Quantum non-Gaussian states are considered a useful resource for many tasks in quantum information processing, from quantum metrology and quantum sensing to quantum communication and quantum key distribution. Another useful tool that is gaining attention is the newly constructed quantum switch. Its applications in many tasks in quantum information have been proved to outperform many existing schemes in quantum communication and quantum thermometry. In this contribution, we demonstrate this to be very useful for engineering highly non-Gaussian states from Gaussian operations whose order is controlled by degrees of freedom of a control qubit. The nonconvexity of the set of Gaussian states and the set of Gaussian operations guarantees the emergence of non-Gaussianity after post-selection on the control qubit deterministically, in contrast to existing protocols in the literature. The nonclassicality of the resulting states is discussed accordingly.
Quantum non-Gaussian states are considered a useful resource for many tasks in quantum information processing, from quantum metrology and quantum sensing to quantum communication and quantum key distribution. Another useful tool that is gaining attention is the newly constructed quantum switch. Its applications in many tasks in quantum information have been proved to outperform many existing schemes in quantum communication and quantum thermometry. In this contribution, we demonstrate this to be very useful for engineering highly non-Gaussian states from Gaussian operations whose order is controlled by degrees of freedom of a control qubit. The nonconvexity of the set of Gaussian states and the set of Gaussian operations guarantees the emergence of non-Gaussianity after post-selection on the control qubit deterministically, in contrast to existing protocols in the literature. The nonclassicality of the resulting states is discussed accordingly.
Quantum Non-Gaussian states are considered as a useful resource for many tasks in quantum information processing, from quantum metrology and quantum sensing to quantum communication and quantum key distribution. Another useful tool that is growing attention is the newly constructed quantum switch. Its applications in many tasks in quantum information have been proved to be outperforming many existing schemes in quantum communication and quantum thermometry. In this contribution, we are addressing this later to be very useful to engineer highly non-Gaussian states from Gaussian operations whose order is controlled by degrees of freedom of a control qubit. The non-convexity of the set of Gaussian states and the set of Gaussian operations guarantees the emergence of non-Gaussianity after postselection on the control qubit deterministically, in contrast to existing protocols in the literature. The non-classicality of the resulting states is discussed accordingly.
Recent results have shown that quantum theory is compatible with novel causal structures where events happen without a definite causal order. In particular, the quantum switch describes a process in which two quantum channels act in a coherent superposition of their two possible orders. Furthermore, the quantum switch can perform communication tasks that are impossible within the framework of the standard quantum Shannon theory. The present paper considers the scenario of one-shot heralded qubit communication using a higher-order quantum switch constructed from two quantum switches. Specifically, we show that two quantum switches put in a superposition of their alternative causal orders can transmit a qubit, without any error, with a probability strictly higher than that achievable with each quantum switch. We discuss three examples that demonstrate this communication advantage. Notably, a higher-order quantum switch not only can outperform useful quantum switches but also becomes useful as a resource even if the quantum switches making it up are useless.
As a cornerstone of quantum science and technology, quantum precision measurement aims to transcend the standard quantum limit (SQL) and achieve sensitivities unattainable by classical approaches by harnessing distinctive quantum resources such as entanglement, squeezing and non-Gaussianity. Within this framework, Gaussian states have historically played a central role, underpinning a series of seminal experimental advances; however, their utility in metrology is fundamentally bounded by theoretical constraints that preclude unlimited gains in measurement precision. In contrast, a growing body of recent research has revealed that non-Gaussian states–endowed with stronger quantum correlations and more pronounced non-classical characteristics — can significantly surpass Gaussian counterparts in key tasks such as phase estimation, quantum imaging and quantum sensing. Under specific conditions, these states even exhibit the potential to approach or saturate the ultimate Heisenberg limit. This review offers a comprehensive overview of the theoretical underpinnings, representative preparation methodologies, experimental progress and emerging applications of non-Gaussian states in quantum metrology. Special attention is devoted to illustrating their transformative potential for the development of next-generation quantum sensors and high-precision measurement instruments, while also addressing prevailing challenges and delineating promising future research trajectories in this rapidly advancing field.
Gaussian states are central to continuous-variable quantum systems, as they are experimentally accessible and admit a compact mathematical description. Nevertheless, many proposed quantum technologies require non-Gaussian elements. In resource-theoretic terms, non-Gaussian states are resources, while Gaussian states and operations are free. The task of broadcasting, then, asks whether the resource content of a state can be meaningfully cloned. In this Letter, we prove that broadcasting of non-Gaussian states via Gaussian operations is not possible. We first show that the relative entropy of non-Gaussianity is not superadditive, ruling it out for such no-go analyses. Our proof instead uses fixed points of Gaussian operations and relates to control theory. The theorem also implies that if two initially uncorrelated systems interact by Gaussian dynamics, and one subsystem gains non-Gaussianity, the other must lose it irreversibly. Keeping the set of free operations fixed to Gaussian operations, we also comment on the broadcasting of Wigner negativity and genuine quantum non-Gaussianity.
We study general quantum correlations of continuous variable Gaussian states and their interplay with entanglement. Specifically, we investigate the existence of a quantum protocol activating all nonclassical correlations between the subsystems of an input bipartite continuous variable system, into output entanglement between the system and a set of ancillae. For input Gaussian states, we prove that such an activation protocol cannot be accomplished with Gaussian operations, as the latter are unable to create any output entanglement from an initial separable yet nonclassical state in a worst-case scenario. We then construct a faithful non-Gaussian activation protocol, encompassing infinite-dimensional generalizations of controlled-not gates to generate entanglement between system and ancillae, in direct analogy with the finite-dimensional case. We finally calculate the negativity of quantumness, an operational measure of nonclassical correlations defined in terms of the performance of the activation protocol, for relevant classes of two-mode Gaussian states.
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.