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Chinese Physics B

Witnessing quantum steering and nonlocal advantage of quantum coherence via quantum steering ellipsoid

Huan 欢 Yang 杨, Ling-Ling Xing, Zong Xue Xu, Gang Zhang

Published Mar 4, 2026• 0 citations
Publisher

Abstract

Abstract An arbitrary bipartite state can be visually characterized through a quantum steering ellipsoid (QSE), and different nonclassical correlations can be visually revealed via the geometric traits of the QSE. Here, we characterize the QSE of bipartite Bell diagonal states subject to the influences of the bit flip (BF), the depolarizing (DP), and the phase damping (PD) channels, and ascertain the influences of various noise channels on the QSE. By employing nonlinear asymmetric quantum steering criterion (NAC), linear asymmetric quantum steering criterion (LAC), quantum steering criterion from the entropic uncertainty relation (SCEUR), and the shape of the QSE, we reveal and witness the quantum steering and the nonlocal advantage of quantum coherence (NAQC) of the system under these noise channels. It turns out that noise channels can significantly affect the shape of the QSE, one can effectively capture quantum steering and the NAQC via the QSE. Among the NAC, LAC, and SCEUR, the LAC (the NAC) is the most promising avenue for detecting the quantum steering under the DP and PD channels (under the the BF channels). It is particularly important to note that the shape of the QSE can visually display the abilities of these criteria in witnessing quantum steering. Moreover, based on the ${l_1}$ norm of coherence, the NAQC can be achieved under the BF, DP, and PD channels if the sum of three semiaxis lengths of the QSE can surpass $\sqrt 6 $.

