In this paper, we present a formulation based on the Green's function to study the backaction cooling of a levitated nanosphere in an arbitrary structure. This formulation has enabled us to study the dynamical backaction effect and the possibility of cooling in the absence of a cavity or when the nanosphere is trapped outside a cavity and excites a continuum of electromagnetic modes. We also investigate the roles of the Stokes and anti-Stokes processes, separately, and show that the anti-Stokes process is not necessarily the sole cooling agent. This is in sheer contrast with the intracavity cooling scenario.

We derive a Lindblad master equation that approximates the dynamics of a Lipkin-Meshkov-Glick (LMG) model weakly coupled to a bosonic bath. By studying the time evolution of operators under the adjoint master equation we prove that, for large system sizes, these operators attain their thermal equilibrium expectation values in the long-time limit, and we calculate the rate at which these values are approached. Integrability of the LMG model prevents thermalization in the absence of a bath, and our work provides an explicit proof that the bath indeed restores thermalization. Imposing thermalization on this otherwise nonthermalizing model outlines an avenue towards probing the unconventional thermodynamic properties predicted to occur in ultracold-atom-based realizations of the LMG model.

In this paper we provide a set of uncertainty principles for unitary operators using a sequence of inequalities with the help of the geometric-arithmetic mean inequality. As these inequalities are “fine-grained” compared with the well-known Cauchy-Schwarz inequality, our framework naturally improves the results based on the latter. As such, the unitary uncertainty relations based on our method outperform the best known bound introduced in Phys. Rev. Lett. 120, 230402 (2018). to some extent. Explicit examples of unitary uncertainty relations are provided to back our claims.

We present a logical type of proof of contextuality for a two-qubit state. We formulate a paradox that cannot be used by a two-qubit system with local measurements to test contextuality while it is possible by using entanglement measurements. With our scheme we achieve $p_{\mathrm{Hardy}}\approx 0.167$. Our approach uses graph theory and the exclusivity principle to give an interpretation of a logical type of proof of quantum correlations. We review the Hardy paradox and find a connection to the Klyachko-Can-Binicioğlu-Shumovsky inequality. We apply the same method to build a paradox based on the Clauser-Horne-Shimony-Holt inequality.

Entanglement distillation is a key primitive for distributing high-quality entanglement between remote locations. Probabilistic noiseless linear amplification based on the quantum scissors is a candidate for entanglement distillation from noisy continuous-variable (CV) entangled states. Being a non-Gaussian operation, the quantum scissors is challenging to analyze. We present a derivation of the non-Gaussian state heralded by multiple quantum scissors in a pure loss channel with two-mode squeezed vacuum input. We choose the reverse coherent information (RCI), a proven lower bound on the distillable entanglement of a quantum state under one-way local operations and classical communication (LOCC), as our figure of merit. We evaluate a Gaussian lower bound on the RCI of the heralded state. We show that it can exceed the unlimited two-way LOCC-assisted direct transmission entanglement distillation capacity of the pure loss channel. The optimal heralded Gaussian RCI with two quantum scissors is found to be significantly more than that with a single quantum scissors, albeit at the cost of decreased success probability. Our results fortify the possibility of a quantum repeater scheme for CV quantum states using the quantum scissors.

We evaluate the reflectivity of neutron mirrors composed of certain heavy nuclei which possess strong neutron-nucleus resonances in the eV energy range. We consider possible corrections to the usual formulas of neutron optics for this case and find that dispersion and multiple scattering effects are negligible but one must take Doppler broadening into account. Effects from surface roughness and phonon scattering are small compared to the Doppler corrections and are either the same as or smaller than those for mirror reflection with meV neutrons. We show that the reflectivity of such a mirror for some nuclei can in principle be high enough near energies corresponding to compound neutron-nucleus resonances to be of interest for certain scientific applications in nondestructive evaluation of subsurface material composition.

