Quantum resource theories characterize distinct forms of nonclassicality in many-body quantum states, raising the question of whether these resources evolve independently under generic ergodic dynamics. Considering diagnostics quadratic in the state, we show that the dynamics of different resource measures become mutually interdependent and are governed by a few common degrees of freedom. For Haar-random circuits, the purity together with a single resource witness suffices to reconstruct the remaining resource measures, as we demonstrate for coherence, various asymmetries, and number entropies. The same relations hold, to a good approximation, under chaotic Floquet and continuous-time Hamiltonian dynamics, establishing that this dynamical resource equivalence extends beyond random circuits. We further derive an exact coherence--imaginarity relation, remarkably accurate also beyond Haar-random circuits. Our results reveal an emergent simplification of many-body dynamics, in which sufficiently strong scrambling reduces seemingly distinct quantum resources to a few common dynamical degrees of freedom.Quantum resource theories characterize distinct forms of nonclassicality in many-body quantum states, raising the question of whether these resources evolve independently under generic ergodic dynamics. Considering diagnostics quadratic in the state, we show that the dynamics of different resource measures become mutually interdependent and are governed by a few common degrees of freedom. For Haar-random circuits, the purity together with a single resource witness suffices to reconstruct the remaining resource measures, as we demonstrate for coherence, various asymmetries, and number entropies. The same relations hold, to a good approximation, under chaotic Floquet and continuous-time Hamiltonian dynamics, establishing that this dynamical resource equivalence extends beyond random circuits. We further derive an exact coherence--imaginarity relation, remarkably accurate also beyond Haar-random circuits. Our results reveal an emergent simplification of many-body dynamics, in which sufficiently strong scrambling reduces seemingly distinct quantum resources to a few common dynamical degrees of freedom.

quant-pharXiv:2608.15197Aug 18, 20260 citations

The type-independent resource theory of local operations and shared randomness

David Schmid, Denis Rosset, Francesco Buscemi

In space-like separated experiments and other scenarios where multiple parties share a classical common cause but no cause-effect relations, quantum theory allows a variety of nonsignaling resources which are useful for distributed quantum information processing. These include quantum states, nonlocal boxes, steering assemblages, teleportages, channel steering assemblages, and so on. Such resources are often studied using nonlocal games, semiquantum games, entanglement-witnesses, teleportation experiments, and similar tasks. We introduce a unifying framework which subsumes the full range of nonsignaling resources, as well as the games and experiments which probe them, into a common resource theory: that of local operations and shared randomness (LOSR). Crucially, we allow these LOSR operations to locally change the type of a resource, so that players can convert resources of any type into resources of any other type, and in particular into strategies for the specific type of game they are playing. We then prove several theorems relating resources and games of different types. These theorems generalize a number of seminal results from the literature, and can be applied to lessen the assumptions needed to characterize the nonclassicality of resources. As just one example, we prove that semiquantum games are able to perfectly characterize the LOSR nonclassicality of every resource of any type (not just quantum states, as was previously shown). As a consequence, we show that any resource can be characterized in a measurement-device-independent manner.In space-like separated experiments and other scenarios where multiple parties share a classical common cause but no cause-effect relations, quantum theory allows a variety of nonsignaling resources which are useful for distributed quantum information processing. These include quantum states, nonlocal boxes, steering assemblages, teleportages, channel steering assemblages, and so on. Such resources are often studied using nonlocal games, semiquantum games, entanglement-witnesses, teleportation experiments, and similar tasks. We introduce a unifying framework which subsumes the full range of nonsignaling resources, as well as the games and experiments which probe them, into a common resource theory: that of local operations and shared randomness (LOSR). Crucially, we allow these LOSR operations to locally change the type of a resource, so that players can convert resources of any type into resources of any other type, and in particular into strategies for the specific type of game they are playing. We then prove several theorems relating resources and games of different types. These theorems generalize a number of seminal results from the literature, and can be applied to lessen the assumptions needed to characterize the nonclassicality of resources. As just one example, we prove that semiquantum games are able to perfectly characterize the LOSR nonclassicality of every resource of any type (not just quantum states, as was previously shown). As a consequence, we show that any resource can be characterized in a measurement-device-independent manner.

