Remotely detecting the signal of a local decohering process in spin chains

Abstract

Abstract. We study the dynamics of a one dimensional quantum spin chain evolving from unentangled or entangled initial state. At a given instant of time a quantum dynamical process (ex. measurement) is performed on a single spin at one end of the chain, decohering the system. Through the further unitary evolution, a signal propagates in the spin chain, which can be detected from a measurement on a different spin at later times. From the dynamical unitary evolution of the decohered state from the epoch time, it is possible to detect the occurrence of the dynamical process. The propagation of the signal for the dynamical process, and the speed of the signal are investigated for various spin models, viz. using the Ising, Heisenberg, and the transverse-XY dynamics.

Interference of the signal from a local dynamical process with the quantum state propagation in spin chains

“…First, we consider a non-unitary QDP that is a local decohering process, as an example, a projective measurement of σ z m which has two outcomes, corresponding projectors P 0 = (1+σ z m )/2 and P 1 = (1−σ z m )/2. A more general measurement operators, for example measuring an arbitrary component of σ m , have been considered and seen to be qualitatively similar [21]. Thus, now we have marked three qubits, at three different locations, namely, the first qubit where the initial information is coded, the l'th qubit where we recover the desired state transfer, and the m'th qubit where a local QDP occurs.…”

“…where the time-dependent function G x x (t) [21] is given in terms of the wave functions defined above as,…”

“…This is a useful detector function to see the effect of the QDP, similar to the Loschmidt echo, but a lot simpler to calculate. This function has been studied in detail for various Hamiltonians in conjunction with a non-unitary QDP [21]. One can also study similar detector functions constructed from the off-diagonal matrix elements, and the von-Neumann entropy of the RDM.…”

“…The QDP can be a non-unitary decohering operation or a unitary operation different from the back ground evolution. The QDP signal, the effect of the occurrence of the process at a given time and location, and its propagation have been investigated using both magnetisation conserving and nonconserving dynamics for initial states with and without entanglement for various model Hamiltonian dynamics [21]. The signal propagation speed in general depends on the type of interaction of the qubits, the strength of the interaction, the spatial range of the interaction and the initial state.…”

Quantum counterpart of measure synchronization: A study on a pair of Harper systems

“…where the momentum p is determined by an integer I = 1, 2, ..., N. The one-magnon eigenvalue is given by 1 (p) = − cos p. The time evolution of the system will transport the single down spin from site x to another site x and the time dependent probability is given by one magnon Green function, where the time-dependent function G x x (t) (Subrahmanyam, 2004;Sur and Subrahmanyam, 2017) is given by:…”