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.
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.
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.
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.
Quantum compositions of channels can grant advantages over classical compositions in quantum information processing or thermodynamical tasks. One of such quantum composition is one with indefinite causal order, where multiple quantum channels are placed in a superposition of different causal or operation orders. The advantages of indefinite causal order were demonstrated in an experimentally realizable setup known as the quantum switch and were often attributed to this new quantum resource of indefinite causality, but some doubts and disagreements still remains as compositions without indefinite causal order can achieve the same advantages. In this work, we proposed that the quantum switch's uniqueness lies in its ability to exhibit coherent non-Markovianity, where memory effects acts across different paths of superposition. We showed that the quantum switch violates completely positive or CP-divisibility and thus has intrinsic non-Markovianity in its evolution, which allows for non-Markovian backflow of information from the environment. This backflow of information can then play a role in the many advantages seen in the quantum switch, and by extending the quantum switch operation such that the non-Markovianity is controllable, we showed that these advantages depend on the presence and amount of non-Markovianity, achieving the quantum switch case when the system is fully non-Markovian. Particularly, we demonstrated this for the quantum switch's advantages in communication capacities, work extraction via daemonic ergotropy, and refrigeration via heat extraction. Other quantum compositions that are often compared to indefinite causal order, such as the superposition of independent channels and superposition of trajectories, are also captured by this extended construction of the quantum switch, and we showed that their difference with the quantum switch lies in the presence or absence of non-Markovianity. Our work suggests that non-Markovianity is an important recipe for the quantum switch or indefinite causal order, and is a nonnegligible factor for its advantages.
This thesis presents an investigation into the generation and characterisation of non-Gaussian states in continuous variable quantum optics. Beginning by placing the study of continuous variables within the context of quantum information processing more generally, we then motivate the need for non-Gaussianity within quantum computing protocols. The focus then narrows to the consideration of two particular sets of non-Gaussian states: orthogonal superposition states and the cubic resource state. The superposition of two orthogonal states has been shown to enhance certain continuous variable quantum information processing protocols that rely on entanglement, and within this section two distinct methods for generating such states are considered. While one of these methods provides a specific example, the other introduces a general orthogonaliser that relies solely on knowledge of the expectation value for the chosen orthogonalising operator in order to produce the superposition. The second case for non-Gaussian state generation employs current results demonstrating the production of a weak approximation of the cubic resource state in order to illustrate the use of such single-mode states to generate multimode states with similar features. These states are implemented as ancillas for a deterministic non-Gaussian gate operation on a system of choice. We show that generating multimode states through this distribution scheme allows an enhancement of the output state to better approximate the nonlinear features. Finally, we consider methods of characterising non-Gaussian states. In particular, we introduce a witness for pure states existing outside of the Gaussian convex hull. Such states exclude Gaussian pure states as well as non-Gaussian states generated from mixtures of squeezed and coherent states, and therefore consist of non-Gaussian states generated from non-Gaussian operations. We present a detection-independent bound for such states based on the generalised quasiprobability distribution.
Higher-order maps account for the most general transformations in quantum mechanics—they transform input quantum maps to output quantum maps. In this thesis, I focus on the application of such higher-order maps representing two important processes: (1) a particular type of non-Markovian quantum dynamics, and (2) indefinite causal order. First, I will introduce our work on the non-Markovian evolution of quantum states. Such a situation occurs when the past system-environment interaction leads the environment to memorize the information about the system. The measure of the non-Markovianity is given by the temporal correlation among the operations on the system. One way to estimate such correlation is to employ a full tomography of the process matrix, which is computationally intractable. Instead, we utilize machine learning algorithms without using tomographically complete measurement, to estimate the measure of non-Markovianity. We apply our model to a dataset obtained from an optical experiment and show that we are able to predict the measure of non-Markovianity with 90% accuracy. I then introduce various aspects of indefinite causal order. Ordinary experience points only to a definite causal structure, but quantum mechanics admits a more general causal structure that allows for the superposition of different causal orders. That means that the statements, is in the causal past of event B, and B is in the causal past of event A can both be true. The quantum switch can physically realise such an indefinite causal structure where a control quantum system controls the order of operations acting on a target quantum system. Superposition in the control leads to the superposition of the order. We experimentally realise a quantum switch with the control qubit being the polarisation of light and the target qubit being the transverse spatial mode of light. We first verify our quantum switch by measuring a `causal witness'. We then demonstrate an advantage of the quantum switch for classical communication. Finally, I present our work on classical communication through the most general quantum causal structures, represented by the process matrix. We formulate different classical capacities of a bi-partite process matrix. We also study one-way and bidirectional communication protocols through such a process and establish the relevant communication bounds. These enable further analyses of higher-order maps that take advantage of the full suite of processes that quantum mechanics allows.
Indefinite causal order extends quantum information processing beyond fixed causal structures, with the quantum SWITCH serving as its canonical realization. By coherently superposing different orders of quantum channels, the quantum SWITCH has been shown to provide operational advantages in communication, computation, metrology, and related tasks. Despite these advances, the physical resources responsible for these advantages remains unclear. Recent studies have further revealed that the quantum SWITCH can generate memory effects, manifested as non-Markovian information backflow. In this work, we examine the origin of such memory and determine whether they reflect genuine (quantum) non-Markovianity or instead arises from classical origin. To this end, we analyze two representative scenarios: one based on discrete-time evolution and another formulated through dynamical maps in open quantum systems. We show that the memory effects generated by the quantum SWITCH are not genuinely quantum non-Markovian, thereby prompting a re-examination of the source of quantum advantage in indefinite causal order frameworks.