Sudden change of interferometric power for X shape states

TL;DR

This work investigates the dynamics of quantum interferometric power (IP) for two-qubit X-shape states under several noise models, showing that IP behaves as a discordlike measure with sudden-change phenomena. An analytic IP formula for X states, IP$(\rho_{AB})=\min\{M_{11},M_{22},M_{33}\}$, is derived, enabling precise tracking under noisy channels. The authors demonstrate that IP can undergo sudden changes under one-sided amplitude and phase noise, and also under two-qubit dephasing with colored noise or a common bath, with conditions identifiable in terms of the initial state parameters $c_i$. Notably, IP's sudden-change behavior does not always align with quantum discord, and a sudden IP change can occur even when discord does not exhibit such a transition, underscoring IP as a robust and distinct discordlike resource for quantum metrology under noise.

Abstract

Quantum interferometric power (IP) is a discordlike measure. We study the dynamics of IP for two-qubit X shape states under different noisy environments. Our study shows that IP exhibits sudden change, and one side quantum channel is enough for the occurrence of a sudden change of IP. In particular, we show that the initial state having no sudden change of quantum discord exhibits a sudden change of IP under the dynamics of amplitude noise, but the converse is not true. Besides, we also investigate the dynamics of IP under two different kinds of composite noises. Our results also confirm that sudden change of IP occurs under such composite noises.

Figures (5)

• Figure 1: The evolution of IP ((a) and (c)) versus the evolution of quantum discord ((b) and (d)) under amplitude noise acting on the first qubit of the bipartite system. Considering the initial state not satisfying the condition of a sudden change of quantum discord ($c_1 = 0.4, c_2 = 0.2, c_3 = 0.3$), we can see that IP exhibits a sudden change with the same situation. On the other hand, if we consider the initial state satisfying the condition of a sudden change of quantum discord ($c_1 = 0.3, c_2 = 0.2, c_3 = 0.301$), one can see that a sudden change of IP still occurs with the same situation.
• Figure 2: IP of the initial Bell-diagonal states under phase noise acting on the first qubit of the quantum system. (1) $c_1 = 0.4, c_2 = 0.1, c_3 = 0.3$ (solid line). (2) $c_1 = 0.1, c_2 = 0.3, c_3 = 0.4$ (dashed line). (3) $c_1 = 0.4, c_2 = 0.3, c_3 = 0$ (dotted line). The sudden change only happens at situation (1).
• Figure 3: IP of the initial Bell-diagonal states under depolarizing noise acting on the first qubit of the quantum system. (1) $c_1 = 0.4, c_2 = 0.3, c_3 = 0.2$ (solid line). (2) $c_1 = 0.1, c_2 = 0.3, c_3 = 0.4$ (dashed line). (3) $c_1 = 0.1, c_2 = 0.4, c_3 = 0.2$ (dotted line).
• Figure 4: The dynamics of the IP of the initial Bell-diagonal state $\rho$, described by parameters $c_1=0.3, c_2=0.4, c_3=0.2$, independently interacting with identical colored dephasing noise having $a=1s$, $\tau=0.5s$. The decay rate of IP sudden changes at $\nu = 0.455$.
• Figure 5: IP of the initial Bell-diagonal states under the two-qubit dephasing model with colored noise with (1) $c_1=0.4, c_2=-0.1, c_3=0.16$ (solid line) and (2) $c_1=0.4, c_2=-0.1, c_3=0.14$ (dotted line), respectively. Sudden change of IP happens only at situation (2).