Many-particle entanglement is a fundamental concept of quantum physics that still presents conceptual challenges. While spin-squeezed and other nonclassical states atomic ensembles were used to enhance measurement precision in metrology, the notion these systems remained controversial because correlations between indistinguishable atoms witnessed by collective measurements only. Here we use highresolution imaging directly measure spin spatially separated parts Bose-Einstein condensate. We...

Characterizing many-body systems through the quantum correlations between their constituent particles is a major goal of physics. Although entanglement routinely observed in many systems, we report here detection stronger - Bell spins about 480 atoms Bose-Einstein condensate. We derive correlation witness from many-particle inequality involving only one- and two-body functions. Our measurement on spin-squeezed state exceeds threshold for by 3.8 standard deviations. work shows that strongest...

The superposition principle is one of the most fundamental principles quantum mechanics. According to Schr\"odinger equation, a physical system can be in any linear combination its possible states. While validity this routinely validated for microscopic systems, it still unclear why we do not observe macroscopic objects superpositions states that distinguished by some classical property. Here demonstrate preparation mechanical resonator with an effective mass 16.2 micrograms cat motion,...

Recently, solid-state mechanical resonators have become a platform for demonstrating nonclassical behavior of systems involving truly macroscopic number particles. Here, we perform the most quantum test in resonator to date, which probes validity mechanics by ruling out classical description at microgram mass scale. This is done direct measurement Wigner function high-overtone bulk acoustic wave mode, monitoring gradual decay negativities over tens microseconds. While obtained macroscopicity...

The Einstein-Podolsky-Rosen (EPR) paradox plays a fundamental role in our understanding of quantum mechanics, and is associated with the possibility predicting results non-commuting measurements precision that seems to violate uncertainty principle. This apparent contradiction complementarity made possible by nonclassical correlations stronger than entanglement, called steering. Quantum information recognises steering as an essential resource for number tasks but, contrary its metrology has...

Abstract Mechanical degrees of freedom are natural candidates for continuous-variable quantum information processing and bosonic simulations. However, these applications require the engineering squeezing nonlinearities in regime. Here we demonstrate below zero-point fluctuations a gigahertz-frequency mechanical resonator coupled to superconducting qubit. This is achieved by parametrically driving qubit, which results an effective two-phonon drive. In addition, show that mode inherits...

The existence of fundamentally identical particles represents a foundational distinction between classical and quantum mechanics. Because their exchange symmetry, can appear to be entangled—another uniquely phenomenon with far-reaching practical implications. However, long-standing debate has questioned whether particle entanglement is physical or merely mathematical artifact. In this work, we provide such consistent theoretical description as resource in processes frequently encountered...

Abstract In recent years, important progress has been made towards encoding and processing quantum information in the large Hilbert space of bosonic modes. Mechanical resonators have several practical advantages for this purpose, because they confine many high-quality-factor modes into a small volume can be easily integrated with different systems. However, it is challenging to create direct interactions between mechanical that used emulate gates. Here we demonstrate an situ tunable...

Although strong nonlinear interactions between quantized excitations are an important resource for quantum technologies based on bosonic oscillator modes, most electromagnetic and mechanical nonlinearities far too weak to allow effects be observed at the single-quantum level. This limitation has been overcome in resonators by coupling them other strongly systems such as atoms superconducting qubits. We demonstrate realization of single-phonon regime a solid-state system. The anharmonicity...

High-dimensional entanglement has been identified as an important resource in quantum information processing, and also a main obstacle for simulating systems. Its certification is often difficult, most widely used methods experiments are based on fidelity measurements with respect to highly entangled states. Here, instead, we consider covariances of collective observables, the well-known Covariance Matrix Criterion (CMC) \cite{guhnecova} present generalization CMC determining Schmidt number...

Abstract Fast control of quantum systems is essential to make use properties before they degrade by decoherence. This important for quantum-enhanced information processing, as well pushing towards the boundary between and classical physics. ‘Bang–bang’ attains ultimate speed limit making large changes fields much faster than system can respond, but often challenging implement experimentally. Here we demonstrate bang–bang a trapped-ion oscillator using nanosecond switching trapping...