arXiv:1909.04065QuantumApr 30, 202060 citations

Information and Randomness

Vincenzo Manca, Vincenzo Bonnici

Emergence, complexity and computationJan 1, 20230 citations

Random exclusion codes: Quantum advantages of single-shot communication

Joonwoo Bae, Kieran Flatt, Teiko Heinosaari +4 more

Useful applications of quantum information technologies can be found by identifying tasks in which quantum resources outperform their classical counterparts. In this work, we introduce a two-party communication primitive, random exclusion code (REC), which is a single-shot prepare-and-measure protocol where a sender encodes a random message into a shorter sequence and a receiver attempts to a randomly chosen letter in the original message. We present quantum advantages in RECs in two ways: and . We show that RECs with quantum resources achieve higher success probabilities than classical strategies. We verify that, with the additional constraint that successful outcomes occur uniformly and without error, the quantum resources required to describe detection events of RECs have a smaller dimension than classical ones. We also show that a guessing counterpart, random access codes, may not have a dimension advantage over classical resources. Our results elucidate various possibilities of achieving quantum advantages in two-party communication.Useful applications of quantum information technologies can be found by identifying tasks in which quantum resources outperform their classical counterparts. In this work, we introduce a two-party communication primitive, random exclusion code (REC), which is a single-shot prepare-and-measure protocol where a sender encodes a random message into a shorter sequence and a receiver attempts to a randomly chosen letter in the original message. We present quantum advantages in RECs in two ways: and . We show that RECs with quantum resources achieve higher success probabilities than classical strategies. We verify that, with the additional constraint that successful outcomes occur uniformly and without error, the quantum resources required to describe detection events of RECs have a smaller dimension than classical ones. We also show that a guessing counterpart, random access codes, may not have a dimension advantage over classical resources. Our results elucidate various possibilities of achieving quantum advantages in two-party communication.

arXiv:2506.07701Physical Review ResearchJan 12, 20260 citations

Gluing Randomness via Entanglement: Tight Bound from Second Rényi Entropy

Wonjun Lee, Hyukjoon Kwon, Gil Young Cho

The efficient generation of random quantum states is a long-standing challenge, motivated by their diverse applications in quantum information processing tasks. In this work, we identify entanglement as the key resource that enables local random unitaries to generate global random states by effectively gluing randomness across the system. Specifically, we demonstrate that approximate random states can be produced from an entangled state $|ψ\rangle$ through the application of local random unitaries. We show that the resulting ensemble forms an approximate state design with an error saturating as $Θ(e^{-\mathcal{N}_2(ψ)})$ , where $\mathcal{N}_2(ψ)$ is the second Rényi entanglement entropy of $|ψ\rangle$ . Furthermore, we prove that this tight bound also applies to the second Rényi entropy of coherence when the ensemble is constructed using coherence-free operations. These results imply that, when restricted to resource-free gates, the quality of the generated random states is determined entirely by the resource content of the initial state. Notably, we find that among all $α$ -Rényi entropeis, the second Rényi entropy yields the tightest bounds. Consequently, these second Rényi entropies can be interpreted as the maximal capacities for generating randomness using resource-free operations. Finally, moving beyond approximate state designs, we utilize this entanglement-assisted gluing mechanism to present a novel method for generating pseudorandom states in multipartite systems from a locally entangled state via pseudorandom unitaries in each of parties.The efficient generation of random quantum states is a long-standing challenge, motivated by their diverse applications in quantum information processing tasks. In this work, we identify entanglement as the key resource that enables local random unitaries to generate global random states by effectively gluing randomness across the system. Specifically, we demonstrate that approximate random states can be produced from an entangled state $|ψ\rangle$ through the application of local random unitaries. We show that the resulting ensemble forms an approximate state design with an error saturating as $Θ(e^{-\mathcal{N}_2(ψ)})$, where $\mathcal{N}_2(ψ)$ is the second Rényi entanglement entropy of $|ψ\rangle$. Furthermore, we prove that this tight bound also applies to the second Rényi entropy of coherence when the ensemble is constructed using coherence-free operations. These results imply that, when restricted to resource-free gates, the quality of the generated random states is determined entirely by the resource content of the initial state. Notably, we find that among all $α$-Rényi entropeis, the second Rényi entropy yields the tightest bounds. Consequently, these second Rényi entropies can be interpreted as the maximal capacities for generating randomness using resource-free operations. Finally, moving beyond approximate state designs, we utilize this entanglement-assisted gluing mechanism to present a novel method for generating pseudorandom states in multipartite systems from a locally entangled state via pseudorandom unitaries in each of parties.

quant-pharXiv:2601.16454Jan 26, 20260 citations

|ψ\rangle

through the application of local random unitaries. We show that the resulting ensemble forms an approximate state design with an error saturating as

Θ(e^{-\mathcal{N}_2(ψ)})

, where

\mathcal{N}_2(ψ)

is the second Rényi entanglement entropy of

|ψ\rangle

. Furthermore, we prove that this tight bound also applies to the second Rényi entropy of coherence when the ensemble is constructed using coherence-free operations. These results imply that, when restricted to resource-free gates, the quality of the generated random states is determined entirely by the resource content of the initial state. Notably, we find that among all

α

-Rényi entropeis, the second Rényi entropy yields the tightest bounds. Consequently, these second Rényi entropies can be interpreted as the maximal capacities for generating randomness using resource-free operations. Finally, moving beyond approximate state designs, we utilize this entanglement-assisted gluing mechanism to present a novel method for generating pseudorandom states in multipartite systems from a locally entangled state via pseudorandom unitaries in each of parties.