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arXiv:2607.05643

Coherent Control of Channel Dilations Activate Temporal Bell Nonclassicality

H S Karthik, Akshata Shenoy H, A R Usha Devi, Marcin Pawłowski

quant-phSubmitted Jul 6, 2026• Announced Jul 8, 2026• 0 citations
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Abstract

The temporal Clauser-Horne-Shimony-Holt (CHSH) inequality witnesses the nonclassicality of temporal correlations, but its violation is generally degraded by environmental noise. Here, we show that violation of the temporal CHSH inequality can be revived through coherent control of noisy quantum evolutions. We compare two physically distinct implementations: coherent control of noisy evolutions induced by interaction of the system with independent environments, and coherent control of two physically distinct, unitarily equivalent Stinespring dilations of the same noisy channel. Although these constructions generate identical deterministic system dynamics, they induce distinctly different post-selected evolutions. With a focus on the amplitude damping channel (ADC), we show that coherent control of equivalent dilations extend the range of temporal CHSH inequality violation well beyond both the incoherently controlled, or deterministic, scenario and what is achievable with independent environments. Under setting-independent post-selection of the coherent control implementation, the resulting violation further certifies that the channel is not strongly CHSH nonlocality-breaking. Our results identify the choice of Stinespring dilation as an operationally relevant resource in coherently controlled tests of temporal quantum correlations.

