Variational quantum tomography with incomplete information by means of semidefinite programs

Abstract

We introduce a new method to reconstruct unknown quantum states out of incomplete and noisy information. The method is a linear convex optimization problem, therefore with a unique minimum, which can be efficiently solved with Semidefinite Programs. Numerical simulations indicate that the estimated state does not overestimate purity, and neither the expectation value of optimal entanglement witnesses. The convergence properties of the method are similar to compressed sensing approaches, in the sense that, in order to reconstruct low rank states, it needs just a fraction of the effort correspondig to an informationally complete measurement.

8 pages, 6 figures. In the previous version there was a mistake about lower bounds to arbitrary expectation values. It is now corrected

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Cited by in corpus (12)

• Five measurement bases determine pure quantum states on any dimension
• Communication games reveal preparation contextuality
• Minimum tomography of two entangled qutrits using local measurements of one-qutrit SIC-POVM
• Quantum State Tomography with incomplete data: Maximum Entropy and Variational Quantum Tomography
• Experimental implementation of a NMR entanglement witness
• Experimental determination of multipartite entanglement with incomplete information
• Self-consistent quantum measurement tomography based on semidefinite programming
• Quantum process tomography with informational incomplete data of two $J$-coupled heterogeneous spins relaxation in a time window much greater than $T_1$
• Ptychography of pure quantum states
• Efficient Quantum Tomography of Two-Mode Wigner Functions
• Parameterizing density operators with arbitrary symmetries to gain advantage in quantum state estimation
• Exciton propagation via quantum walks based on non-Hermitian coin flip operations