14 problems

The lower bound on the infidelity factor enforced by purity of coherence is considered for qubit-clock distillation, where the noise level parametrizes the input clock state and th…

Consider a lossy multimode passive bosonic channel and let the probe be a quantum state prepared in a single spatial mode belonging to the linear span of the modes on which the cha…

Consider estimation of a small transverse displacement using an optimal single-mode Gaussian state, and let the quantum Fisher information (QFI) quantify the attainable information…

A single spatial mode is excited in a Gaussian state, with the state potentially displaced and squeezed. Optimal Gaussian probe conjecture. The optimum Gaussian-state probe is a si…

Kolotouros's random-measurement conjecture. The classical Fisher information matrix averaged over random choice of measurement basis should give the quantum Fisher information matr…

Universal NHCRB bound conjecture. For every such model,

Maximally mixed-state tomography conjecture. The maximum enhancement $\mathcal{R}^{\mathrm{NH}}$ is attained by orthonormal tomography of the maximally mixed state.

NHCRB dimension-bound conjecture. Based on analytical and numerical results,

Linear-GMM maximization conjecture. The linear GMM model at $\theta=0$ maximizes the ratio defining $\mathcal{R}^{\mathrm{NH}}$, and therefore attains $\mathcal{R}^{\mathrm{NH}}$.

Maximum-enhancement conjecture. The maximum collective quantum enhancement in any local estimation scenario is linear in the probe dimension $d$.

Consider a sensing network of $K$ sensors containing $N$ atoms, with the atoms distributed among the sensors, and suppose the target is a linear function of the sensor fields…

Consider the two multiparameter estimation problems studied in the paper, and compare generalized NOON states (GNSs) with states that are separable across modes. Mode-separable per…

Let $\boldsymbol{v}$ be a vector whose components are rationally proportioned, let $\theta_1=\boldsymbol{v}^T\boldsymbol{\phi}$, and let $\mathcal{S}(N_{\max})$ be the subspace wit…

Let $\mathcal{S}_N$ be the symmetric subspace of $N$ qubits, let $\mu(\mathcal{S}_N)$ denote its unitarily invariant probability measure, and let…