Light propagation through a normal medium is determined not only by the real part of the refractive index but also by its imaginary part, which represents optical gain and loss. Therefore, two media with different gain and loss landscapes can have very different transmission and reflection spectra, even when their real parts of the refractive index are identical. Here we show that while this observation is true for an arbitrary one-dimensional medium with refractive index $n\left(x\right)$ and its time-reversed partner with refractive index $n^{*}\left(x\right)$, there exists a universal scaling that gives identical transmittance and reflectance in these corresponding systems. Interestingly, the scaled transmittance and reflectance reduce to their standard, unscaled forms in a time-reversal-invariant system, i.e., one without gain or loss.

We propose an atom-assisted cavity optomechanical system consisting of a single $\mathrm{\Lambda }$-type three-level atom, a mechanical resonator, and a sideband-driven cavity. The analytic expression of the system's evolution is constructed under the consideration of sideband-driven fields, then steady-state solution of electromagnetically and optomechanically induced transparency and amplification is presented. In the resolved red sideband case, we demonstrate the appearance of electromagnetically and optomechanically induced transparency when the two sets of two-photon resonances are satisfied. Moreover, we set up the eigenstate structure for this atom-assisted cavity optomechanical system, which gives an explicit explanation for the mechanism of the transparency. In the resolved blue sideband case, we can achieve the controllable amplification of the probe light, which is induced by the constructive interactions of photon, atom, and phonon. The proposed scheme offers insight for the tripartite coherent interaction among photons, atoms, and phonons, which will provide great flexibility for phonon storage and motivate the development of quantum information processing.

The wave or particle duality has long been considered a fundamental signature of the nonclassical behavior of quantum phenomena, especially in a delayed choice experiment, where the experimental setup revealing either the particle or the wave nature of the system is decided after the system has entered the apparatus. However, as counterintuitive as it might seem, usual delayed choice experiments do have a simple causal explanation. Here, we take a different route and under a natural assumption about the dimensionality of the system under examination, we present an experimental proof of the nonclassicality of a delayed choice experiment based on the violation of a dimension witness inequality. Our conclusion is reached in a device-independent and detection loophole-free manner, that is, based solely on the observed data and without the need of special assumptions about the measurement apparatus.

The common wisdom in the field of quantum information theory is that when a system is initially correlated with its environment, the map describing its evolution may fail to be completely positive. If true, this would have practical and foundational significance. We here demonstrate, however, that the common wisdom is mistaken. We trace the error to the standard proposal for how the evolution map ought to be defined. We summarize this standard proposal and then show that it sometimes fails to define a linear map or any map at all. Further, we show that these pathologies persist even in completely classical examples. Drawing inspiration from the framework of classical causal models, we argue that the correct definition of the evolution map is obtained by considering a counterfactual scenario wherein the system is reprepared independently of any systems in its causal past while the rest of the circuit remains the same, yielding a map that is always completely positive. In a postmortem of the standard proposal, we highlight two distinct mistakes that retrospectively become evident (in its application to completely classical examples): (i) The types of constraints to which it appealed are constraints on what one can infer about the final state of a system based on its initial state; however, such inferences reflect not just the cause-effect relation between them—which is the basis for defining the correct evolution map—but also the common-cause relation. (ii) In a (retrospectively unnecessary) attempt to introduce variability in the input state, it inadvertently introduced variability in the inference map itself, and then tried to fit the input-output pairs associated to these different maps with a single map.

We introduce both a theoretical and an experimental scheme for simulating a quantum thermal engine through an all-optical approach, with the behavior of the working substance and the thermal reservoirs implemented via internal degrees of freedom of a single photon. By using the polarization and propagation path, we encode two quantum bits and then implement the thermodynamical steps of an Otto cycle. To illustrate the feasibility of our proposal, we experimentally realize such simulation through an intense laser beam, evaluating heat and work at each individual step of the thermodynamical cycle. In addition, from the analysis of the entropy production during the entire cycle, we can study the amount of quantum friction produced in the Otto cycle as a function of the difference of temperature between hot and cold reservoirs. Our paper constitutes, therefore, an all-optical-based thermal machine simulation and opens perspectives for other optical simulations in quantum thermodynamics.

