Adaptive compressive tomography: a numerical study

Abstract

We perform several numerical studies for our recently published adaptive compressive tomography scheme [D. Ahn et al. Phys. Rev. Lett. 122, 100404 (2019)], which significantly reduces the number of measurement settings to unambiguously reconstruct any rank-deficient state without any a priori knowledge besides its dimension. We show that both entangled and product bases chosen by our adaptive scheme perform comparably well with recently-known compressed-sensing element-probing measurements, and also beat random measurement bases for low-rank quantum states. We also numerically conjecture asymptotic scaling behaviors for this number as a function of the state rank for our adaptive schemes. These scaling formulas appear to be independent of the Hilbert space dimension. As a natural development, we establish a faster hybrid compressive scheme that first chooses random bases, and later adaptive bases as the scheme progresses. As an epilogue, we reiterate important elements of informational completeness for our adaptive scheme.

12 pages, 12 figures

References in corpus (25)

• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
• Scalable multi-particle entanglement of trapped ions
• Quantum state tomography via compressed sensing
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Unknown Quantum States and Operations, a Bayesian View
• Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
• Diluted maximum-likelihood algorithm for quantum tomography
• Certifying the restricted isometry property is hard
• Experimental quantum compressed sensing for a seven-qubit system
• Minimal Informationally Complete Measurements for Pure States
• Superfast maximum likelihood reconstruction for quantum tomography
• Knowledge and ignorance in incomplete quantum state tomography
• Hilbert--Schmidt volume of the set of mixed quantum states
• Quantum Tomography Protocols with Positivity are Compressed Sensing Protocols
• Direct dialling of Haar random unitary matrices
• Five measurement bases determine pure quantum states on any dimension
• Scalable on-chip quantum state tomography
• Experimentally exploring compressed sensing quantum tomography
• Adaptive compressive tomography with no a priori information
• Strictly-complete measurements for bounded-rank quantum-state tomography
• The power of being positive: Robust state estimation made possible by quantum mechanics
• Informational completeness in bounded-rank quantum-state tomography
• Local random quantum circuits are approximate polynomial-designs - numerical results
• Multiphoton Tomography with Linear Optics and Photon Counting
• Constrained Quantum Tomography of Semi-Algebraic Sets with Applications to Low-Rank Matrix Recovery

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