Optimal quantum tomography of permutationally invariant qubits

Abstract

Mutually unbiased bases determine an optimal set of measurements to extract complete information about the quantum state of a system. However, quite often a priori information about the state exist, making some of the measurement bases superfluous. This is, for example, the case when multiqubit states belong to the permutationally invariant subspace. In this paper we derive the minimal sets of mutually unbiased bases needed to tomographically reconstruct such states.

6 pages. To be published in Phys. Rev. A

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Cited by in corpus (18)

• Quantum State Tomography via Linear Regression Estimation
• On the permutationally invariant part of a density matrix and nonseparability of N-qubit states
• Permutation-invariant quantum codes
• Experimental Comparison of Efficient Tomography Schemes for a Six-Qubit State
• Five measurement bases determine pure quantum states on any dimension
• Genuine multiparticle entanglement of permutationally invariant states
• Optimal two-qubit tomography based on local and global measurements: Maximal robustness against errors as described by condition numbers
• An alternative representation for pure symmetric states of qubits and its applications to entanglement classification
• Quantum Polarimetry
• Generalized Weyl-Heisenberg algebra, qudit systems and entanglement measure of symmetric states via spin coherent states
• Symmetric quantum states: a review of recent progress
• Coarse graining the phase space of $N$ qubits
• Tomography from collective measurements
• Parameterizing density operators with arbitrary symmetries to gain advantage in quantum state estimation
• Least-bias state estimation with incomplete unbiased measurements
• Practical implementation of mutually unbiased bases using quantum circuits
• Spectrum of Single-Photon Scattering in a Strong-Coupling Hybrid Optomechanical System
• Enhanced Compressive Threshold Quantum State Tomography for Qudit Systems