A Bell inequality is a constraint on a set of correlations whose violation can be used to certify nonlocality. They are instrumental for device-independent tasks such as key distribution or randomness expansion. In this work, we consider bipartite Bell inequalities where two parties have $m_A$ and $m_B$ possible inputs and give $n_A$ and $n_B$ possible outputs, referring to this as the $(m_A,m_B,n_A,n_B)$ scenario. By exploiting knowledge of the set of extremal no-signaling distributions, we find all 175 Bell inequality classes in the (4,4,2,2) scenario as well as provide a partial list of 18 277 classes in the (4,5,2,2) scenario. We also use a probabilistic algorithm to obtain 5 classes of inequality in the (2,3,3,2) scenario, which we confirmed to be complete, 25 classes in the (3,3,2,3) scenario, and a partial list of 21 170 classes in the (3,3,3,3) scenario. Our inequalities are given as Supplemental Material. Finally, we discuss the application of these inequalities to the detection loophole problem and provide lower bounds on the detection efficiency threshold for small numbers of inputs and outputs.

The theory of quantum information constitutes the functional value of the quantum entanglement, i.e., quantum entanglement is essential for high fidelity of quantum protocols, while fundamental physical processes behind the formation of quantum entanglement are less relevant for practical purposes. In the present work, we explore physical mechanisms leading to the emergence of quantum entanglement in the initially disentangled system. In particular, we analyze spin entanglement of outgoing electrons in a nonrelativistic quantum $(e,2e)$ collision on a target with one active electron. Our description exploits the time-dependent scattering formalism for typical conditions of scattering experiments, and contrary to the customary stationary formalism operates with realistic scattering states. We quantify the spin entanglement in the final scattering channel through the pair concurrence and express it in terms of the experimentally measurable spin-resolved $(e,2e)$ triple differential cross sections. Besides, we consider Bell's inequality and inspect the regimes of its violation in the final channel. We address both the pure and the mixed initial spin state cases and uncover kinematical conditions of the maximal entanglement of the outgoing electron pair. The numerical results for the pair concurrence, entanglement of formation, and violation of Bell's inequality obtained for the $(e,2e)$ ionization process of atomic hydrogen show that the entangled electron pairs indeed can be formed in the $(e,2e)$ collisions even with spin-unpolarized projectile and target electrons in the initial channel. The positive entanglement balance—the difference between entanglements of the initial and final electron pairs—can be measured in the experiment.

In this article we study the role that quantum resources play in quantum-error-correction-assisted quantum metrology (QECQM) schemes. We show that there exist classes of such problems where entanglement is not necessary to retrieve noise-free evolution and Heisenberg scaling in the long time limit. Over short timescales, noise-free evolution is also possible even without any form of quantum correlations. In particular, for qubit probes, we show that whenever noise-free quantum metrology is possible via QECQM, entanglement-free schemes over long timescales and correlation-free schemes over short timescales are always possible.

Modern applications of quantum control in quantum information science and technology require the precise characterization of quantum states and quantum channels. In particular, high-performance quantum state engineering often demands that quantum states are transferred with optimal efficiency via realizable controlled evolution, the latter often modeled by quantum channels. When an appropriate quantum control model for an interested system is constructed, the exploration of optimal bounds on state transfer for the underlying quantum channel is then an important task. In this work, we analyze the state transfer efficiency problem for different classes of quantum channels, including unitary, mixed unitary, and Markovian. We then apply the theory to nuclear magnetic resonance (NMR) experiments. We show that two most commonly used control techniques in NMR, namely gradient field control and phase cycling, can be described by mixed unitary channels. Then we show that employing mixed unitary channels does not extend the unitarily accessible region of states. Also, we present a strategy of optimal experiment design, which incorporates coherent radio-frequency field control, gradient field control, and phase cycling, aiming at maximizing state transfer efficiency and meanwhile minimizing the number of experiments required. Finally, we perform pseudopure state preparation experiments on two- and three-spin systems, in order to test the bound theory and to demonstrate the usefulness of nonunitary control means.

