The joint weak value is a counterfactual quantity related to quantum correlations and quantum dynamics, which can be retrieved via weak measurements, as initiated by Aharonov and colleagues. In this paper, we provide a full analytical extension of the method described by Puentes et al. [Phys. Rev. Lett. 109, 040401 (2012)], to extract the joint weak values of single-particle operators from two-dimensional spatial displacements of Laguerre-Gauss probe states, for the case of the azimuthal index
∣l∣>1. This method has a statistical advantage over previous ones since information about the conjugate observable, i.e., the momentum displacement of the probe, is not required. Moreover, we demonstrate that, under certain conditions, the joint weak value can be extracted directly from spatial displacements without any additional data processing.
Weak measurements are a unique tool for accessing information about weakly interacting quantum systems with minimal back action. Joint weak measurements of single-particle operators with pointer states characterized by a two-dimensional Gaussian distribution can provide, in turn, key information about quantum correlations that can be relevant for quantum information applications. Here we demonstrate that by employing two-dimensional pointer states endowed with orbital angular momentum (OAM), it is possible to extract weak values of the higher order moments of single-particle operators, an inaccessible quantity with Gaussian pointer states only. We provide a specific example that illustrates the advantages of our method both in terms of signal enhancement and information retrieval.
This paper proposes a novel approach to distributed storage and retrieval, termed Quantum Entanglement-Based Distributed Storage and Retrieval (QDSL), leveraging the unique properties of quantum entanglement to achieve ultra-high density storage and near-instantaneous retrieval. The core concept involves encoding data into entangled states distributed across a network of nodes. Retrieval is then performed by measuring these entangled states, effectively extracting the desired information without the need for data transmission. This approach fundamentally differs from traditional distributed systems reliant on classical physics, offering the potential to overcome limitations imposed by Shannon's information theory. We detail the theoretical framework, focusing on entanglement distribution, data encoding, retrieval protocols, and discuss potential challenges and future research directions. The key performance metrics, including storage capacity, retrieval latency, and error correction, are analyzed. Ultimately, QDSL presents a paradigm shift in information processing, promising significant advancements in areas requiring high bandwidth, low latency, and secure data storage.