A set of $4d-3$ observables to determine any pure qudit state

Abstract

We present a tomographic method which requires only $4d-3$ measurement outcomes to reconstruct \emph{any} pure quantum state of arbitrary dimension $d$. Using the proposed scheme we have experimentally reconstructed a large number of pure states of dimension $d=7$, obtaining a mean fidelity of $0.94$. Moreover, we performed numerical simulations of the reconstruction process, verifying the feasibility of the method for higher dimensions. In addition, the \emph{a priori} assumption of purity can be certified within the same set of measurements, what represents an improvement with respect to other similar methods and contributes to answer the question of how many observables are needed to uniquely determine any pure state.

References in corpus (7)

• Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
• Permutationally invariant quantum tomography
• SLOCC classification of n qubits invoking the proportional relationships for spectrums and for standard Jordan normal forms
• Permutationally invariant state reconstruction
• Applying the simplest Kochen-Specker set for quantum information processing
• Determination of any pure spatial qudits from a minimum number of measurements by phase stepping interferometry
• Experimental quantum tomography assisted by multiply symmetric states in higher dimensions

Cited by in corpus (6)

• Spin qudit tomography and state reconstruction error
• Parameterizing density operators with arbitrary symmetries to gain advantage in quantum state estimation
• Ptychographic reconstruction of pure quantum states
• Minimal orthonormal bases for pure quantum state estimation
• Experimental characterization of quantum processes: a selective and efficient method in arbitrary finite dimension
• Determination of spatial quantum states by using Point Diffraction Interferometry