Exploiting quantum mechanics for sensing offers unprecedented possibilities. State-of-the-art proposals for novel quantum sensors often rely on the creation of large superpositions and generally detect a field. However, what is the optimal superposition size for detecting an incident particle from a specific direction? This question is nontrivial as, in general, this incident particle will scatter off with varied momenta, imparting varied recoils to the sensor, resulting in decoherence rather than a well-defined measurable phase. By considering scattering interactions of directional particulate environments with a system in a quantum superposition, we find that there is an optimal superposition size for measuring particles via a relative phase. As a consequence of the anisotropy of the environment, we observe a feature in the limiting behavior of the real and imaginary parts of the system's density matrix, linking the optimality of the superposition size to the wavelength of the scatterer. Published by the American Physical Society 2024
Exploiting quantum mechanics for sensing offers unprecedented possibilities. State-of-the-art proposals for novel quantum sensors often rely on the creation of large superpositions and generally detect a field. However, what is the optimal superposition size for detecting an incident particle from a specific direction? This question is nontrivial as, in general, this incident particle will scatter off with varied momenta, imparting varied recoils to the sensor, resulting in decoherence rather than a well-defined measurable phase. By considering scattering interactions of directional particulate environments with a system in a quantum superposition, we find that there is an optimal superposition size for measuring particles via a relative phase. As a consequence of the anisotropy of the environment, we observe a feature in the limiting behavior of the real and imaginary parts of the system's density matrix, linking the optimality of the superposition size to the wavelength of the scatterer. Published by the American Physical Society 2024
It has been a long-standing goal to bring massive objects into a superposition of different locations in real space, not only to confirm quantum theory in new regimes, but also to explore the interface with gravity. The main challenge is usually thought to arise from forces or scattering due to environmental fields and particles that decohere the large object's wave function into a statistical mixture. We unveil a decoherence channel which cannot be eliminated by improved isolation from the environment. It originates from sound waves within the object, which are excited as part of any splitting process and carry partial information. This puts stringent constraints on future spatial superpositions of large objects. Published by the American Physical Society 2024
Quantum Mechanics has revolutionized not only our understanding of Nature but also, being the foundation of electronics and lasers, virtually all the instruments we use every day. Then again, we have not yet been able to harness the consequences of the most profoundly quantum phenomena such as state superpositions and particle entanglement. The Second Quantum Revolution has the ambition of building novel "quantum machines" able to fully exploit the properties of both microscopic and macroscopic quantum states. Quantum sensors, making use of the phenomenon of entanglement in systems promise to reach the fundamental measurement limits determined by the laws of physics and correspondingly improve the current performance of the sensors by orders of magnitude in terms of precision and accuracy, with important application implications in the scientific, industrial, and commercial fields. They can measure with unprecedented precision a wide class of physical quantities, such as magnetic, electric, and inertial fields, times, frequencies, temperatures and pressures.
Using quantum systems as sensors or probes has been shown to greatly improve the precision of parameter estimation by exploiting unique quantum features such as entanglement. A major task in quantum sensing is to design the optimal protocol, i.e., the most precise one. It has been solved for some specific instances of the problem, but in general even numerical methods are not known. Here, we focus on the single-shot Bayesian setting, where the goal is to find the optimal initial state of the probe (which can be entangled with an auxiliary system), the optimal measurement, and the optimal estimator function. We leverage the formalism of higher-order operations to develop a method based on semidefinite programming that finds a protocol that is close to the optimal one with arbitrary precision. Crucially, our method is not restricted to any specific quantum evolution, cost function, or prior distribution, and thus can be applied to any estimation problem. Moreover, it can be applied to both single-parameter or multiparameter estimation tasks. We demonstrate our method with three examples, consisting of unitary phase estimation, thermometry in a bosonic bath, and multiparameter estimation of an SU(2) transformation. Exploiting our methods, we extend several results from the literature. For example, in the thermometry case, we find the optimal protocol at any finite time and quantify the usefulness of entanglement. Published by the American Physical Society 2024
The quantum trajectory sensing problem seeks quantum sensor states which enable the trajectories of incident particles to be distinguished using a single measurement. For an n-qubit sensor state to unambiguously discriminate a set of trajectories with a single projective measurement, all post-trajectory output states must be mutually orthogonal; therefore, the 2n state coefficients must satisfy a system of constraints which is typically very large. Given that this system is generally challenging to solve directly, we introduce a group-theoretic framework which simplifies the criteria for sensor states and exponentially reduces the number of equations and variables involved when the trajectories obey certain symmetries. These simplified criteria yield general families of trajectory sensor states and provide bounds on the particle-sensor interaction strength required for perfect one-shot trajectory discrimination. Furthermore, we establish a link between trajectory sensing and quantum error correction, recognizing their common motivation to identify perturbations using projective measurements. Our sensor states in fact form novel quantum codes, and conversely, a number of familiar stabilizer codes (such as toric codes) also provide trajectory sensing capabilities. This connection enables noise-resilient trajectory sensing through the concatenation of sensor states with quantum error-correcting codes.
The quantum trajectory sensing problem seeks quantum sensor states which enable the trajectories of incident particles to be distinguished using a single measurement. For an n-qubit sensor state to unambiguously discriminate a set of trajectories with a single projective measurement, all post-trajectory output states must be mutually orthogonal; therefore, the 2n state coefficients must satisfy a system of constraints which is typically very large. Given that this system is generally challenging to solve directly, we introduce a group-theoretic framework which simplifies the criteria for sensor states and exponentially reduces the number of equations and variables involved when the trajectories obey certain symmetries. These simplified criteria yield general families of trajectory sensor states and provide bounds on the particle-sensor interaction strength required for perfect one-shot trajectory discrimination. Furthermore, we establish a link between trajectory sensing and quantum error correction, recognizing their common motivation to identify perturbations using projective measurements. Our sensor states in fact form quantum codes, and conversely, a number of familiar stabilizer codes (such as toric codes) also provide trajectory sensing capabilities. This connection enables noise-resilient trajectory sensing through the concatenation of sensor states with quantum error-correcting codes.
We consider the problem of correctly identifying a malfunctioning quantum device that forms part of a network of N such devices, which can be considered as the quantum analog of classical anomaly detection. In the case where the devices in question are sources assumed to prepare identical quantum pure states, with the faulty source producing a different anomalous pure state, we show that the optimal probability of successful identification requires a global quantum measurement. We also put forth several local measurement strategies—both adaptive and nonadaptive—that achieve the same optimal probability of success in the limit where the number of devices to be checked is large. In the case where the faulty device performs a known unitary operation, we show that the use of entangled probes provides an improvement that even allows perfect identification for values of the unitary parameter that surpass a certain threshold. Finally, if the faulty device implements a known qubit channel, we find that the optimal probability for detecting the position of rank-one and rank-two Pauli channels can be achieved by product state inputs and separable measurements for any size of network, whereas for rank-three and general amplitude damping channels, optimal identification requires entanglement with N qubit ancillas. Published by the American Physical Society 2024