Maximal Randomness Generation from Steering Inequality Violations Using Qudits

Observation of Diverse Asymmetric Structures in High-Dimensional Einstein-Podolsky-Rosen Steering

Einstein-Podolsky-Rosen (EPR) steering, a distinctive quantum correlation, reveals a unique and inherent asymmetry. This research delves into the multifaceted asymmetry of EPR steering within high-dimensional quantum systems, exploring both theoretical frameworks and experimental validations. We introduce the concept of genuine high-dimensional one-way steering, wherein a high Schmidt number of bipartite quantum states is demonstrable in one steering direction but not reciprocally. Additionally, we explore two criteria to certify the lower and upper bounds of the Schmidt number within a one-sided device-independent context. These criteria serve as tools for identifying potential asymmetric dimensionality of EPR steering in both directions. By preparing two-qutrit mixed states with high fidelity, we experimentally observe asymmetric structures of EPR steering in the C^{3}⊗C^{3} Hilbert space. Our Letter offers new perspectives to understand the asymmetric EPR steering beyond qubits and has potential applications in asymmetric high-dimensional quantum information tasks.

Activation of Einstein-Podolsky-Rosen steering sharing with unsharp nonlocal measurements

Einstein-Podolsky-Rosen (EPR) steering is commonly shared among multiple observers by utilizing unsharp measurements. Nevertheless, their usage is restricted to local measurements and does not encompass all nonlocal measurement-based cases. In this work, a method for finding beneficial local measurement settings has been expanded to include nonlocal measurement cases. This method is applicable for any bipartite state and offers benefits even in scenarios with a high number of measurement settings. Using the Greenberger-Horne-Zeilinger state as an illustration, we show that employing unsharp nonlocal measurements can activate the phenomenon of steering sharing in contrast to using local measurements. Furthermore, our findings demonstrate that nonlocal measurements with unequal strength possess a greater activation capability compared to those with equal strength. Our activation method generates fresh concepts for conservation and recycling quantum resources.

Randomness Certification from Multipartite Quantum Steering for Arbitrary Dimensional Systems

Entanglement in bipartite systems has been applied to generate secure random numbers, which are playing an important role in cryptography or scientific numerical simulations. Here, we propose to use multipartite entanglement distributed between trusted and untrusted parties for generating randomness of arbitrary dimensional systems. We show that the distributed structure of several parties leads to additional protection against possible attacks by an eavesdropper, resulting in more secure randomness generated than in the corresponding bipartite scenario. Especially, randomness can be certified in the group of untrusted parties, even when there is no randomness in either of them individually. We prove that the necessary and sufficient resource for quantum randomness in this scenario is multipartite quantum steering when each untrusted party has a choice between only two measurements. However, the sufficiency no longer holds with more measurement settings. Finally, we apply our analysis to some experimentally realized states and show that more randomness can be extracted compared with the existing analysis.

Detecting the steerability through an optimized steering criterion in two-photon systems

The steerability of a quantum state can be detected by steering inequalities. The linear steering inequalities show that more steerable states can be discovered with the increase of measurements. In order to detect more steerable states in two-photon systems, we first theoretically derive an optimized steering criterion based on infinity measurements for an arbitrary two-qubit state. The steering criterion is only determined by the spin correlation matrix of the state, and do not require infinity measurements. Then, we prepared the Werner-like states in two-photon systems, and measure their spin correlation matrices. Finally, we apply three steering criteria, which include our steering criterion, the three-measurement steering criterion and the geometric Bell-like inequality, to distinguish the steerability of these states. The results show that our steering criterion can detect the most steerable states under the same experimental conditions. Thus, our work provides a valuable reference for detecting the steerability of quantum states.

Two‐Qubit Steerability, Nonlocality, and Average Steered Coherence under Classical Dephasing Channels

When two qubits are prepared in a mixture of two Bell states and exposed to local transmission channels, the dynamics of steerability, Bell nonlocality, and average steered coherence are investigated. Disorders are assumed to influence the channels, resulting in either Markovian Ornstein–Uhlenbeck noise or non‐Markovian static noise in two models: a single noisy channel or two local noisy channels. Their findings show that the type and number of classical channels, noise, and initial state must be in an optimal setting in order to preserve quantum correlations.

Complete classification of steerability under local filters and its relation with measurement incompatibility

Quantum steering is a central resource for one-sided device-independent quantum information. It is manipulated via one-way local operations and classical communication, such as local filtering on the trusted party. Here, we provide a necessary and sufficient condition for a steering assemblage to be transformable into another via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables (SEO), first proposed to connect the problem of steerability and measurement incompatibility. We provide an efficient method to compute the extractable steerability that is maximal via local filters and show that it coincides with the incompatibility of the SEO. Moreover, we show that there always exists a bipartite state that provides an assemblage with steerability equal to the incompatibility of the measurements on the untrusted party. Finally, we investigate the optimal success probability and rates for transformation protocols (distillation and dilution) in the single-shot scenario together with examples.

