Local basis-dependent noise-induced Bell-nonlocality sudden death in tripartite systems
Introduction
It has been increasingly recognized that the rates of loss of joint-state coherence and of entanglement, two fundamental characteristics of quantum states, may differ within a composite system subject to local external noise [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]. Moreover, it has been shown that for some classes of states entanglement sudden death (ESD) [8], the disentanglement of bipartite systems in finite time subject only to the mechanism of basis-dependent local phase noise, occurs. Thus, qualitative as well as quantitative differences in coherence and nonlocality have been demonstrated [4], [5], [6], [7], [8], [9], [10]. Here, this investigation is further advanced.
Previously, such differences of noise-induced behavior have been carefully explored only in bipartite systems. The study of ESD under local dephasing noise has not been demonstrated in any multipartite system of more than two components because properly quantifying multipartite entanglement, particularly for mixed states which it involves by necessity, is problematic for systems of more than two qudits [11], [12]. Nonetheless, as we demonstrate here, one may still demonstrate the existence of local-noise induced death of nonlocal behavior with tools currently at hand. In particular, one can find classes of states in which generalized Bell-nonlocality in multipartite systems can go to zero in finite time while state coherence continues to be maintained for all finite times, an effect which we term Bell-nonlocality sudden death (BNSD). Here, BNSD is demonstrated in the tripartite context: the destruction of nonlocality as measured by the extent of violation of tripartite Bell inequalities in finite time under basis-dependent multi-local asymptotic dephasing noise is demonstrated in a class of initially Bell-nonlocal pure states of three-qubit systems, namely, the W class of states.
The extension of the consideration of the sudden death of nonlocal properties due to local dephasing noise beyond the bipartite case to the tripartite case is important because tripartite systems can exhibit fundamental characteristics impossible in bipartite systems, even at the three-qubit level, for example, see [13], [14]. The exhibition of BNSD illuminates the quantum–classical transition, quantum measurement, and quantum information processing where joint-state coherence and nonlocality are typically considered crucial. Our demonstration of BNSD shows that quantum information processing may be even more challenging to carry out in a noisy environment than previously thought.
Section snippets
Model: Initial state and noise model
There are two distinct classes of entangled pure states for three-qubit systems, the GHZ class and the W class, each represented by a characteristic state related to all others of their class by stochastic local operations and classical communication [15].1 Here, we restrict our attention to systems initially prepared in pure states of the W class in order to show that tripartite
Bell-nonlocality sudden death
In the multi-local noise environment described in the previous section, when a three-qubit system is prepared at the initial time in the generic pure W state , the time-evolved state , that is, the solution of Eq. (2) is The off-diagonal elements of this matrix undergo a simple exponential decay, the three-qubit state fully
Conclusions
We have demonstrated the destruction of Bell-nonlocal behavior under basis-dependent local asymptotic dephasing noise, as measured by the extent of violation of a tripartite Bell inequality, in finite time while state coherence remains for all finite times in a class of initial states of three-qubit systems. This illuminates the quantum–classical transition, and quantum information processing in particular, because it shows in the multipartite context that nonlocal behavior can be lost simply
References (22)
- et al.
Opt. Commun.
(2006) - et al.
Phys. Lett. A
(2008) - et al.
Phys. Rev. B
(2003) - et al.
Phys. Rev. B
(2007) - G. Jaeger, K. Ann, J. Mod. Opt. (2007), in...
- et al.
Phys. Rev. A
(2004) - et al.
Phys. Rev. Lett.
(2004) - et al.
Phys. Rev. Lett.
(2006) - et al.
Science
(2007) - et al.
Phys. Rev. A
(2007)
Phys. Rev. A
Cited by (44)
Optimal control of entanglement in atom pairs with dipole-dipole interaction by quantum phase space formalism
2024, Physics Letters, Section A: General, Atomic and Solid State PhysicsMemory effect of a dephasing channel on measurement uncertainty, dense coding, teleportation, and quantum Fisher information
2022, Results in PhysicsCitation Excerpt :While quantum correlations play an important role in guaranteeing quantum advantage of quantum information processing tasks, there is unavoidable decoherence due to the interaction of a system with the environments [30,31]. In particular, while coherence and quantum correlations characterize different aspects of quantumness, they could be converted into each other [32–39], therefore the quantum correlations of a system will also be affected by the decoherence effects [40–47]. Thus from a practical point of view, it is essential to identify ways to protect quantum properties of a system, at least to prolong their decay time so as to use them for practical applications.
Dynamics of Bell-nonlocality and entanglement in a ring cavity induced by spontaneous emission
2017, Optics CommunicationsEstimation of quantum correlations in magnetic materials by neutron scattering data
2014, Physics Letters, Section A: General, Atomic and Solid State PhysicsDisentanglement, Bell-nonlocality violation and teleportation capacity of the decaying tripartite states
2012, Annals of PhysicsCitation Excerpt :For instance, Ann and Jaeger have demonstrated the occurrence of BNSD for the initial three-qubit W class state as measured by its violation of the MABK inequality [18], as well as for the initial generic class of tripartite state as measured by its violation of the Svetlichny and WWZB inequalities [19].
Residual entanglement and sudden death: A direct connection
2011, Physics Letters, Section A: General, Atomic and Solid State Physics