Quantum steering is an important nonclassical resource for quantum information processing. However, even though lots of steering criteria exist, it is still very difficult to efficiently determine whether an arbitrary two-qubit state shared by Alice and Bob is steerable or not, because the optimal measurement directions of Alice are unknown. In this work, we provide an efficient quantum steering detection scheme for an arbitrary two-qubit state with the help of machine learning, where Alice and Bob only need to measure in a few fixed measurement directions. In order to prove the validity of this method, we first realize a high-performance quantum steering classifier with the whole information. Furthermore, a high-performance quantum steering classifier with partial information is realized, where Alice and Bob only need to measure in three fixed measurement directions. Our method outperforms the existing methods in generic cases in terms of both speed and accuracy, opening up the avenues to explore quantum steering via the machine learning approach.

Quantum electrodynamic fluctuations cause an attractive force between metallic surfaces. At separations where the finite speed of light affects the interaction, it is called the Casimir force. Thermal motion determines the fundamental sensitivity limits of its measurement at room temperature, but several other systematic errors contribute uncertainty as well and become more significant in air relative to vacuum. Here, we discuss the viability of the force modulation measurement technique in air (compared to frequency modulation, which is typically used in vacuum, and quasistatic deflection, which is usually used in fluid), characterize its sensitivity and accuracy by identifying several dominant sources of uncertainty, and compare the results to the fundamental sensitivity limits dictated by thermal motion and to the uncertainty inherent to calculations of the Casimir force. Finally, we explore prospects for mitigating the sources of uncertainty to enhance the range and accuracy of Casimir force measurements.

We present a quantum optimal control theory study combined with theoretical analysis to determine a pulsed laser field, capable of generating a maximally entangled state in two trapped two-level atoms. By expanding the time-dependent unitary operator to the first leading term of Magnus expansion, we reexamine the pulse area theorem for the trapped atoms driven by an arbitrarily temporary field. Due to the dipole-dipole interaction blockade, we find that the two trapped atoms described by a three-level ladder system can be reduced into an equivalent two-level model by using narrow-bandwidth pulses, leading to an analytical solution for generating the maximally entangled state. We also solve a highly constrained optimization problem to search for optimal laser pulses with broad bandwidths. A zero pulse-area constraint is employed to remove the dc offset of the optimized laser pulses, and a fixed fluence limitation combined with a constant pulse-area constraint at the resonant frequency of the equivalent two-level system are utilized to restrict the unitary evolution of quantum systems by the first leading term of Magnus expansion. This work provides a potentially useful approach to find all-optical control schemes for generating the maximally entangled state by using ultrafast laser pulses while satisfying multiple strict limitations.

Composite pulses—sequences of pulses with well-defined relative phases—are an efficient, robust, and flexible technique for coherent control of quantum systems. Composite sequences can compensate for a variety of experimental errors in the driving field (e.g., in the pulse amplitude, duration, detuning, chirp, etc.) or in the quantum system and its environment (e.g., inhomogeneous broadening, stray electric or magnetic fields, unwanted couplings, etc.). The control parameters are the relative phases between the constituent pulses in the composite sequence, an accurate control over which is required in all composite sequences reported hitherto. In this paper, we introduce two types of composite pulse sequences which, in addition to error compensation in the basic experimental parameters, compensate for systematic errors in the composite phases. In the first type of such composite sequences, which compensate for pulse area errors, relative phase errors of over 10% can be tolerated with reasonably short sequences while maintaining the fidelity above the 99.99% quantum computing benchmark. In the second type of composite sequences, which compensate for simultaneous pulse area and detuning errors, relative phase errors of over 5% can be compensated.

An exciton-polariton condensate loaded in a single active miniband in a one-dimensional microcavity wire with a complex-valued periodic potential changes its state with an increase of the polariton-polariton repulsion. This effect depends on the type of the single-particle dispersion of the miniband, which can be fine tuned by the real and imaginary components of the potential. As a result, the condensate can be formed in a zero state, $\pi$ state, or mixed state of spatiotemporal intermittency, depending on the shape of the miniband, strength of interparticle interaction, and distribution of gain in the system. The change of the condensate wave function with increasing interaction takes place by proliferation of dark solitons, which are the building blocks of the new condensate phase. We show that, in general, the interacting polaritons are not condensed in the state with minimal losses, nor do they accumulate in the state with a well-defined wave vector.