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Deep Thermalization and Measurements of Quantum Resources
Quantum Physics · Submitted 10 Dec 2025 · Published version
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our work connects deep thermalization to resource quantification, offering a new perspective on the essential role of various resources in generating state designs and enabling efficient estimation of quantum resources in experiment.
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The abstract, sentence by sentence
Quantum resource theories provide a unified framework for characterizing useful quantum phenomena subject to physical constraints but are notoriously hard to assess in experimental systems. In this letter, we introduce a unified protocol for quantifying the resource-generating power of arbitrary quantum evolutions applicable to multiple resource theories. It is based on deep thermalization, which has recently gained attention for its role in the emergence of quantum state designs from partial projective measurements. Central to our approach is the use of projected ensembles, recently employed to probe deep thermalization, together with new twirling identities that allow us to directly infer the resource-generating powers of the underlying dynamics. These identities further reveal how resources build up and thermalize in generic quantum circuits. Finally, we show that quantum resources themselves undergo deep thermalization at the subsystem level, offering a complementary and another experimentally accessible route to infer the resource-generating powers. Our work connects deep thermalization to resource quantification, offering a new perspective on the essential role of various resources in generating state designs and enabling efficient estimation of quantum resources in experiment.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Quantum resource theories provide a unified framework for characterizing useful quantum phenomena subject to physical constraints but are notoriously hard to assess in experimental systems. | background 0.94 | 0.03 | 0.03 | asserted 1.00 |
| s1 | In this letter, we introduce a unified protocol for quantifying the resource-generating power of arbitrary quantum evolutions applicable to multiple resource theories. | contribution 1.00 | 0.93 | 0.15 | asserted 1.00 |
| s2 | It is based on deep thermalization, which has recently gained attention for its role in the emergence of quantum state designs from partial projective measurements. | method 0.64 | 0.09 | 0.05 | asserted 0.96 |
| s3 | Central to our approach is the use of projected ensembles, recently employed to probe deep thermalization, together with new twirling identities that allow us to directly infer the resource-generating powers of the underlying dynamics. | method 0.94 | 0.80 | 0.12 | asserted 1.00 |
| s4 | These identities further reveal how resources build up and thermalize in generic quantum circuits. | interpretation 0.57 | 0.84 | 0.10 | asserted 0.98 |
| s5 | Finally, we show that quantum resources themselves undergo deep thermalization at the subsystem level, offering a complementary and another experimentally accessible route to infer the resource-generating powers. | result 0.92 | 0.92 | 0.30 | asserted 1.00 |
| s6 | Our work connects deep thermalization to resource quantification, offering a new perspective on the essential role of various resources in generating state designs and enabling efficient estimation of quantum resources in experiment. | interpretation 0.93 | 0.69 | 0.67 | asserted 1.00 |
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The paper
Original abstract
Quantum resource theories provide a unified framework for characterizing useful quantum phenomena subject to physical constraints, but are notoriously hard to assess in experimental systems. In this letter, we introduce a unified protocol for quantifying the resource-generating power of arbitrary quantum evolutions applicable to multiple resource theories. It is based on deep thermalization, which has recently gained attention for its role in the emergence of quantum state designs from partial projective measurements. Central to our approach is the use of projected ensembles, recently employed to probe deep thermalization, together with new twirling identities that allow us to directly infer the resource-generating powers of the underlying dynamics. These identities further reveal how resources build up and thermalize in generic quantum circuits. Finally, we show that quantum resources themselves undergo deep thermalization at the subsystem level, offering a complementary and another experimentally accessible route to infer the resource-generating powers. Our work connects deep thermalization to resource quantification, offering a new perspective on the essential role of various resources in generating state designs and on efficient estimation of quantum resources in experiment.
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References
How the literature uses it
7 arXiv papers cite this in 12 sentences
Papers citing it · 8 sentences without a confident label
Cites it as background 4 papers
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This phenomenon, known as deep thermalization, extends quantum thermalization to the higher-order fluctuations of the underlying pure-state distribution, and uncovers new universal behavior in quantum many-body systems [ref] .
Entanglement governs early-time growth of randomness in projected ensembles · Introduction · 0.81
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The stabilizer Rényi entropy has emerged in recent years as a key measure of non-stabilizerness that is relevant for quantum error correction [ref] , magic-state distillation [ref] , classical simulability [ref] , and quantum chaos [ref] .
Quantum resources in non-stoquastic quantum annealing · Quantum resources · 0.92
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Evolution of quantum resource measures in interacting many-body systems, therefore, offers a natural probe of how quantumness is dynamically generated, redistributed, and ultimately scrambled, connecting resource dynamics to quantum chaos [ref] , information scrambling [ref] , thermalization [ref] , critical phenomena [ref] , conformal field theory [ref] , monitored dynamics [ref] , resource Mpemba effect [ref] and metrological response [ref] .
Equivalence of quantum resources under ergodic dynamics · Introduction · 0.87
What it cites · 16 sentences without a confident label
Uses the method or tool of 1 paper
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Equipped with these tools, we now establish the twirling identity for the $Z_2$-asymmetry [ref] : [equation] where $Π^(2)=Π^(2)/Tr(Π^(2))$ and $Π^(2)=(𝕀+SWAP)/2$ [ref] .
Matrix integrals over unitary groups: An application of Schur-Weyl duality · Introduction · 0.92
Cites as support 2 papers
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Free-states and -unitaries, being highly structured, tend to generate projected ensembles that deviate from designs [ref] , whereas resourceful states well approximate higher-order designs [ref] .
The Clifford group fails gracefully to be a unitary 4-design · Introduction · 0.97
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Free-states and -unitaries, being highly structured, tend to generate projected ensembles that deviate from designs [ref] , whereas resourceful states well approximate higher-order designs [ref] .
2510.18369 · Introduction · 0.97
Cites as background 12 papers
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Particularly little is known about their “deep thermalization” [ref] , a refined notion of statistical relaxation in many-body quantum systems [ref] that goes beyond the conventional Eigenstate thermalization Hypothesis (ETH) framework [ref] .
2510.18369 · Introduction · 0.91
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Particularly little is known about their “deep thermalization” [ref] , a refined notion of statistical relaxation in many-body quantum systems [ref] that goes beyond the conventional Eigenstate thermalization Hypothesis (ETH) framework [ref] .
2305.01465 · Introduction · 0.91
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Particularly little is known about their “deep thermalization” [ref] , a refined notion of statistical relaxation in many-body quantum systems [ref] that goes beyond the conventional Eigenstate thermalization Hypothesis (ETH) framework [ref] .
2505.07795 · Introduction · 0.91
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