Quantum state and process tomography via adaptive measurements

We investigate quantum state tomography(QST) for pure states and quantum process tomography(QPT) for unitary channels via adaptive measurements. For a quantum system with a d-dimensional Hilbert space, we first propose an adaptive protocol where only 2d. 1 measurement outcomes are used to accomplish the QST for all pure states. This idea is then extended to study QPT for unitary channels, where an adaptive unitary process tomography(AUPT) protocol of d2+d.1measurement outcomes is constructed for any unitary channel. We experimentally implement the AUPT protocol in a 2-qubit nuclear magnetic resonance system. We examine the performance of the AUPT protocol when applied to Hadamard gate, T gate(/8 phase gate), and controlled-NOT gate,respectively, as these gates form the universal gate set for quantum information processing purpose. As a comparison, standard QPT is also implemented for each gate. Our experimental results show that the AUPT protocol that reconstructing unitary channels via adaptive measurements significantly reduce the number of experiments required by standard QPT without considerable loss of fidelity.

Experimental demonstration of nonlinear quantum metrology with optimal quantum state

Nonlinear quantum metrology may exhibit better precision scalings. For example, the uncertainty of an estimated phase may scale as △φ∝ 1/N2 under quadratic phase accumulation, which is 1/N times smal-ler than the linear counterpart, where N is probe number. Here, we experimentally demonstrate the non-linear quantum metrology by using a spin-I（I 〉 1/2） nuclear magnetic resonance （NMR） ensemble that can be mapped into a system ofN = 2I spin-1/2 particles and the quadratic interaction can be utilized for the quadratic phase accumulation. Our experimental results show that the phase uncertainty can scale as △φ∝1/（N2-1） by optimizing the input states, when N is an odd number. In addition, the interferomet-tic measurement with quadratic interaction provides a new way for estimating the quadrupolar coupling strength in an NMR system. Our system may be further extended to exotic nonlinear quantum metrology with higher order many-body interactions.

Erratum to: Algorithmic cooling based on cross-relaxation and decoherence-free subspace [Sci. China-Phys. Mech. Astron. 63, 270311 (2020)]

In this work,HengYan Wang and Jian Pan contributed equally to this work.The annotation for the contribution was omitted in the original publication of this paper[I].It can be conformed in the submitted PDF version of the manuscript.Hence,the sentence“HengYan Wang and Jian Pan conjtributed equally to this work.”should be added.