Superposition Of Paths Research Articles

An Architecture Superposing Indefinite Causal Order and Path Superposition Improving Pauli Channels’ Parameter Estimation

Quantum Parameter Estimation (QPE) is commonly led using quantum probe states for the characterization of quantum systems. For these purposes, Quantum Fisher Information (QFI) plays a crucial role by imposing a lower bound for the parametric estimation of quantum channels. Several schemes for obtaining QFI lower bounds have been proposed, particularly for Pauli channels regarding qubits. Those schemes commonly employ either the individual channel, multiple copies of it, or arrangements including communication architectures. The present work aims to propose an architecture involving path superposition and causal indefinite order in superposition. Thus, by controlling the symmetry balance of this superposition, it reaches notable improvements in quantum parameter estimation. The proposed architecture has been tested to find the best possible QPE bounds for a representative and emblematic set of Pauli channels. Further, for the most reluctant channels, it was revisited testing the architecture again under a primary path superposition (using double teleportation) and also using entangled probe states to recombine their outputs with the original undisturbed state. Notable outcomes practically near zero were found for the QPE bounds, stating a hierarchy between the approaches, but anyway reaching a perfect theoretical QPE, particularly for the last path superposition including the proposed architecture.

Unambiguous joint detection of spatially separated properties of a single photon in the two arms of an interferometer

The quantum superposition principle implies that a particle entering an interferometer evolves by simultaneously taking both arms. If a non-destructive, minimally-disturbing interaction coupling a particle property to a pointer is implemented on each arm while maintaining the path superposition, quantum theory predicts that, for a fixed state measured at the output port, certain particle properties can be associated with only one or the other path. This phenomenon is known as the quantum Cheshire cat effect. Here we report the realization of this prediction through joint observation of the spatial and polarization degrees of freedom of a single photon in the two respective arms of an interferometer. Significant pointer shifts ( ~ 50 microns), corresponding to measured weak values, are observed in each arm. This observation, involving coupling distinct properties of a quantum system in spatially separated regions, opens new possibilities for quantum information protocols and for tests of quantumness for mesoscopic systems.

Single-Gate In-Transistor Readout of Current Superposition and Collapse Utilizing Quantum Tunneling and Ferroelectric Switching.

In nanostructure assemblies, the superposition of current paths forms microscopic electric circuits, and different circuit networks produce varying results, particularly when utilized as transistor channels for computing applications. However, the intricate nature of assembly networks and the winding paths of commensurate currents hinder standard circuit modeling. Inspired by the quantum collapse of superposition states for information decoding in quantum circuits, the implementation of analogous current path collapse to facilitate the detection of microscopic circuits by modifying their network topology is explored. Here, the superposition and collapse of current paths in gate-all-around polysilicon nanosheet arrays are demonstrated to enrich the computational resources within transistors by engineering the channel length and quantity. Switching the ferroelectric polarization of Hf0.5 Zr0.5 O2 gate dielectric, which drives these transistors out-of-equilibrium, decodes the output polymorphism through circuit topological modifications. Furthermore, a protocol for the single-electron readout of ferroelectric polarization is presented with tailoring the channel coherence. The introduction of lateral path superposition results into intriguing metal-to-insulator transitions due to transient behavior of ferroelectric switching. This ability to adjust the current networks within transistors and their interaction with ferroelectric polarization in polycrystalline nanostructures lays the groundwork for generating diverse current characteristics as potential physical databases for optimization-based computing.

Parametric Symmetries in Architectures Involving Indefinite Causal Order and Path Superposition for Quantum Parameter Estimation of Pauli Channels

Parameter estimation for devices containing or supporting quantum systems is a field of quantum metrology using quantum probe states to reach their characterization. Pauli channels are ideal structures where qubits are transmitted or contained, commonly altering them with specific fingerprints. The ultimate limit imposed on such estimation is addressed using the quantum Fisher information, stating a lower bound for it. Although the most simple scheme suggests performing such an estimation directly using the individual channel, other approaches have shown improved outcomes by repeating identical copies of the channel for the characterization, or otherwise those connected inside of specific circuit arrangements. These connections commonly include path superposition or causal indefinite architectures. In addition, other improvements have been observed in concrete channels when complementary unitary controls are included. The current research analyses the complete set of Pauli channels under some of those architectures in a comparative approach to reach a better estimation, thus stating hierarchies. It is observed that the use of those unitary controls notably improves previous outcomes by several orders of magnitude.

