# Quantum Hypercube States

## TL;DR

Quantum hypercube states are a new class of continuous-variable quantum states with unique geometric and phase-space properties, showing high sensitivity to small displacements and robustness to thermal noise, demonstrated experimentally in optomechanics.

## Contribution

This paper introduces quantum hypercube states, revealing their geometry, phase-space features, and potential for high-precision sensing, supported by theoretical analysis and experimental validation.

## Key findings

- Hypercube states have phase-space features smaller than Planck's constant.
- They exhibit large Wigner-negativity and sensitivity to tiny displacements.
- Experimental observation of hypercube states matches theoretical predictions.

## Abstract

We introduce quantum hypercube states, a class of continuous-variable quantum states that are generated as orthographic projections of hypercubes onto the quadrature phase-space of a bosonic mode. In addition to their interesting geometry, hypercube states display phase-space features much smaller than Planck's constant, and a large volume of Wigner-negativity. We theoretically show that these features make hypercube states sensitive to displacements at extremely small scales in a way that is surprisingly robust to initial thermal occupation and to small separation of the superposed state-components. In a high-temperature proof-of-principle optomechanics experiment we observe, and match to theory, the signature outer-edge vertex structure of hypercube states.