Quantum phase estimation using a multi-headed cat state

TL;DR

This paper introduces a four-headed cat state (4HCS) for quantum phase estimation, demonstrating its superior performance over previous states, especially at low photon numbers and under photon loss, with potential for further improvements using more component states.

Contribution

The paper proposes a novel four-headed cat state (4HCS) for quantum phase estimation, showing enhanced performance over existing states and extending the concept to larger superpositions.

Findings

4HCS outperforms 2HCS in phase estimation at low photon numbers

Entangled states based on 4HCS improve phase estimation under photon loss

Increasing component states in superposition enhances phase estimation capabilities

Abstract

It was recently shown that an entangled coherent state, which is a superposition of two different coherent states, can surpass the performance of noon state in estimating an unknown phase-shift. This may hint at further enhancement in phase estimation by incorporating more component states in the superposition of resource state. We here introduce a four-headed cat state (4HCS), a superposition of four different coherent states, and propose its application to quantum phase estimation. We demonstrate the enhanced performance in phase estimation by employing an entangled state via the 4HCS, which can surpass that of the two-headed cat state (2HCS), particularly in the regime of small average photon numbers. Moreover, we show that an entangled state modified from the 4HCS can further enhance the phase estimation, even in the regime of large average photon number under a photon-loss channel. Our investigation further extends to incorporate an increasingly large number of component states in the resource superposition state and clearly show its merit in phase estimation.