Quantum Correlations in Nonlocal BosonSampling

Determination of the quantum nature of correlations between two spatially separated systems plays a crucial role in quantum information science. Of particular interest is the questions of if and how these correlations enable quantum information protocols to be more powerful. Here, we report on a distributed quantum computation protocol in which the input and output quantum states are considered to be classically correlated in quantum informatics. Nevertheless, we show that the correlations between the outcomes of the measurements on the output state cannot be efficiently simulated using classical algorithms. Crucially, at the same time, local measurement outcomes can be efficiently simulated on classical computers. We show that the only known classicality criterion violated by the input and output states in our protocol is the one used in quantum optics, namely, phase-space nonclassicality. As a result, we argue that the global phase-space nonclassicality inherent within the output state of our protocol represents true quantum correlations.Comment: 5 pages, 1 figure, comments are very welcome

Quantum Correlations and Global Coherence in Distributed Quantum Computing

Deviations from classical physics when distant quantum systems become correlated are interesting both fundamentally and operationally. There exist situations where the correlations enable collaborative tasks that are impossible within the classical formalism. Here, we consider the efficiency of quantum computation protocols compared to classical ones as a benchmark for separating quantum and classical resources and argue that the computational advantage of collaborative quantum protocols in the discrete variable domain implies the nonclassicality of correlations. By analysing a toy model, it turns out that this argument implies the existence of quantum correlations distinct from entanglement and discord. We characterize such quantum correlations in terms of the net global coherence resources inherent within quantum states and show that entanglement and discord can be understood as special cases of our general framework. Finally, we provide an operational interpretation of such correlations as those allowing two distant parties to increase their respective local quantum computational resources only using locally incoherent operations and classical communication.Comment: Minor modifications and correction

What can quantum optics say about computational complexity theory?

Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory point of view. We derive a general formula for calculating the output probabilities, and by considering input thermal states, we show that the output probabilities are proportional to permanents of positive-semidefinite Hermitian matrices. It is believed that approximating permanents of complex matrices in general is a #P-hard problem. However, we show that these permanents can be approximated with an algorithm in BPP^NP complexity class, as there exists an efficient classical algorithm for sampling from the output probability distribution. We further consider input squeezed-vacuum states and discuss the complexity of sampling from the probability distribution at the output.Comment: 5 pages, 1 figur

Why are those computers sitting over there gathering dust

The purpose of this project was to create electronic books (E-books) for kindergartens to read during their center time. The E-books are intended for kindergarten teachers to use to help their students learn to read while utilizing the technology resources in their classroom. These E-books are teacher created so the cost is minimal and they can be copied and distributed to each student without worrying about copyright laws. Teachers can customize them to fit the current thematic unit they are teaching and once created, they can be used repeadedly without being damaged like paper books

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Recreational Rights and Titles to Beds on Western Lakes and Streams

What rights do riparians, their licensees, and the public have to use the small lakes and streams of the West when the beds are privately owned? This is the question which this Article attempts to answer. However, to do this, an analysis had to be made of which lake and stream beds were privately owned. Thus, the Article covers both the questions of title to beds and rights of surface use. This Article represents the first time that an effort has been made to systematically and comprehensively survey the lake and stream surface use cases of the Western part of the Nation, or of any large section of the Nation, and to critically compare and evaluate these cases

Recreational Rights and Titles to Bed on Western Lakes and Streams

What rights do riparians, their licensees, and the public have to use the small lakes and streams of the West when the beds are privately owned? This is the question which this Article attempts to answer. However, to do this, an analysis had to be made of which lake and stream beds were privately owned. Thus, the Article covers both the questions of title to beds and rights of surface use. This Article represents the first time that an effort has been made to systematically and comprehensively survey the lake and stream surface use cases of the Western part of the Nation, or of any large section of the Nation, and to critically compare and evaluate these cases

Measurement-based Lorentz-covariant Bohmian trajectories of interacting photons

In a recent article [Foo et. al., Nature Comms. 13, 2 (2022)], we devised a method of constructing the Lorentz-covariant Bohmian trajectories of single photons via weak measurements of the photon's momentum and energy. However, whether such a framework can consistently describe multiparticle interactions remains to be seen. Here, we present a nontrivial generalisation of our framework to describe the relativistic Bohmian trajectories of two interacting photons exhibiting nonclassical interference due to their indistiguishability. We begin by deriving the average velocity fields of the indistinguishable photons using a conditional weak measurement protocol, with detectors that are agnostic to the identity of the respective photons. We demonstrate a direct correspondence between the operationally-derived trajectories with those obtained using a position- and time-symmetrised multiparticle Klein-Gordon wavefunction, whose dynamics are manifestly Lorentz-covariant. We propose a spacetime metric that depends nonlocally on the positions of both particles as a curvature based interpretation of the resulting trajectories. Contrary to prior expectations, our results demonstrate a consistent trajectory-based interpretation of relativistic multiparticle interactions in quantum theory.Comment: 10+10 pages, 7 figure

Maximum entanglement of formation for a two-mode Gaussian state over passive operations

We quantify the maximum amount of entanglement of formation (EoF) that can be achieved by continuous-variable states under passive operations, which we refer to as EoF-potential. Focusing, in particular, on two-mode Gaussian states we derive analytical expressions for the EoF-potential for specific classes of states. For more general states, we demonstrate that this quantity can be upper-bounded by the minimum amount of squeezing needed to synthesize the Gaussian modes, a quantity called squeezing of formation. Our work, thus, provides a new link between non-classicality of quantum states and the non-classicality of correlations.Comment: Revised versio