DOI
10.1088/1674-1056/ae4d2b

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Abstract An arbitrary bipartite state can be visually characterized through a quantum steering ellipsoid (QSE), and different nonclassical correlations can be visually revealed via the geometric traits of the QSE. Here, we characterize the QSE of bipartite Bell diagonal states subject to the influences of the bit flip (BF), the depolarizing (DP), and the phase damping (PD) channels, and ascertain the influences of various noise channels on the QSE. By employing nonlinear asymmetric quantum steering criterion (NAC), linear asymmetric quantum steering criterion (LAC), quantum steering criterion from the entropic uncertainty relation (SCEUR), and the shape of the QSE, we reveal and witness the quantum steering and the nonlocal advantage of quantum coherence (NAQC) of the system under these noise channels. It turns out that noise channels can significantly affect the shape of the QSE, one can effectively capture quantum steering and the NAQC via the QSE. Among the NAC, LAC, and SCEUR, the LAC (the NAC) is the most promising avenue for detecting the quantum steering under the DP and PD channels (under the the BF channels). It is particularly important to note that the shape of the QSE can visually display the abilities of these criteria in witnessing quantum steering. Moreover, based on the l1{l_1}l1​ norm of coherence, the NAQC can be achieved under the BF, DP, and PD channels if the sum of three semiaxis lengths of the QSE can surpass 6\sqrt 6 6​.
A quantum steering ellipsoid (QSE) is a visual characterization for bipartite qubit systems, and it is also a novel avenue for describing and detecting quantum correlations. Herein, by using a QSE, we visualize and witness the first-order coherence (FOC), Bell nonlocality (BN) and purity under non-inertial frames. Also, the collective influences of the depolarizing channel and the non-coherence-generating channel (NCGC) on the FOC, BN and purity are investigated in the QSE formalism. The results reveal that the distance from the center of the QSE to the center of the Bloch sphere visualizes the FOC of a bipartite system, the lengths of the QSE semiaxis visualize the BN, and the QSE’s shape and position dominate the purity of the system. One can capture the FOC, BN and purity via the shape and position of the QSE in the non-inertial frame. The depolarizing channel (the NCGC) gives rise to the shrinking and degradation (the periodical oscillation) of the QSE. One can use these traits to visually characterize and detect the FOC, BN and purity under the influence of external noise. Of particular note is that the condition for the QSE to achieve the center of the Bloch sphere cannot be influenced by the depolarizing channel and the NCGC. The characterization shows that the conditions for the disappearance of the FOC are invariant under the additional influences of the depolarizing channel and NCGC.
Abstract Quantum steering ellipsoid (QSE) can faithfully characterize arbitrary bipartite state, and provide a new method to visually investigate and capture various quantum nonlocalities. Note that the dissipation of quantum nonlocalities can be accelerated by the coupling between the system and the decoherence channel, which induces great challenges in detecting quantum nonlocalities. Herein, considering the scenario in which the subsystem of a two-qubit system is coupled with a decoherence channel, the quantum discord (QD) and concurrence are visually characterized and detected by employing the QSE. The results reveal that the QSE y and z semiaxes are responsible for the traits of the QD and concurrence under the bit flip channel. The x and y semiaxes dominate and visualize the QD and concurrence under the phase damping channel. Of particular note is that one can realize the detections of the QD and concurrence via the shape of the QSE. To be clearer, the disappearance of the QD can be ascertained according to a needle-shaped QSE or a vanishing QSE in the Bloch sphere. In contrast, one can witness the concurrence if the total semiaxis length is greater than one. Beyond this, our results visually reveal that quantum entanglement is a stronger quantum nonlocality than the QD from the perspective of geometry, and thus deepens the understanding of the quantum nonlocality.
The important applications of quantum dot system are to implement logic operations and achieve universal quantum computing based on different quantum nonlocalities. Here, we characterize the quantum steering, Bell nonlocality, and nonlocal advantage of quantum coherence (NAQC) of quantum dot system suffering nonunital and unital channels. The results reveal that quantum steering, Bell nonlocality, and NAQC can display the traits of dissipation, enhancement, and freezing. One can achieve the detections of quantum steering, Bell nonlocality, and NAQC of quantum dot system in different situations. Among these quantum nonlocalities, NAQC is the most fragile, and it is most easily influenced by different system parameters. Furthermore, considering quantum dot system coupling with amplitude damping channel and phase damping channel, these quantum nonlocalities degenerate with the enlargement of the channel parameters t and Γ. Remarkably, measurement reversal can effectively control and enhance quantum steering, Bell nonlocality, and NAQC of quantum dot system suffering from decoherence, especially in the scenarios of the amplitude damping channel and strong operation strength.
Nonclassical correlations are a key resource to explore foundational quantum information tasks and find applications in device-independent protocols. Quantum steering was formalized in 2007 [1] and is distinct from other nonclassical correlations such as Bell nonlocality [2] and entanglement. Steering describes the effect of a local measurement on one system and affecting the measurement results on the other system. This can be visualized for two-qubit states using quantum steering ellipsoids (QSE), which is the set of Bloch vectors that Alice can collapse Bob's state to. They are theoretically well studied [3-6] and have been recently experimentally demonstrated [7].
The effect of a local trace-preserving single-qubit channel on a two-qubit state is investigated in the frame of quantum steering ellipsoids (QSEs). The phenomenon of locally increased quantum discord is visualized in this picture. We strictly prove that a BBB-side two-qubit discordant state can be locally prepared from a classical state by a trace-preserving channel on qubit BBB if and only if its QSE of BBB is a nonradial line segment. For states with higher-dimensional QSEs, the phenomenon of locally increased quantum correlation generally happens when the shape of the QSE is like a baguette. Based on this observation, we find a class of entangled states whose quantum discord can be increased by the local amplitude-damping channel. Further, we find that the local quantum channel does not increase the size of the QSEs of either qubit AAA or qubit BBB, for the needle-shaped QSE states, or for the Bell diagonal states with higher-dimensional QSEs.
Nonlocal advantage of quantum coherence (NAQC) based on coherence complementarity relations is generally viewed as a stronger nonclassical correlation than Bell nonlocality. An arbitrary two-qubit state with NAQC must be an entangled state, which demonstrates that the criterion of NAQC can also be regarded as an entanglement witness. In this paper, we experimentally investigate the NAQC for Bell-diagonal states with high fidelity in an optics-based platform. We perform local measurements on a subsystem in three mutually unbiased bases and reconstruct the density matrices of the measured states by a quantum state tomography process. By analyzing characteristics of the l1{l}_{1}l1​ norm, relative entropy, and skew information of coherence with parameters of quantum states, NAQC for the quantum states is accurately captured, and it shows that our experimental results are well compatible with the theoretical predictions. Our results have shown that NAQC could be a new kind of entanglement witness and a useful physical resource for quantum information processing.