Tight Bounds on Pauli Channel Learning without Entanglement

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum Machine Learning

Background:

• Quantum entanglement is vital for advanced natural property learning.
• Characterizing entanglement's precise advantage remains a challenge.
• Separable algorithms, using only non-entangled states/operations, are a key focus.

Purpose of the Study:

• To establish a tight lower bound for learning Pauli channels without entanglement.
• To compare the efficiency of entangled versus non-entangled learning algorithms.
• To provide a foundation for experimental demonstrations of entanglement's benefits.

Main Methods:

• Defined non-entangled learning algorithms as those using separable states, measurements, and operations.
• Demonstrated equivalence between non-entangled algorithms and those with mid-circuit measurements and classical feedforward.
• Derived a tight lower bound for estimating Pauli channel eigenvalues without entanglement.

Main Results:

• Non-entangled Pauli channel learning requires Θ(2ⁿϵ⁻²) measurement rounds for an n-qubit system.
• Entangled learning algorithms need only Θ(ϵ⁻²) channel copies for comparable accuracy.
• A significant gap between upper and lower bounds for non-entangled learning was closed.

Conclusions:

• Entanglement offers an exponential advantage in learning Pauli channels.
• The derived lower bound solidifies the understanding of non-entangled learning limitations.
• This work supports experimental efforts to showcase entanglement-enhanced quantum characterization.