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Physical Review A

Experimental certification of the steering criterion based on the local uncertainty relation

Fa Zhao, Huan Yang, Xue‐Ke Song, Dong Wang, Liu Ye

Published Nov 23, 2021• 4 citations
Publisher

Abstract

Quantum nonlocality is a prominent discrepancy when we compare quantum physics with classical physics, and it manifests in different forms, one of which is quantum steering. Quantum steering refers to a correlation produced from a bipartite entangled state between the local measurement outcomes of one party and the postmeasurement states of the other. Combining with uncertainty relation, local measurements can be used to distinguish whether a quantum state is steerable. Thus, this method can be treated as an effective steering criterion. In this work, we certify this steering criterion based on the local uncertainty relation by an all-optical setup with a mixed state which consists of two Bell-like states. Furthermore, we also testify that the quantum steering criterion based on the local uncertainty relation is not only superior to the linear steering criterion but also superior to the steering criterion based on the entropic uncertainty relation in our scenario. Our efforts may promote the use of this criterion in quantum information processing tasks.

DOI
10.1103/physreva.104.052425

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Quantum nonlocality is a prominent discrepancy when we compare quantum physics with classical physics, and it manifests in different forms, one of which is quantum steering. Quantum steering refers to a correlation produced from a bipartite entangled state between the local measurement outcomes of one party and the postmeasurement states of the other. Combining with uncertainty relation, local measurements can be used to distinguish whether a quantum state is steerable. Thus, this method can be treated as an effective steering criterion. In this work, we certify this steering criterion based on the local uncertainty relation by an all-optical setup with a mixed state which consists of two Bell-like states. Furthermore, we also testify that the quantum steering criterion based on the local uncertainty relation is not only superior to the linear steering criterion but also superior to the steering criterion based on the entropic uncertainty relation in our scenario. Our efforts may promote the use of this criterion in quantum information processing tasks.
Quantum steering describes a phenomenon whereby one system can immediately influence another via local measurements. It can be detected by violating the powerful and useful steering criterion based on a general entropic uncertainty relation. This criterion can be straightforwardly evaluated by using probability distributions from a finite set of measurements. Herein, we experimentally verify the steering criterion by means of the two-photon Werner-like states and three Pauli measurements. The results indicate that quantum steering can be captured by the criterion in a convenient way. In particular, there is no need to perform the usual quantum state tomography in the experiment, which greatly reduces experimental resources. Moreover, we demonstrate that the criterion is stronger than the linear one for detecting quantum steering of the Werner-like states.
Quantum steering describes the ability of one observer to nonlocally affect the other observer's state through local measurements, which represents a new form of quantum nonlocal correlation and has potential applications in quantum information and quantum communication. In this paper, we propose a computable steering criterion that is applicable to bipartite quantum systems of arbitrary dimensions. The criterion can be used to verify a wide range of steerable states directly from a given density matrix without constructing measurement settings. Compared with the existing steering criteria, it is readily computable and testable in experiment, which can also be used to verify entanglement as all steerable quantum states are entangled.
Steering is one of the three in-equivalent forms of nonlocal correlations intermediate between Bell nonlocality and entanglement. Schrodinger-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 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.
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.
Quantum entanglement is a key resource for foundational quantum information and communication tasks, such as teleportation, entanglement swapping and quantum key distribution [1]. Quantum steering is a quantum correlation that is distinct from other nonclassical correlations such as Bell nonlocality [2] and entanglement. Steering describes the effect of measuring one system, let's say Alice, and affecting the measurement results on the other system, let's say Bob. Moving through the hierarchy of nonlocal classes, from Bell nonlocality towards nonsepa-rability, requires an increasing number of parties and apparatus that need to be trusted but gives access to protocols which are more robust to noise for projective measurements [3,4]. In a quantum steering task [5] the correlations of Alice and Bob's measurement outcomes are tested against a classical probability bound which can be only violated if the state shared between the parties is quantum steerable.
It is well known that quantum correlations such as quantum nonlocality and steering can be revealed by means of the implementation of local filters or stochastic local operation and classical communication (SLOCC). This means that bipartite quantum states that are entangled but local (unsteerable), can be driven locally to quantum nonlocal (steerable) states. However, there does not exist a criterion telling us whether the revealed quantum correlation is accessible by locally implementing on a single party, or both parties are required to cooperate by implementing local filters. In this work, we proposed a criterion based on the quantum steering ellipsoid and provided examples of two-qubit states with locally inaccessible quantum correlations.