We study the minimum number of orthogonal projective measurement settings needed to estimate multiple observables without bias for arbitrary input states. We derive structural bounds that go beyond dimension counting and combine them with explicit constructions to certify minimum setting counts for selected target spaces. A classical variational algorithm searches for shared measurement bases and optimizes their readout coefficients and sample allocation. For the collective first and second moments of two qubits, we certify that four projective settings are necessary and sufficient. For this task, a numerically optimized four-setting design achieves a Haar-averaged variance within approximately $0.0341\%$ of a lower bound valid for any number of projective settings in our fixed-allocation, unbiased linear estimation model. Numerical examples show that shared measurements can improve precision relative to the comparison protocols. For finite-depth circuits, we account for reconstruction bias and identify finite-sample regimes in which this advantage persists.
Randomized measurements provide state-independent readout for multiparameter quantum sensing. Although 3-designs retain a constant fraction of the quantum Fisher information (QFI) for every pure state, we show that 2-designs need not. In dimension \(d\), complete mutually unbiased bases (MUBs) retain exactly \(1/(d+1)\...
Nonstabilizerness, commonly referred to as magic, is essential for universal quantum computation. Yet, for pure $n$-qubit states this property is directly linked to the hardness of direct fidelity estimation. We propose a scheme to bound the fidelity on non-stabilizer states by choosing operators with low measurement o...
A circuit parameter can change measured features without changing their projected Gaussian kernel. We characterize this lost dependence and distinguish recovery by metric design from nonlinear feature expansion. With analytic feature coefficients, a fixed finite data basis affinely independent on the input domain, a fi...
H. K. Park, Jahoon Jeong, Joonkyo Shim et al.· 0 citations
Together, these results turn symmetry relaxation into a statistically justified model-selection decision and connect global signal detection to local, loss-dependent improvement.
Classical shadows allow the prediction of many quantum-state properties from measurement data, but their efficiency strongly depends on the underlying measurement ensemble. We introduce selective GHZ measurement (SGM) shadows, which perform Greenberger-Horne-Zeilinger (GHZ)-basis measurements on randomly selected subse...
Nicolas Faross, Marc Wanner, Pingal Pratyush Nath et al.· 0 citations
Quantum state tomography (QST), a required technology for the characterization of quantum communication or computing systems, remains an active research area to increase the throughput of any quantum information system. Traditional fixed Pauli-basis routines take many measurement shots to reach the fidelities demanded...
Phillip Cornett, Albert B. Dinkins V, Kwang-Cheng Chen· IEEE Journal on Selected Are...· 2 citations
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