Quantum steering is considered one of the most well-known nonlocal phenomena in quantum mechanics. Unlike entanglement and Bell nonlocality, the asymmetry of quantum steering makes it vital for one-sided device-independent quantum information processing. Although there has been much progress on steering detection for bipartite systems, the criterion for Einstein-Podolsky-Rosen steering in tripartite systems remains challenging and inadequate. In this paper we first derive a promising steering criterion for any three-qubit states via correlation matrix. Furthermore, we propose the monogamy relation between the tripartite steering of system and the bipartite steering of subsystems based on the derived criterion. Finally, as illustrations, we demonstrate the performance of the steering criterion and the monogamy relation by means of several representative examples. We believe that the results and methods presented in this work could be beneficial to capture genuine multipartite steering in the near future.
Quantum steering is considered one of the most well-known nonlocal phenomena in quantum mechanics. Unlike entanglement and Bell nonlocality, the asymmetry of quantum steering makes it vital for one-sided device-independent quantum information processing. Although there has been much progress on steering detection for bipartite systems, the criterion for Einstein-Podolsky-Rosen steering in tripartite systems remains challenging and inadequate. In this paper we first derive a promising steering criterion for any three-qubit states via correlation matrix. Furthermore, we propose the monogamy relation between the tripartite steering of system and the bipartite steering of subsystems based on the derived criterion. Finally, as illustrations, we demonstrate the performance of the steering criterion and the monogamy relation by means of several representative examples. We believe that the results and methods presented in this work could be beneficial to capture genuine multipartite steering in the near future.
Quantum steering plays a fundamental role in quantum information processing regime. In particular, there are two steering-related concepts: one is the quantum steering ellipsoid, which has been used to visualize the two-qubit state, and the other is the Einstein-Podolsky-Rosen (EPR) steering that is a nonlocal correlation between entanglement and Bell nonlocality. In this work, we study the monogamy phenomenon for these two steering properties of the general n-qubit states with n > 4. First, we conjecture that there is a universal tradeoff relation in terms of the spin correlation matrices of reduced bipartite states. From this relation, we can derive the similar monogamy relation for the volume of quantum steering ellipsoids and the linear EPR-steering witness.
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum nonlocality which is intermediate between entanglement and Bell nonlocality. EPR steering is a resource for quantum key distribution that is device independent on only one side in that it certifies bipartite entanglement when one party's device is not characterized while the other party's device is fully characterized. In this work, we introduce two types of genuine tripartite EPR steering, and derive two steering inequalities to detect them. In a semi-device-independent scenario where only the dimensions of two parties are assumed, the correlations which violate one of these inequalities also certify genuine tripartite entanglement. It is known that Alice can demonstrate bipartite EPR steering to Bob if and only if her measurement settings are incompatible. We demonstrate that quantum correlations can also detect tripartite EPR steering from Alice to Bob and Charlie, even if Charlie's measurement settings are compatible.
Monogamy inequalities for the way bipartite Einstein-Podolsky-Rosen (EPR) steering can be distributed among N systems are derived. One set of inequalities is based on witnesses with two measurement settings, and may be used to demonstrate correlation of outcomes between two parties, that cannot be shared with more parties. It is shown that the monogamy for steering is directional. Two parties cannot independently demonstrate steering of a third system, using the same two-setting steering witness, but it is possible for one party to steer two independent systems. This result explains the monogamy of two-setting Bell inequality violations and the sensitivity of the continuous variable (CV) EPR criterion to losses on the steering party. We generalize to m settings. A second type of monogamy relation gives the quantitative amount of sharing possible, when the number of parties is less than or equal to m, and takes a form similar to the Coffman-Kundu-Wootters relation for entanglement. The results enable characterization of the tripartite steering for CV Gaussian systems and qubit Greenberger-Horne-Zeilinger and W states.
Einstein-Podolsky-Rosen (EPR) steering, a category of quantum nonlocal correlations describing the ability of one observer to influence another party's state via local measurements, is different from both entanglement and Bell nonlocality by possessing an asymmetric property. For multipartite EPR steering, the monogamous situation, where two observers cannot simultaneously steer the state of the third party, has been investigated rigorously both in theory and experiment. In contrast to the monogamous situation, the shareability of EPR steering in reduced subsystems allows the state of one party to be steered by two or more observers and thus reveals more configurations of multipartite EPR steering. However, the experimental implementation of such a kind of shareability has still been absent until now. Here, in an optical experiment, we provide a proof-of-principle demonstration of the shareability of EPR steering without the constraint of monogamy in a three-qubit system. Moreover, based on the reduced bipartite EPR steering detection results, we verify the genuine three-qubit entanglement results. This work provides a complementary viewpoint for understanding multipartite EPR steering and has potential applications in many quantum information protocols, such as multipartite entanglement detection, quantum cryptography, and the construction of quantum networks.
Quantum nonlocality manifests in multipartite systems through entanglement, Bell's nonlocality, and Einstein-Podolsky-Rosen (EPR) steering. While Peres's positive-partial-transpose criterion provides a simple and powerful test for entanglement, a comparably elegant spectral criterion for detecting EPR steering remains an open challenge. In this work, we systematically explore whether a Peres-type criterion can be established for EPR steering in the two-qubit system. Focusing on rank-2 (including rank-1) states and the two-qubit Werner state, we analyze the eigenvalues of their partially transposed density matrices and construct a significant steering criterion based on symmetric combinations of these eigenvalues. We prove that this criterion serves as a necessary and sufficient condition for steerability for the Werner state, all two-qubit pure states, all two-qubit rank-2 states. Furthermore, we validate the criterion for higher-rank states (rank-3 and rank-4) and show that the results align with known steering inequalities. Our findings suggest a more unified framework for detecting quantum nonlocality via partial transposition and open avenues for further theoretical and numerical investigations into steering detection.
Einstein-Podolsky-Rosen (EPR) steering is a kind of quantum nonlocal correlation characterizing the ability of one party to remotely affect another party's state by local measurements. It is regarded as an essential resource for one-sided device-independent quantum information processing. Although identification of EPR steerable states has been widely studied, it remains a hard issue under arbitrary local measurements. In this paper, we propose a steerability criterion for arbitrary dimensional bipartite systems via correlation matrices of local observables. In particular, we apply the steering criterion to three classes of local measurements which are of special significance: local orthogonal observables, mutually unbiased measurements, and general symmetric informationally complete measurements. We obtain some useful criteria that are operational and experimentally testable. We further illustrate the criteria through several examples, compare them with some steering criteria in the literature, and exhibit their power and advantages in certain cases.