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

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.

Quantum Steering with Imprecise Measurements

We study quantum steering experiments without assuming that the trusted party can perfectly control their measurement device. Instead, we introduce a scenario in which these measurements are subject to small imprecision. We show that small measurement imprecision can have a large detrimental influence in terms of false positives for steering inequalities, and that this effect can become even more relevant for high-dimensional systems. We then introduce a method for taking generic measurement imprecision into account in tests of bipartite steering inequalities. The revised steering bounds returned by this method are analytical, easily computable, and are even optimal for well-known families of arbitrary-dimensional steering tests. Furthermore, it applies equally well to generalized quantum steering scenarios, where the shared quantum state does not need to be separable, but is instead limited by some other entanglement property.

Stronger EPR-steering criterion based on inferred Schrödinger-Robertson uncertainty relation

Steering is one of the three in-equivalent forms of nonlocal correlations intermediate between Bell nonlocality and entanglement. Schrödinger-Robertson uncertainty relation (SRUR), has been widely used to detect entanglement and steering. However, the steering criterion in earlier works, based on SRUR, did not involve complete inferred-variance uncertainty relation. In this paper, by considering the local hidden state model and Reid's formalism, we derive a complete inferred-variance EPR-steering criterion based on SRUR in the bipartite scenario. Furthermore, we check the effectiveness of our steering criterion with discrete variable bipartite two-qubit and two-qutrit isotropic states.

Heralded quantum multiplexing entanglement between stationary qubits via distribution of high-dimensional optical entanglement

Quantum entanglement between pairs of remote quantum memories (QMs) is a prerequisite for realizing many applications in quantum networks. Here, we present a heralded protocol for the parallel creation of quantum entanglement among multiple pairs of QMs placed in spatially separated nodes, where each QM, encoding a stationary qubit, couples to an optical cavity and deterministically interacts with single photons. Our protocol utilizes an entangled photon pair encoded in the high-dimensional time-bin degree of freedom to simultaneously entangle multiple QM pairs, and is efficient in terms of reducing the time consumption and photon loss during transmission. Furthermore, our approach can be extended to simultaneously support spatial-temporal multiplexing, as its success is heralded by the detection of single photons. These distinguishing features make our protocol particularly useful for long-distance quantum communication and large-scale quantum networks.

Complete Hierarchy for High-Dimensional Steering Certification

High-dimensional quantum steering can be seen as a test for the dimensionality of entanglement, where the devices at one side are not characterized. As such, it is an important component in quantum informational protocols that make use of high-dimensional entanglement. Although it has been recently observed experimentally, the phenomenon of high-dimensional steering is lacking a general certification procedure. We provide necessary and sufficient conditions to certify the entanglement dimension in a steering scenario. These conditions are stated in terms of a hierarchy of semidefinite programs, which can also be used to quantify the phenomenon using the steering dimension robustness. To demonstrate the practical viability of our method, we characterize the dimensionality of entanglement in steering scenarios prepared with maximally entangled states measured in mutually unbiased bases. Our methods give significantly stronger bounds on the noise robustness necessary to experimentally certify high-dimensional entanglement.

Self-healing of Einstein-Rosen-Podolsky steering after an obstruction

Einstein-Rosen-Podolsky (EPR) steering describes the "spooky action at a distance" that one party can instantaneously affect the states of another distant party if they share quantum correlations. Due to its intriguing properties, EPR steering is recognized as an essential resource for a number of quantum information tasks. However, EPR steering may be destroyed when distributed in practical environments. Here, we experimentally show that EPR steering can self-heal after being destroyed by an obstruction. Such self-healing of EPR steering originates from the self-healing property of Bessel-Gaussian beams which are utilized to distribute EPR steering. For comparison, we show that when distributed using fundamental Gaussian beams, EPR steering cannot self-heal after an obstruction under similar conditions. Our results shed new light on constructing EPR-steering-based quantum information tasks in practical environments and provide a promising platform to study EPR steering.