Generation of Entanglement from Mechanical Rotation.

Many phenomena and fundamental predictions, ranging from Hawking radiation to the early evolution of the Universe rely on the interplay between quantum mechanics and gravity or more generally, quantum mechanics in curved spacetimes. However, our understanding is hindered by the lack of experiments that actually allow us to probe quantum mechanics in curved spacetime in a repeatable and accessible way. Here we propose an experimental scheme for a photon that is prepared in a path superposition state across two rotating Sagnac interferometers that have different diameters and thus represent a superposition of two different spacetimes. We predict the generation of genuine entanglement even at low rotation frequencies and show how these effects could be observed even due to the Earth's rotation. These predictions provide an accessible platform in which to study the role of the underlying spacetime in the generation of entanglement.

Proposal to observe path superpositions in a double-slit setup

The interference pattern produced by a quantum particle in Young's double-slit setup is attributed to the particle's wave function having gone through both slits. In the path integral formulation, this interference involves a superposition of paths, going through either slit, linking the source to the detection point. We show how these paths superpositions can in principle be observed by implementing a series of minimally perturbing weak measurements between the slits and the detection plane. We further propose a simplified protocol in order to observe these ``weak trajectories'' with single photons.

Quantum switch in the gravity of Earth

We introduce a protocol for a quantum switch in the gravitational field of a spherical mass and determine the time interval required for its realization in the gravity of Earth. One of the agents that perform operations with indefinite order is a quantum system in a path superposition state. Entanglement between its proper time and position is explored as a resource for the implementation of the quantum switch. The realization of the proposed protocol would probe the physical regime described by quantum mechanics on curved spacetimes, which has not yet been explored experimentally.

Indefinite causal order enables perfect quantum communication with zero capacity channels

Quantum mechanics is compatible with scenarios where the relative order between two events can be indefinite. Here we show that two independent instances of a noisy process can behave as a perfect quantum communication channel when used in a coherent superposition of two alternative orders. This phenomenon occurs even if the original process has zero capacity to transmit quantum information. In contrast, perfect quantum communication does not occur when the message is sent directly from the sender to the receiver through a superposition of alternative paths, with an independent noise process acting on each path. The possibility of perfect quantum communication through independent noisy channels highlights a fundamental difference between the superposition of orders in time and the superposition of paths in space.

Performance of two redundant quantum channels for single qubits under indefinite causal order

Indefinite causal order has introduced novel procedures to improve the quality of quantum communication. The superposition of paths on a set of consecutive quantum channels has demonstrated enhancement in communication on some of them. This work models a generic quantum channel for single qubits in terms of Kraus operators in the form of Pauli operators. The output state going through the channel can be obtained analytically to then analyse the quality by means of the quantum fidelity.

Quantum Erasure Using Entangled Surface Acoustic Phonons

Using the deterministic, on-demand generation of two entangled phonons, we demonstrate a quantum eraser protocol in a phononic interferometer where the which-path information can be heralded during the interference process. Omitting the heralding step yields a clear interference pattern in the interfering half-quanta pathways; including the heralding step suppresses this pattern. If we erase the heralded information after the interference has been measured, the interference pattern is recovered, thereby implementing a delayed-choice quantum erasure. The test is implemented using a closed surface-acoustic-wave communication channel into which one superconducting qubit can emit itinerant phonons that the same or a second qubit can later re-capture. If the first qubit releases only half of a phonon, the system follows a superposition of paths during the phonon propagation: either an itinerant phonon is in the channel, or the first qubit remains in its excited state. These two paths are made to constructively or destructively interfere by changing the relative phase of the two intermediate states, resulting in a phase-dependent modulation of the first qubit's final state, following interaction with the half-phonon. A heralding mechanism is added to this construct, entangling a heralding phonon with the signalling phonon. The first qubit emits a phonon herald conditioned on the qubit being in its excited state, with no signaling phonon, and the second qubit catches this heralding phonon, storing which-path information which can either be read out, destroying the signaling phonon's self-interference, or erased.

