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Communications in Theoretical Physics

EPR steering and Bell nonlocality via the filtering operation of two coupled double quantum dots system

Hao Wang

Published Mar 3, 2025• 2 citations
Publisher

Abstract

Abstract In this work, we mainly study Bell nonlocality and quantum steerability of two-coupled double quantum dots (DQDs) system via local filtering operation. We compare and analyze the influence of the Coulomb potential, temperature, tunneling parameter and local filtering operation on quantum steering and Bell nonlocality in the system. The results show that quantum steering and nonlocality first increase and then decrease but never vanish even for the stronger value of the Coulomb potential. Quantum steering and Bell nonlocality would degrade with the increase of temperature. The filtering process does not increase the degree of steerability, but decreases the range of quantum steerability. In addition, it is noteworthy that a peculiar phenomenon exists: the Einstein–Podolsky–Rosen (EPR) steering asymmetry between Alice and Bob first increase, then decrease to zero and finally increases as the tunneling strength increases. However, this phenomenon does not appear with no operation between Alice and Bob.

DOI
10.1088/1572-9494/adbbbc

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Bell's Nonlocality Can be Tested through Einstein-Podolsky-Rosen Steering

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Quantum nonlocality has recently been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Experimentally Bell's nonlocality is usually tested by quantum violation of the Clause-Horne-Shimony-Holt (CHSH) inequality in the two-qubit system. Bell's nonlocality is the strongest type of nonlocality, also due this reason Bell-test experiments have encountered both the locality loophole and the detection loophole for a very long time. As a weaker nonlocality, EPR steering naturally escapes from the locality loophole and is correspondingly easier to be demonstrated without the detection loophole. In this work, we trigger an extraordinary approach to investigate Bell's nonlocality, which is strongly based on the EPR steering. We present a theorem, showing that for any two-qubit state $τ$, if its mapped state $ρ$ is EPR steerable, then the state $τ$ must be Bell nonlocal. The result not only pinpoints a deep connection between EPR steering and Bell's nonlocality, but also sheds a new light to realize a loophole-free Bell-test experiment (without the CHSH inequality) through the violation of steering inequality.