Comments
12 pages, 5 figures, comments welcome

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The temporal Clauser-Horne-Shimony-Holt (CHSH) inequality witnesses the nonclassicality of temporal correlations, but its violation is generally degraded by environmental noise. Here, we show that violation of the temporal CHSH inequality can be revived through coherent control of noisy quantum evolutions. We compare two physically distinct implementations: coherent control of noisy evolutions induced by interaction of the system with independent environments, and coherent control of two physically distinct, unitarily equivalent Stinespring dilations of the same noisy channel. Although these constructions generate identical deterministic system dynamics, they induce distinctly different post-selected evolutions. With a focus on the amplitude damping channel (ADC), we show that coherent control of equivalent dilations extend the range of temporal CHSH inequality violation well beyond both the incoherently controlled, or deterministic, scenario and what is achievable with independent environments. Under setting-independent post-selection of the coherent control implementation, the resulting violation further certifies that the channel is not strongly CHSH nonlocality-breaking. Our results identify the choice of Stinespring dilation as an operationally relevant resource in coherently controlled tests of temporal quantum correlations.
Abstract We investigate the Bell nonlocality dynamics of bipartite quantum systems under three distinct types of global decoherence environments: global amplitude damping noise, globally correlated classical noise, and global phase-damping noise. By combining numerical optimization techniques over Bell inequalities—specifically the Clauser–Horne–Shimony–Holt inequality—and describing the global noise-evolution process of a two-qubit system with the Kraus operator formalism, we systematically characterize the evolution of quantum nonlocality in a two-qubit system. Our results demonstrate that, under a global amplitude damping noise environment, precise temporal modulation of the amplitude damping channel enables the composite system to retain maximal Bell-nonlocal correlations in its final state. In contrast, globally correlated classical noise fields induce exponential suppression of Bell inequality violations. Remarkably, the systems subjected to global phase-damping noise exhibit pronounced robustness to nonlocality. These findings highlight the critical role of global noise in nonlocality dynamics.
Abstract The Clauser–Horne–Shimony–Holt (CHSH) inequality test is widely used as a mean of invalidating the local deterministic theories. Most attempts to experimentally test nonlocality have presumed unphysical idealizations that do not hold in real experiments, namely, noiseless measurements. We demonstrate an experimental violation of the CHSH inequality that is free of idealization and rules out local models with high confidence. We show that the CHSH inequality can always be violated for any nonzero noise parameter of the measurement. Intriguingly, less entanglement exhibits more nonlocality in the CHSH test with noisy measurements. Furthermore, we theoretically propose and experimentally demonstrate how the CHSH test with noisy measurements can be used to detect weak entanglement on two-qubit states. Our results offer a deeper insight into the relation between entanglement and nonlocality.
Abstract It is known that the inevitable interaction of the entangled qubits with their environments may result in the degradation of quantum correlation. We study the decoherence of two remote qubits under general local single- and two-sided amplitude-damping channel (ADC). By using concurrence, quantum discord and Clauser–Horne–Shimony–Holt (CHSH) inequality, we find that the relation between the residual quantum correlations and the initial ones are different. Recently, Wang et al. [Int. J. Theor. Phys. 54 (2015) 5] showed that there exist a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence, fully entangled fraction and quantum discord, respectively. Here we find that both in single- and two-sided ADC, only the evolution of CHSH inequality with the initial parameter is proportional to that of the initial nonlocality. That means the initial state with maximally nonlocality will retain its role in the evolution. It implies that the evolution of nonlocality may reveal the characteristics of quantum state better. Furthermore, we discuss the evolutions of the three different quantum measurements with the initial parameter under generalized amplitude damping channel (GADC) and find that they are all proportional to that of the initial state.
The Leggett-Garg inequality (LGI) distinguishes nonmacrorealistic channels from macrorealistic ones by constraining the experimental outcomes of the underlying system. In this work, we propose a class of channels which, initially, cannot violate the LGI (in the form of the temporal Bell inequality) but can violate it after the application of stochastic pre- and post-operations (SPPOs). As a proof-of-principle experiment, we demonstrate the stochastic pre- and post-operations in an amplitude-damping channel with photonic qubits. We denote the above phenomenon as hidden nonmacrorealistic channels. We also discuss the relationship between these hidden nonmacrorealistic channels [in terms of the temporal Clauser-Horne-Shimony-Holt (CHSH) inequality] and the strongly nonlocality-breaking channel, which breaks the hidden spatial CHSH nonlocality for arbitrary states. In general, if the channel satisfies hidden nonmacrorealism, it is not a strongly CHSH nonlocality-breaking channel.
Incompatibility and nonlocality are not only of foundational interest but also act as important resources for quantum information theory. In the Clauser-Horne-Shimony-Holt (CHSH) scenario, the incompatibility of a pair of observables is known to be equivalent to Bell nonlocality. Here, we investigate these notions in the context of qubit channels. The Bell-CHSH inequality has a greater perspective---compared to any genuine tripartite nonlocality scenario---while determining the interplay between nonlocality breaking qubit channels and incompatibility breaking qubit channels. In the Bell-CHSH scenario, we prove that if the conjugate of a channel is incompatibility breaking, then the channel is itself nonlocality breaking and vice versa. However, this equivalence is not straightforwardly generalized to multipartite systems, due to the absence of an equivalence relation between incompatibility and nonlocality in the multipartite scenario. We investigate this relation in the tripartite scenario by considering some well-known states like Greenberger-Horne-Zeilinger and WWW states and using the notion of Mermin and Svetlichny nonlocality. By subjecting the parties in question to unital qubit channels, we identify the range of state and channel parameters for which incompatibility coexists with nonlocality. Further, we identify the set of unital qubit channels that is Mermin or Svetlichny nonlocality breaking irrespective of the input state.
Contextuality and measurement incompatibility are two fundamental aspects of nonclassicality, and their manifestations in observed quantum correlations are often deeply interconnected. Recently, measurement incompatibility has been studied in connection with nonlocality, particularly in terms of their robustness under various quantum channels. This line of investigation helps establish a connection between the channels that break nonlocality and those that break incompatibility. In this study, we focus on an asymmetric bipartite Bell scenario involving three and four inputs on Alice and Bob sides, respectively, with each of these inputs having dichotomous outcomes. Under the assumption of locality, the observed statistics in this asymmetric scenario obeys the Elegant Bell inequality (EBI). Here, we use a different version of the EBI that relies on the assumption of the preparation noncontextuality. By taking the violation of this noncontextual version of EBI as a witness of preparation contextuality we establish a connection between the channels that break contextuality and the channels that break triple-wise measurement incompatibility. Our results suggest that any channel which breaks EBI contextuality will also break Clauser-Horne-Shimony-Holt (CHSH) nonlocality; however, the reverse does not hold. We also show that a depolarising channel that breaks N-wise incompatibility can also break a certain form of contextuality, witnessed by a generalised inequality involving N measurements on one wing of a bipartite Bell scenario.