The study of quantum steering has both foundational and practical interest. Here, the authors show that transformability of a steerable resource into another via local filtering at the trusted party is determined by whether they have the same steering equivalent observables (SEO).

Retrieving High-Dimensional Quantum Steering from a Noisy Environment with N Measurement Settings

One of the most often implied benefits of high-dimensional (HD) quantum systems is to lead to stronger forms of correlations, featuring increased robustness to noise. Here, we experimentally demonstrate the n-setting linear HD quantum steering criterion. We verify the large violation of the steering inequalities without full-state tomography. The lower bound of the violation is 2.24±0.01 in 11 dimensions, exceeding the bound (V<2) of two-setting criteria. Hence, a higher strength of steering has been revealed. Moreover, we demonstrate the method for enhancing the noise robustness without increasing dimension, alternatively, by increasing measurement settings. Using the entanglement in 11 dimensions, we experimentally retrieve steering nonlocality with 63.4±1.4% isotropic noise fraction, surpassing the 50% limitation of two-setting criteria. Our Letter offers the potential for practical one-sided device-independent quantum information processing that tolerates the noisy environment, lossy detection, and transcends the present transmission distance limitation.

Genuine High-Dimensional Quantum Steering

High-dimensional quantum entanglement can give rise to stronger forms of nonlocal correlations compared to qubit systems, offering significant advantages for quantum information processing. Certifying these stronger correlations, however, remains an important challenge, in particular in an experimental setting. Here we theoretically formalize and experimentally demonstrate a notion of genuine high-dimensional quantum steering. We show that high-dimensional entanglement, as quantified by the Schmidt number, can lead to a stronger form of steering, provably impossible to obtain via entanglement in lower dimensions. Exploiting the connection between steering and incompatibility of quantum measurements, we derive simple two-setting steering inequalities, the violation of which guarantees the presence of genuine high-dimensional steering, and hence certifies a lower bound on the Schmidt number in a one-sided device-independent setting. We report the experimental violation of these inequalities using macropixel photon-pair entanglement certifying genuine high-dimensional steering. In particular, using an entangled state in dimension d=31, our data certifies a minimum Schmidt number of n=15.

A generalized multipath delayed-choice experiment on a large-scale quantum nanophotonic chip

Bohr's complementarity is one central tenet of quantum physics. The paradoxical wave-particle duality of quantum matters and photons has been tested in Young's double-slit (double-path) interferometers. The object exclusively exhibits wave and particle nature, depending measurement apparatus that can be delayed chosen to rule out too-naive interpretations of quantum complementarity. All experiments to date have been implemented in the double-path framework, while it is of fundamental interest to study complementarity in multipath interferometric systems. Here, we demonstrate generalized multipath wave-particle duality in a quantum delayed-choice experiment, implemented by large-scale silicon-integrated multipath interferometers. Single-photon displays sophisticated transitions between wave and particle characters, determined by the choice of quantum-controlled generalized Hadamard operations. We characterise particle-nature by multimode which-path information and wave-nature by multipath coherence of interference, and demonstrate the generalisation of Bohr's multipath duality relation. Our work provides deep insights into multidimensional quantum physics and benchmarks controllability of integrated photonic quantum technology.

Certified Randomness From Steering Using Sequential Measurements

The generation of certifiable randomness is one of the most promising applications of quantum technologies. Furthermore, the intrinsic non-locality of quantum correlations allow us to certify randomness in a device-independent way, i.e., we do not need to make assumptions about the devices used. Due to the work of Curchod et al. a single entangled two-qubit pure state can be used to produce arbitrary amounts of certified randomness. However, the obtaining of this randomness is experimentally challenging as it requires a large number of measurements, both projective and general. Motivated by these difficulties in the device-independent setting, we instead consider the scenario of one-sided device independence where certain devices are trusted, and others are not; a scenario motivated by asymmetric experimental set-ups such as ion-photon networks. We show how certain aspects of previous works can be adapted to this scenario and provide theoretical bounds on the amount of randomness that can be certified. Furthermore, we give a protocol for unbounded randomness certification in this scenario, and provide numerical results demonstrating the protocol in the ideal case. Finally, we numerically test the possibility of implementing this scheme on near-term quantum technologies, by considering the performance of the protocol on several physical platforms.

Experimental Measurement-Device-Independent Quantum Steering and Randomness Generation Beyond Qubits

In a measurement-device-independent or quantum-refereed protocol, a referee can verify whether two parties share entanglement or Einstein-Podolsky-Rosen (EPR) steering without the need to trust either of the parties or their devices. The need for trusting a party is substituted by a quantum channel between the referee and that party, through which the referee encodes the measurements to be performed on that party's subsystem in a set of nonorthogonal quantum states. In this Letter, an EPR-steering inequality is adapted as a quantum-refereed EPR-steering witness, and the trust-free experimental verification of higher dimensional quantum steering is reported via preparing a class of entangled photonic qutrits. Further, with two measurement settings, we extract 1.106±0.023 bits of private randomness per every photon pair from our observed data, which surpasses the one-bit limit for projective measurements performed on qubit systems. Our results advance research on quantum information processing tasks beyond qubits.