We investigate and model the behaviour of split spin-squeezed Bose-Einstein condensates (BECs) system. In such a system, spin-polarized BEC is first squeezed using $ (S^z)^2 interaction, then are into two separate clouds. After split, we consider that particle number in each cloud collapses to fixed number. show this procedure equivalent applying an interaction corresponding squeezing individually plus entangling operation. analyse system's entanglement properties it can be detected...

We compare different formulations of the generalized uncertainty principle that have an underlying algebraic structure. show formulation by Kempf, Mangano, and Mann [Phys. Rev. D 52 (1995)], quite popular for phenomenological studies, satisfies Jacobi identities only spin zero particles. In contrast, proposed earlier one us (Maggiore) Lett. B 319 (1993)] has structure valid particles all spins in this sense seems more fundamental. The latter is also much constrained, resulting two possible...

We identify the multiparameter sensitivity of split nonclassical spin states, such as spin-squeezed and Dicke states spatially distributed into several addressable modes. Analytical expressions for spin-squeezing matrix a family that are accessible by current atomic experiments reveal quantum gain in metrology, well optimal strategies to maximize sensitivity. further study mode entanglement these deriving witness genuine $k$-partite from matrix. Our results highlight advantage sensing,...

Entanglement is known to be an essential resource for a number of tasks, including quantum-enhanced metrology, and can thus quantified by figures merit related those tasks. In quantum metrology this emphasized the connections between Fisher information (QFI), providing ultimate bounds precision, multipartite entanglement quantifiers such as depth entanglement. systems composed many qudits, it also important characterize dimensionality across bipartitions, i.e., loosely speaking, minimal...

In this work, we exploit the methods of an operational formality and extension quasi-monomials to describe realize 2-variable $q$-Legendre polynomials. We introduce generating function polynomials with a context $0^{\text{th}}$ order $q$-Bessel Tricomi functions obtain their properties such as series definition $q$-differential equations. Also, establish $q$-multiplicative $q$-derivative operators these The representations are obtained.

We address the question of assessing number particles sharing genuinely nonlocal correlations in a multipartite system. While interest nonlocality has grown recent years, its existence large quantum systems is difficult to confirm experimentally. This mostly due inadequacy standard Bell inequalities many-body systems: Such usually rely on expectation values involving many parties, all, and require individual addressing each party. In addition, known for genuine are composed that scales...

Entanglement measures quantify nonclassical correlations present in a quantum system, but can be extremely difficult to calculate, even more so, when information on its state is limited. Here, we consider broad families of entanglement criteria that are based variances arbitrary operators and analytically derive the lower bounds these provide for two relevant measures: best separable approximation generalized robustness. This yields practical method quantifying realistic experimental...

A protocol for remote state preparation is proposed spin ensembles, where the aim to prepare a with given set of expectation values on ensemble using entanglement, local rotations, and measurements in Fock basis. The ensembles could be realized by thermal atomic or spinor Bose-Einstein condensates. works beyond Holstein-Primakoff approximation, such that full Bloch sphere can prepared. main practical obstacle maximally entangled between ensembles. To overcome this, we examine states based...

The holographic entropy cone (HEC) characterizes the entanglement structure of quantum states which admit geometric bulk duals in holography. Due to its intrinsic complexity, date it has only been possible completely characterize HEC for at most $n=5$ numbers parties. For larger $n$, our knowledge falls short incomplete: almost nothing is known about extremal elements. Here, we introduce a symmetrization procedure that projects onto natural lower dimensional subspace. Upon symmetrization,...

We propose a technique to control the macroscopic collective nuclear spin of Helium-3 vapor in quantum regime using light. The scheme relies on metastability exchange collisions mediate interactions between optically accessible metastable states and ground-state spin, giving rise an effective spin-light nondemolition interaction Faraday form. Our enables measurement-based spins, such as preparation spin-squeezed states. This, combined with day-long coherence time Helium-3, opens possibility...

We present an experimentally practical method to reveal Einstein-Podolsky-Rosen (EPR) steering in non-Gaussian spin states by exploiting a connection quantum metrology. Our criterion is based on the Fisher information, and uses bounds derived from generalized spin-squeezing parameters that involve measurements of higher-order moments. This leads us introduce concept conditional parameters, which quantify metrological advantage provided states, as well detect presence EPR paradox.