We investigate the nonseparability of multipartite bosonic and fermionic $GHZ$ and $W$ states in a causal diamond spacetime using the Abe-Rajagopal (AR) $q$ -conditional entropy. The finite lifetime of the observer gives rise to a causal diamond horizon, which induces an Unruh-like thermal effect and leads to a nontrivial restructuring of nonseparability in $N$ -partite systems. Our main result is that the thermal effect can enhance a net nonseparability of fermionic $W$ states, in sharp contrast to the general expectation that relativistic thermalization leads to a monotonic degradation of bosonic nonseparability. In addition, we find that fermionic nonseparability is generally more robust than its bosonic counterpart under causal diamond restrictions. Among different entangled resources, $GHZ$ states exhibit stronger nonseparability and greater robustness than $W$ states under identical causal conditions. We further show that the nonseparability of $W$ states decreases with increasing particle number $N$ , whereas that of $GHZ$ states remains independent of $N$ in causal diamond spacetime. These results demonstrate that particle statistics, entanglement structure, and observer lifetime jointly determine the persistence of nonseparability in causally restricted spacetimes, providing insights for relativistic quantum information processing.We investigate the nonseparability of multipartite bosonic and fermionic $GHZ$ and $W$ states in a causal diamond spacetime using the Abe-Rajagopal (AR) $q$-conditional entropy. The finite lifetime of the observer gives rise to a causal diamond horizon, which induces an Unruh-like thermal effect and leads to a nontrivial restructuring of nonseparability in $N$-partite systems. Our main result is that the thermal effect can enhance a net nonseparability of fermionic $W$ states, in sharp contrast to the general expectation that relativistic thermalization leads to a monotonic degradation of bosonic nonseparability. In addition, we find that fermionic nonseparability is generally more robust than its bosonic counterpart under causal diamond restrictions. Among different entangled resources, $GHZ$ states exhibit stronger nonseparability and greater robustness than $W$ states under identical causal conditions. We further show that the nonseparability of $W$ states decreases with increasing particle number $N$, whereas that of $GHZ$ states remains independent of $N$ in causal diamond spacetime. These results demonstrate that particle statistics, entanglement structure, and observer lifetime jointly determine the persistence of nonseparability in causally restricted spacetimes, providing insights for relativistic quantum information processing.

gr-qcCross-listedarXiv:2608.07869Aug 11, 20260 citations

Quantum superpositions of causal orders as an operational resource

Márcio M. Taddei, Ranieri V. Nery, Leandro Aolita

Causal nonseparability refers to processes where events take place in a coherent superposition of different causal orders.These may be the key resource for experimental violations of causal inequalities and have been recently identified as resources for concrete information-theoretic tasks.Here, we take a step forward by deriving a complete operational framework for causal nonseparability as a resource.Our first contribution is a formal definition for the specific notion of quantum control of causal orders, a stronger form of causal nonseparability-with the celebrated quantum switch as best-known example-where the causal orders of events for a target system are coherently controlled by a control system.We then build a resource theory-for both generic causal nonseparability as well as quantum control of causal orders-with a physically motivated class of free operations, based on process-matrix concatenations.We present the framework explicitly in the mindset with a control register.However, our machinery is totally versatile, being directly applicable also to scenarios with a target register alone.Moreover, an important subclass of our operations is free not only with respect to causal nonseparability and quantum control of causal orders but it also preserves the very causal structure of causal processes.Hence, our treatment contains, as a built-in feature, the basis of a resource theory of quantum causal networks too.As applications, first, we establish a simple sufficient condition for pure-process free convertibility.This imposes a hierarchy of quantum control of causal orders with the quantum switch at the top.Second, we prove that causal-nonseparability distillation exists.More precisely, we show how to convert multiple copies of a process with arbitrarily little causal nonseparability into fewer copies of a quantum switch.Our findings reveal conceptually new, unexpected phenomena, with both fundamental and practical implications.Causal nonseparability refers to processes where events take place in a coherent superposition of different causal orders.These may be the key resource for experimental violations of causal inequalities and have been recently identified as resources for concrete information-theoretic tasks.Here, we take a step forward by deriving a complete operational framework for causal nonseparability as a resource.Our first contribution is a formal definition for the specific notion of quantum control of causal orders, a stronger form of causal nonseparability-with the celebrated quantum switch as best-known example-where the causal orders of events for a target system are coherently controlled by a control system.We then build a resource theory-for both generic causal nonseparability as well as quantum control of causal orders-with a physically motivated class of free operations, based on process-matrix concatenations.We present the framework explicitly in the mindset with a control register.However, our machinery is totally versatile, being directly applicable also to scenarios with a target register alone.Moreover, an important subclass of our operations is free not only with respect to causal nonseparability and quantum control of causal orders but it also preserves the very causal structure of causal processes.Hence, our treatment contains, as a built-in feature, the basis of a resource theory of quantum causal networks too.As applications, first, we establish a simple sufficient condition for pure-process free convertibility.This imposes a hierarchy of quantum control of causal orders with the quantum switch at the top.Second, we prove that causal-nonseparability distillation exists.More precisely, we show how to convert multiple copies of a process with arbitrarily little causal nonseparability into fewer copies of a quantum switch.Our findings reveal conceptually new, unexpected phenomena, with both fundamental and practical implications.

arXiv:1903.06180Physical Review ResearchDec 13, 201915 citations

We investigate the nonseparability of multipartite bosonic and fermionic

GHZ

and

W

states in a causal diamond spacetime using the Abe-Rajagopal (AR)

q

-conditional entropy. The finite lifetime of the observer gives rise to a causal diamond horizon, which induces an Unruh-like thermal effect and leads to a nontrivial restructuring of nonseparability in

N

-partite systems. Our main result is that the thermal effect can enhance a net nonseparability of fermionic

W

states, in sharp contrast to the general expectation that relativistic thermalization leads to a monotonic degradation of bosonic nonseparability. In addition, we find that fermionic nonseparability is generally more robust than its bosonic counterpart under causal diamond restrictions. Among different entangled resources,

GHZ

states exhibit stronger nonseparability and greater robustness than

W

states under identical causal conditions. We further show that the nonseparability of

W

states decreases with increasing particle number

N

, whereas that of

GHZ

states remains independent of

N

in causal diamond spacetime. These results demonstrate that particle statistics, entanglement structure, and observer lifetime jointly determine the persistence of nonseparability in causally restricted spacetimes, providing insights for relativistic quantum information processing.