[Paper Review] Quantum memory assisted entropic uncertainty and entanglement dynamics in classical dephasing channels

Atta Ur Rahman, Nour Zidan|arXiv (Cornell University)|Nov 22, 2021

Quantum Information and Cryptography43 references4 citations

TL;DR

This study investigates entropic uncertainty and entanglement dynamics in two-qubit Werner states under classical dephasing via a Gaussian Ornstein-Uhlenbeck noise process. Using parameter optimization, it demonstrates long-term stability in coherence and entanglement within a limited noise and purity range, despite rapid entropy growth outpacing disentanglement.

ABSTRACT

We investigate the dynamics of entropic uncertainty relations, tightness, and concurrence in two non-interacting qubits produced in the Werner state and subjected to classical channels. In two contexts, common and independent qubit-noise configurations, a Gaussian Ornstein Uhlenbeck process is used to control the noisy effects of the local external fields. Using parameter optimization, we establish long-term stability in two qubits while reducing the environment's disorder entropic impact and maintaining entanglement. Using entropic uncertainty relations, tightness and concurrence, we show that in the presence of Ornstein Uhlenbeck noise, two-qubit coherence and entanglement in local fields are both weak and readily lost. Despite this, longer entanglement and lower entropy can be predicted within a limited range of the noise parameter and the purity estimator of the two-qubit state. Furthermore, the measured rate of entropy rise outpaces the rate of disentanglement generation. In addition, we also utilized the tightness measure to estimate the uncertainty in the dynamics of bipartite entropic relations.

Motivation & Objective

• To analyze the dynamics of entropic uncertainty relations in two non-interacting qubits under classical dephasing channels.
• To evaluate the tightness of entropic uncertainty relations and their role in quantifying measurement uncertainty.
• To investigate concurrence as a measure of entanglement under local noise environments.
• To identify conditions under which entanglement and coherence remain stable despite environmental decoherence.
• To optimize system parameters to minimize environmental disorder and maintain quantum correlations.

Proposed method

• Employed a Gaussian Ornstein-Uhlenbeck process to model time-correlated classical dephasing in local external fields.
• Used the Werner state as the initial two-qubit state to study entanglement and coherence dynamics.
• Applied entropic uncertainty relations to quantify measurement uncertainty in bipartite systems.
• Calculated concurrence to assess the degree of entanglement over time under noise.
• Utilized tightness measure to evaluate the precision of uncertainty bounds in quantum measurements.
• Performed parameter optimization to identify stable regimes of coherence and entanglement.

Experimental results

Research questions

• RQ1 How does classical dephasing, modeled via an Ornstein-Uhlenbeck process, affect entropic uncertainty in two-qubit systems?
• RQ2 What is the relationship between entropy growth and disentanglement rates in noisy local fields?
• RQ3 In what range of noise parameters and state purity is entanglement preserved despite environmental decoherence?
• RQ4 How does the tightness of entropic uncertainty relations evolve during the dynamics of noisy qubits?
• RQ5 Can parameter optimization stabilize coherence and entanglement in the presence of classical dephasing?

Key findings

• Entropic uncertainty increases faster than entanglement degrades, indicating that measurement uncertainty is more sensitive to noise than entanglement.
• Long-term stability in coherence and entanglement is achievable within a limited range of noise parameters and state purity.
• Despite weak and rapidly lost two-qubit coherence under Ornstein-Uhlenbeck noise, stable entanglement and low entropy can be maintained through parameter optimization.
• The tightness measure effectively captures the precision of uncertainty bounds, offering insight into the reliability of entropic uncertainty relations.
• Optimal parameter settings significantly reduce the environmental disorder's impact on quantum correlations.
• The study identifies a non-trivial window where both low entropy and preserved entanglement coexist, even under persistent local noise.