationship beyond the traditional local regime. This work provides an operational notion of thermal equivalence becoming increasingly important with the expansion of experimentally accessible operations.
The team achieved this breakthrough by meticulously examining the extractable work from various many-body pure states under different operational constraints, global operations, LOCC, and strictly local operations. They developed a framework to quantify work extraction, focusing on the infinite-temperature regime where the extractable work is determined solely by the state’s purity. Experiments show that states with asymptotically maximal multipartite entanglement, such as Haar-random states, cannot yield extensive work under LOCC, mirroring the behaviour of thermal states. Conversely, the study unveils that certain states with limited multipartite entanglement, like constant-degree graph states, can allow extensive work extraction despite being locally indistinguishable from thermal states.

This research establishes a clear link between multipartite entanglement and the ability to extract work under LOCC. Specifically, the extractable work under LOCC becomes subextensive when a measure of multipartite entanglement, termed geometric entanglement, is asymptotically maximal. The team explicitly constructed tailored work extraction protocols for each state, deriving a lower bound on the extractable work to validate their findings. This approach allowed them to differentiate between states based on their quantum correlation structure, providing an operational criterion for thermal equivalence beyond the local regime.

Furthermore, the study demonstrates that constant-degree graph states and states sampled from the subset state ensemble exhibit extensive work extraction under LOCC, despite their local equivalence to thermal states. Table I summarises the scaling of extractable work for each type of state ensemble, highlighting the distinct behaviour of highly entangled versus limited-entanglement states. This. Experiments revealed that states with asymptotically maximal multipartite entanglement, including Haar-random states, cannot yield extensive work under LOCC, a significant finding in quantum thermodynamics.

The team measured work extraction capabilities for various states, discovering a crucial distinction between highly entangled and weakly entangled systems. Results demonstrate that constant-degree graph states, despite being locally indistinguishable from thermal states, can allow for extensive work extraction under LOCC. Specifically, the study constructed tailored work extraction protocols, deriving lower bounds on extractable work for these states and those sampled from the subset state ensemble. Measurements confirm that these protocols successfully extract work, highlighting the importance of multipartite correlations.

Data shows that the extractable work under global operations for an N-qudit state is given by Wglobal(ρ) = N ln d − S(ρ), where ‘d’ represents the local dimension and ‘S(ρ)’ is the von Neumann entropy. Conversely, the extractable work restricted to strictly local operations is quantified as Wlocal(ρ) = N ln d − N Σn=1 S(ρn), where ρn is the reduced density operator of the n-th subsystem. The breakthrough delivers an operational criterion that separates pure states locally indistinguishable from thermal states, classifying them based on their quantum correlation structure. Tests prove that the work extractable under LOCC protocols is defined as WLOCC(ρ) = supL∈N W L LOCC(ρ), where ‘L’ denotes the number of rounds in the LOCC protocol.

The research establishes that the difference between global and LOCC extractable work, termed the ‘work deficit’, serves as an operational measure of multipartite quantum correlations. Key observations indicate that while Wglobal = N ln d for any pure state, Wlocal = o(1) for states with reduced states close to the infinite-temperature thermal state, where o(1) denotes a quantity vanishing in the thermodynamic limit. This work sharpens the notion of thermal equivalence, offering a refined understanding of how correlations impact work extraction in quantum systems.

Multipartite Entanglement Dictates Thermal Equivalence

Scientists have established criteria for determining thermal equivalence in many-body pure states, even when local operations are augmented with classical communication (LOCC). Their research demonstrates that a state’s multipartite correlation structure governs whether it behaves equivalently to a thermal state under LOCC, refining our understanding beyond strictly local operations. Specifically, the team showed that states exhibiting asymptotically maximal multipartite entanglement, including Haar-random states, cannot yield extensive work under LOCC, aligning with thermal state behaviour. Conversely, the researchers found that certain states with limited multipartite entanglement, such as constant-degree graph states and those from the subset state ensemble, can allow extensive work extraction despite appearing locally indistinguishable from thermal states, highlighting a crucial distinction. The authors acknowledge a limitation in their current bounds, noting the need for alternative upper limits to fully characterise states with non-maximal geometric entanglement and subextensive work extraction. Future research should focus on quantifying extractable work in real quantum experiments, potentially leveraging techniques from random circuit sampling, to further probe the structure of multipartite quantum correlations and test thermal equivalence.