Measuring shape and motion of a high-speed object with designed features from motion blurred images

Vision-based geometry measurement plays a crucial role in many science and industrial areas. Plenty of researches devoted to measuring static objects, while few focused on motion blurred situations, which inevitably arise when the object being measured moves fast relative to the camera(s). Motion blur usually invalids the vision-based measurement algorithms designated for static objects. In this paper, we devote to accurate three dimensional (3D) reconstruction of moving objects from motion blurred stereo image pairs. A convolutional neural network (CNN) based method is first proposed to recognize the motion blurred visual targets. A motion blur model based on inner-frame path superposition imaging is then established. Finally, an optimization framework is set up to reconstruct the 3D target motion path during the camera exposure. Experiments are involved to demonstrate the validity and accuracy of the method.

Quantum routing of single optical photons with a superconducting flux qubit

Controlling and swapping quantum information in a quantum coherent way between the microwave and optical regimes is essential for building long-range superconducting quantum networks but extremely challenging. We propose a hybrid quantum interface between the microwave and optical domains where the propagation of a single-photon pulse along a nanowaveguide is controlled in a coherent way by tuning electromagnetically induced transparency window with the quantum state of a flux qubit. The qubit can route a single-photon pulse with a single spin in nanodiamond into a quantum superposition of paths without the aid of an optical cavity - simplifying the setup. By preparing the flux qubit in a superposition state our cavity-less scheme creates a hybrid state-path entanglement between a flying single optical photon and a static superconducting qubit, and can conduct heralded quantum state transfer via measurement.

The solution of linear mechanical systems in terms of path superposition

We prove that the solution of any linear mechanical system can be expressed as a linear combination of signal transmission paths. This is done in the framework of the Global Transfer Direct Transfer (GTDT) formulation for vibroacoustic problems. Transmission paths are expressed as powers of the transfer matrix. The key idea of the proof is to generalise the Neumann series of the transfer matrix – which is convergent only if its spectral radius is smaller than one – into a modified Neumann series that is convergent regardless of the eigenvalues of the transfer matrix. The modification consists in choosing the appropriate combination coefficients for the powers of the transfer matrix in the series. A recursive formula for the computation of these factors is derived. The theoretical results are illustrated by means of numerical examples. Finally, we show that the generalised Neumann series can be understood as an acceleration (i.e. convergence speedup) of the Jacobi iterative method.

Experimental violation of a Bell inequality with two different degrees of freedom of entangled particle pairs

We demonstrate hybrid entanglement of photon pairs via the experimental violation of a Bell inequality with two different degrees of freedom (DOF), namely, the path (linear momentum) of one photon and the polarization of the other photon. Hybrid entangled photon pairs are created by spontaneous parametric down conversion and coherent polarization to path conversion for one photon. For that photon, path superposition is analyzed, and polarization superposition for its twin photon. The correlations between these two measurements give an $S$ parameter of $S=2.653\ifmmode\pm\else\textpm\fi{}0.027$ in a Clauser-Horne-Shimony-Holt inequality and thus violate local realism for two different DOF by more than 24 standard deviations. This experimentally supports the idea that entanglement is a fundamental concept which is indifferent to the specific physical realization of Hilbert space.

The Universe as an Eigenstate: Spacetime Paths and Decoherence

This paper describes how the entire universe might be considered an eigenstate determined by classical limiting conditions within it. This description is in the context of an approach in which the path of each relativistic particle in spacetime represents a fine-grained history for that particle, and a path integral represents a coarse-grained history as a superposition of paths meeting some criteria. Since spacetime paths are parametrized by an invariant parameter, not time, histories based on such paths do not evolve in time but are rather histories of all spacetime. Measurements can then be represented by orthogonal states that correlate with specific points in such coarse-grained histories, causing them to decohere, allowing a consistent probability interpretation. This conception is applied here to the analysis of the two slit experiment, scattering and, ultimately, the universe as a whole. The decoherence of cosmological states of the universe then provides the eigenstates from which our real universe can be selected by the measurements carried out within it.