Entanglement as a signature of quantum chaos

Abstract

We explore the dynamics of entanglement in classically chaotic systems by considering a multiqubit system that behaves collectively as a spin system obeying the dynamics of the quantum kicked top. In the classical limit, the kicked top exhibits both regular and chaotic dynamics depending on the strength of the chaoticity parameter in the Hamiltonian. We show that the entanglement of the multiqubit system, considered for both the bipartite and the pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite entanglement is enhanced in the chaotic region, pairwise entanglement is suppressed. Furthermore, we define a timeaveraged entangling power and show that this entangling power changes markedly as moves the system from being predominantly regular to being predominantly chaotic, thus sharply identifying the edge of chaos. When this entangling power is averaged over all states, it yields a signature of global chaos. The qualitative behavior of this global entangling power is similar to that of the classical Lyapunov exponent.

Entanglement and its relationship to classical dynamics

“…Wang et al [5] have argued that in the semiclassical regime, entanglement and chaos show similar dependence on increasing κ once the system has become fully chaotic (κ > 3.5). However, due to the small κ periodicity of the 2-qubit quantum system, we do not expect any connection at all between the classical and quantum systems after κ ≈ 3.…”

“…It has been extensively studied both theoretically and experimentally for over two decades [1][2][3][4][5][6][7][8][9] and continues to be investigated today [10,11].…”

Two-photon entanglement in multiqubit bidirectional-waveguide QED

“…We note that the entanglement quantification for multipartite mixed states is an open problem [37,38]. Here, we use the pairwise average concurrence as an entanglement measure [37,[39][40][41]. To this end, we divide the system into all possible bipartite pairs of atoms, where the concurrence of the ith pair is given by C i (t) and the total concurrence C(t) is given by: C(t) = ( n i=1 C i (t))/n where n = N/2 is the total number of qubit pairs.…”

Multiqubit entanglement in bidirectional-chiral-waveguide QED

“…We note that C = 1 corresponds to a maximally entangled state (for instance, Bell or EPR states), while C = 0 corresponds to an unentangled state. For the case of more than two atoms, we will employ the pairwise average concurrence [31][32][33][34] defined as: C(t) = ( n i=1 C i (t))/n, where n = N/2 is the total number of pairs of atoms in the chain. We note that this definition of concurrence has the same properties as each of the individual pair concurrences.…”