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Laser Physics Letters

Dynamical behavior of maximal steered coherence and concurrence under decoherence

Huan Yang, Ming‐Ming Du, Wen‐Yang Sun, Zhiyong Ding, Dong Wang, Changjin Zhang, Ye Liu

Published Oct 5, 2018• 3 citations
Publisher

Abstract

Abstract In this work, by employing quantum steering ellipsoid (QSE) pictures, we investigate the dynamical characteristics of maximal steered coherence (MSC) and concurrence for an arbitrary Bell-diagonal state when the qubit-system suffers from canonical noisy channels, such as phase damping, bit flip and bit-phase flip channels. It has been found that the MSC is equal to the longest semiaxis length of the QSEs. Remarkably, the QSEs have an invariant semiaxis length under these mentioned unital channels. The dynamical behavior of MSC is dependent of the initial ellipsoid shape, and MSC is frozen to the length of invariant semiaxis ultimately. The time of frozen MSC can be derived by means of QSEs. Moreover, one can obtain that the concurrence depends on the sum of three semiaxis lengths of QSEs under these unital channels. Interestingly, the concurrence will be sudden death, if the sum of three semiaxis lengths is equal to 1. Additionally, we conclude that the time of entanglement sudden death can be deduced via QSE pictures.

DOI
10.1088/1612-202x/aae222

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Abstract In this work, by employing quantum steering ellipsoid (QSE) pictures, we investigate the dynamical characteristics of maximal steered coherence (MSC) and concurrence for an arbitrary Bell-diagonal state when the qubit-system suffers from canonical noisy channels, such as phase damping, bit flip and bit-phase flip channels. It has been found that the MSC is equal to the longest semiaxis length of the QSEs. Remarkably, the QSEs have an invariant semiaxis length under these mentioned unital channels. The dynamical behavior of MSC is dependent of the initial ellipsoid shape, and MSC is frozen to the length of invariant semiaxis ultimately. The time of frozen MSC can be derived by means of QSEs. Moreover, one can obtain that the concurrence depends on the sum of three semiaxis lengths of QSEs under these unital channels. Interestingly, the concurrence will be sudden death, if the sum of three semiaxis lengths is equal to 1. Additionally, we conclude that the time of entanglement sudden death can be deduced via QSE pictures.
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 $\sqrt 6 $.
Abstract Maximal steered coherence (MSC) is a noteworthy resource measure in the field of quantum information, and it is defined under the framework of coherence measure and the formalism of quantum steering ellipsoids (QSEs). Here, we explore the MSC of a two-qubit X state under the common influences of reservoir and noise. The results disclose that the introduction of auxiliary qubits can give rise to enhancement of the MSC in both the strong and weak coupling regimes. Moreover, more auxiliary qubits can decrease the oscillation period of the MSC, and also suppress the oscillation amplitude of the MSC in the strong coupling regime. In contrast, the increases in auxiliary qubits result in the oscillation of the MSC for the setting of the initially weak coupling regime. Of particular interest is that the improvement effects of more auxiliary qubits on the MSC in the initially weak coupling regime are significantly stronger than that in the initially strong coupling regime.
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.
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 In this work, we delve into the dynamic traits of the relative entropy of quantum coherence (REQC) as the quantum system interacts with the different noisy channels, drawing comparisons with entanglement (concurrence). The research results demonstrate the broader prevalence and stronger robustness of the REQC as opposed to concurrence. It’s worth noting that the bit flip channel cannot uphold a constant nonzero frozen the REQC, besides, the concurrence follows a pattern of temporary reduction to zero, followed by recovery after a certain time span. More importantly, the REQC maintains its presence consistently until reaching a critical threshold, whereas concurrence experiences completely attenuation to zero under the influence of phase damping and amplitude damping channels.
We focus our attention on tripartite mixed states as initial states, and apply coherence concurrence to investigate quantum coherence properties in the background of a Schwarzschild black hole under phase damping, phase flip and bit flip channels, respectively. Several analytic complementary relationships based on coherence concurrence for tripartite subsystems are proposed. In the case of the bit flip channel, the behavior of the coherence concurrence is similar to the one of the phase damping channel, the accessible coherence concurrence always degrades as the Hawking acceleration rising, but sudden death never occurs, while the inaccessible coherence increases from zero monotonically. Interestingly, the coherence concurrence is decreasing at first and then increasing as the decay probability rising under phase flip channel. Unlike the case of tripartite pure states, the coherence concurrence of mixed state with X shape is equal to l1l_1l1​ -norm of coherence.