Agnostic Phase Estimation (2403.00054v3)

Abstract: The goal of quantum metrology is to improve measurements' sensitivities by harnessing quantum resources. Metrologists often aim to maximize the quantum Fisher information, which bounds the measurement setup's sensitivity. In studies of fundamental limits on metrology, a paradigmatic setup features a qubit (spin-half system) subject to an unknown rotation. One obtains the maximal quantum Fisher information about the rotation if the spin begins in a state that maximizes the variance of the rotation-inducing operator. If the rotation axis is unknown, however, no optimal single-qubit sensor can be prepared. Inspired by simulations of closed timelike curves, we circumvent this limitation. We obtain the maximum quantum Fisher information about a rotation angle, regardless of the unknown rotation axis. To achieve this result, we initially entangle the probe qubit with an ancilla qubit. Then, we measure the pair in an entangled basis, obtaining more information about the rotation angle than any single-qubit sensor can achieve. We demonstrate this metrological advantage using a two-qubit superconducting quantum processor. Our measurement approach achieves a quantum advantage, outperforming every entanglement-free strategy.

• The paper introduces an agnostic phase estimation method using entangled qubits to retrieve maximal quantum Fisher information without prior knowledge of the rotation axis.
• The proposed protocol achieves a 50% boost in QFI, validated on a two-qubit superconducting processor, outperforming traditional single-qubit sensors.
• This approach expands quantum metrology by enabling optimal phase measurements in systems with hidden parameters, paving the way for advanced quantum sensing applications.

Agnostic Phase Estimation: An Overview

The paper, "Agnostic Phase Estimation," presents a novel approach in quantum metrology to enhance phase estimation without prior knowledge of the rotation axis. Quantum metrology aims to improve measurement sensitivities by utilizing quantum resources, with a common goal of maximizing the quantum Fisher information (QFI). This paper addresses a significant challenge in metrology: estimating an unknown rotation angle in a qubit system when the rotation axis is also unknown. Conventionally, achieving maximal QFI requires knowledge about the system's parameters, including the rotation axis. This paper proposes an innovative method inspired by theoretical simulations of closed timelike curves (CTCs) to circumvent this requirement, thus providing a strategy for optimal phase estimation in such agnostic settings.

Motivation and Methodology

The central problem addressed is the optimal estimation of a rotation angle in a qubit system when both the angle and the axis of rotation are unknown. Traditionally, maximizing QFI necessitates knowing these parameters, where the optimal single-qubit sensor state maximizes the variance of the rotation-inducing operator. However, if the axis is unknown, preparing such an optimal state is unfeasible. The authors propose an alternative approach by initially entangling the probe qubit with an ancilla. By measuring this entangled pair in a specific basis, they claim to retrieve more information about the rotation angle than any single-qubit sensor can. This method allows achieving the maximal quantum Fisher information about the rotation angle, effectively outperforming entanglement-free strategies.

Experimental Validation

The authors validate their theoretical claims through experimentation on a two-qubit superconducting quantum processor. They demonstrate that their proposed measurement approach confers a metrological advantage, superior to classical strategies that rely on single-qubit sensors without entanglement. The experiments revealed that entanglement manipulation enables the retrieval of significant information about the rotation angle, even when the axis remains unknown.

Results and Implications

The paper's results show that the proposed protocol achieves a QFI boost of 50% compared to strategies that do not utilize entanglement. Specifically, the experimental setup attains an average QFI of approximately 0.82, close to the theoretical maximum of 1. Additionally, the agnostic sensing approach using entangled measurements demonstrates the capability of measuring phase optimally without prior or subsequent knowledge of the rotation axis. This insight is crucial for metrological applications where traditional assumptions about the unitary operators are unreliable or unavailable.

Future Directions

The implications of this research are noteworthy in both theoretical and practical realms. Practically, the techniques presented could advance quantum sensing technologies, critical for fields like quantum computing and communications. Theoretically, these findings open avenues for exploring similar strategies in systems where parameters of interest are hidden or not directly measurable. Furthermore, the link to closed timelike curves presents an intriguing foundational question about the nature of time and information flow in quantum mechanics, suggesting potential exploration into quantum information processing paradigms that leverage this relationship.

This paper provides a significant step forward in quantum metrology by pushing the boundaries of phase estimation under uncertain or agnostic conditions. It showcases the power and potential of quantum entanglement as a resource for enhancing measurement precision, suggesting that future metrological studies could benefit from similar approaches, broadening the scope and applicability of quantum technologies.