arXiv:1510.06640•Oct 22, 2015•0 citations
Abstract In this work, we mainly study Bell nonlocality and quantum steerability of two-coupled double quantum dots (DQDs) system via local filtering operation. We compare and analyze the influence of the Coulomb potential, temperature, tunneling parameter and local filtering operation on quantum steering and Bell nonlocality in the system. The results show that quantum steering and nonlocality first increase and then decrease but never vanish even for the stronger value of the Coulomb potential. Quantum steering and Bell nonlocality would degrade with the increase of temperature. The filtering process does not increase the degree of steerability, but decreases the range of quantum steerability. In addition, it is noteworthy that a peculiar phenomenon exists: the Einstein–Podolsky–Rosen (EPR) steering asymmetry between Alice and Bob first increase, then decrease to zero and finally increases as the tunneling strength increases. However, this phenomenon does not appear with no operation between Alice and Bob.
Abstract In this paper, we study the dynamics of Bell nonlocality and quantum steering of Fermi-Hubbard model on graphene honeycomb lattice. In the model, Bell nonlocality and Einstein-Podolski-Rosen steering have been exactly solved with and without the local flltering operation (LFO). The influence of flnite temperature, on-site Coulomb repulsion, and nearest-neighbor repulsion on Bell nonlocality and quantum steerability is investigated. The equilibrium state established through the competition between nearest-neighbor and on-site Coulomb repulsions efiectively balances nonlocal quantum correlations. The interplay of these competing interactions drives the system toward a separable regime, wherein both Bell nonlocality and quantum steering violations are completely suppressed. Furthermore, the flltering process not only enhances the degree of quantum steering and Bell nonlocality but also contracts their operational range. These results will provide more theoretical guidance and greater practical signiflcance for the manipulation of Bell nonlocality and quantum steering within graphene systems.
Einstein-Podolsky-Rosen (EPR) steering, a fundamental concept of quantum nonlocality, describes one observer's capability to remotely affect another distant observer's state by local measurements. Unlike quantum entanglement and Bell nonlocality, both associated with the symmetric quantum correlation, EPR steering depicts the unique asymmetric property of quantum nonlocality. With the local filter operation in which some system components are discarded, quantum nonlocality can be distilled to enhance the nonlocal correlation and even the hidden nonlocality can be activated. However, asymmetric quantum nonlocality in the filter operation still lacks a well-rounded investigation, especially considering the discarded parts where quantum nonlocal correlations may still exist with probabilities. Here, in both theory and experiment, we investigate the effect of reusing the discarded particles from local filter. We observe all configurations of EPR steering simultaneously and other intriguing evolution of asymmetric quantum nonlocality, such as reversing the direction of one-way EPR steering. This work provides a perspective to answer ``what is the essential role of utilizing quantum steering as a resource?'' and demonstrates a practical toolbox for manipulating asymmetric quantum systems with significant potential applications in quantum information tasks.
Bell nonlocality and Einstein-Podolsky-Rosen (EPR) steering are every important quantum correlations of a composite quantum system. Bell nonlocality of a bipartite state is a quantum correlation demonstrated by some local quantum measurements, while EPR steering is another form of quantum correlations, observed firstly by Schrodinger in the context of famous EPR paradox. In this paper, we give some remarks on Bell nonlocality and EPR steering of bipartite states, including mathematical definitions and characterizations of these two quantum correlations, the convexity and closedness of the set of all Bell local states and the set of all EPR unsteerable states. We also derive a EPR-steering criteria, with which the EPR steerability of the maximally entangled states are checked.
Einstein-Podolsky-Rosen (EPR) steering describes the ability of one observer to nonlocally "steer" the other observer's state through local measurements. EPR steering exhibits a unique asymmetric property; i.e., the steerability can differ between observers, which can lead to one-way EPR steering in which only one observer obtains steerability in the steering process. This property is inherently different from the symmetric concepts of entanglement and Bell nonlocality, and it has attracted increasing interest. Here, we experimentally demonstrate asymmetric EPR steering for a class of two-qubit states in the case of two measurement settings. We propose a practical method to quantify the steerability. We then provide a necessary and sufficient condition for EPR steering and clearly demonstrate one-way EPR steering. Our work provides new insight into the fundamental asymmetry of quantum nonlocality and has potential applications in asymmetric quantum information processing.
Einstein–Podolsky–Rosen (EPR) steering is an example of nontrivial quantum nonlocality and characteristic in the non-classical world. The directivity (or asymmetry) is a fascinating trait of EPR steering, and it is different from other quantum nonlocalities. Here, we consider the strategy in which two atoms compose a two-qubit X state, and the two atoms are owned by Alice and Bob, respectively. The atom of Alice suffers from a reservoir, and the atom of Bob couples with a bit flip channel. The influences of auxiliary qubits on EPR steering and its directions are revealed by means of the entropy uncertainty relation. The results indicate that EPR steering declines with growing time t when adding fewer auxiliary qubits. The EPR steering behaves as damped oscillation when introducing more auxiliary qubits in the strong coupling regime. In the weak coupling regime, the EPR steering monotonously decreases as t increases when coupling auxiliary qubits. The increases in auxiliary qubits are responsible for the fact that the steerability from Alice to Bob (or from Bob to Alice) can be more effectively revealed. Notably, the introductions of more auxiliary qubits can change the situation that steerability from Alice to Bob is certain to a situation in which steerability from Bob to Alice is certain.
Quantum nonlocality has recently been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Experimentally Bell's nonlocality is usually tested by quantum violation of the Clause-Horne-Shimony-Holt (CHSH) inequality in the two-qubit system. Bell's nonlocality is the strongest type of nonlocality, also due this reason Bell-test experiments have encountered both the locality loophole and the detection loophole for a very long time. As a weaker nonlocality, EPR steering naturally escapes from the locality loophole and is correspondingly easier to be demonstrated without the detection loophole. In this work, we trigger an extraordinary approach to investigate Bell's nonlocality, which is strongly based on the EPR steering. We present a theorem, showing that for any two-qubit state τττ, if its mapped state ρρρ is EPR steerable, then the state τττ must be Bell nonlocal. The result not only pinpoints a deep connection between EPR steering and Bell's nonlocality, but also sheds a new light to realize a loophole-free Bell-test experiment (without the CHSH inequality) through the violation of steering inequality.