Experimental Virtual Distillation of Entanglement and Coherence.

Noise is, in general, inevitable and detrimental to practical and useful quantum communication and computation. Under the resource theory framework, resource distillation serves as a generic tool to overcome the effect of noise. Yet, conventional resource distillation protocols generally require operations on multiple copies of resource states, and strong limitations exist that restrict their practical utilities. Recently, by relaxing the setting of resource distillation to only approximating the measurement statistics instead of the quantum state, a resource-frugal protocol, "virtual resource distillation," is proposed, which allows more effective distillation of noisy resources. Here, we report its experimental implementation on a photonic quantum system for the distillation of quantum coherence (up to dimension four) and bipartite entanglement. We show the virtual distillation of the maximal superposed state of dimension four from the state of dimension two, an impossible task in conventional coherence distillation. Furthermore, we demonstrate the virtual distillation of entanglement with operations acting only on a single copy of the noisy Einstein-Podolsky-Rosen (EPR) pair and showcase the quantum teleportation task using the virtually distilled EPR pair with a significantly improved fidelity of the teleported state. These results illustrate the feasibility of the virtual resource distillation method and pave the way for accurate manipulation of quantum resources with noisy quantum hardware.

Experimental Quantum State Measurement with Classical Shadows.

A crucial subroutine for various quantum computing and communication algorithms is to efficiently extract different classical properties of quantum states. In a notable recent theoretical work by Huang, Kueng, and Preskill [Nat. Phys. 16, 1050 (2020)NPAHAX1745-247310.1038/s41567-020-0932-7], a thrifty scheme showed how to project the quantum state into classical shadows and simultaneously predict M different functions of a state with only O(log_{2}M) measurements, independent of the system size and saturating the information-theoretical limit. Here, we experimentally explore the feasibility of the scheme in the realistic scenario with a finite number of measurements and noisy operations. We prepare a four-qubit GHZ state and show how to estimate expectation values of multiple observables and Hamiltonians. We compare the measurement strategies with uniform, biased, and derandomized classical shadows to conventional ones that sequentially measure each state function exploiting either importance sampling or observable grouping. We next demonstrate the estimation of nonlinear functions using classical shadows and analyze the entanglement of the prepared quantum state. Our experiment verifies the efficacy of exploiting (derandomized) classical shadows and sheds light on efficient quantum computing with noisy intermediate-scale quantum hardware.

The Tightness of Multipartite Coherence from Spectrum Estimation.

Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems. Along this line of research, several efficient procedures have been proposed to detect multipartite quantum coherence without quantum state reconstruction, among which the spectrum-estimation-based method is suitable for various coherence measures. Here, we first generalize the spectrum-estimation-based method for the geometric measure of coherence. Then, we investigate the tightness of the estimated lower bound of various coherence measures, including the geometric measure of coherence, the l1-norm of coherence, the robustness of coherence, and some convex roof quantifiers of coherence multiqubit GHZ states and linear cluster states. Finally, we demonstrate the spectrum-estimation-based method as well as the other two efficient methods. We observe that the spectrum-estimation-based method outperforms other methods in various coherence measures, which significantly enhances the accuracy of estimation.

[The symmetry of nasal maxillary complex of patients with unilateral complete cleft lip and palate at the stage of mixed dentition-A cone beam CT study].

PURPOSE: To investigate the symmetry of nasal maxillary complex in the three-dimensional directions of patients with unilateral complete cleft lip and palate(UCLP) at the stage of mixed dentition. METHODS: Craniofacial cone-beam CT(CBCT) images of 20 UCLP patients at the stage of mixed dentition were selected. Three-dimensional reconstruction of bone tissue was carried out by Mimics software, nasal root point and 32 markers with the same name of the healthy side and the cleft side of the nasal maxillary complex were traced, three-dimensional reference planes were set up, then the distances between the points to the three-dimensional planes were measured respectively. SPSS 22.0 software package was used to analyze the data. RESULTS: In the horizontal direction, compared with the non-cleft side, the width of the cleft side of the maxilla at INM and SPC was smaller, the width of maxilla at LPA and SPr was larger, the differences were statistically significant (P<0.05). In the sagittal direction, compared with the non-cleft side, the depth of LPA, Maz and SPr at the cleft side was larger, the depth of SPM and SPC was smaller, the differences were statistically significant (P<0.05).In the vertical direction, the positions of LPA, INM and Maz at the cleft side was lower than the non-cleft side, SPC and SPr were higher, the differences were statistically significant(P<0.05). The remaining points had no significant difference (P>0.05). CONCLUSIONS: The nasal maxillary complex of UCLP patients at the stage of mixed dentition is asymmetric in three directions. The asymmetric locations were mainly located in the nasal cavity and alveolar bone. No obvious asymmetry is found in the orbital region and the maxillary region far from the cleft.

[Association between cervical vertebral maturation stages and dental calcification stages in patients with unilateral complete cleft lip and palate].

OBJECTIVE: The purpose of the study is to investigate the relationship between dental calcification stages (DCS) and cervical vertebral maturation stages (CVMS) in patients with unilateral complete cleft lips and palates (UCLP) and to provide a theoretical basis for the treatment time selection of cleft lip and palate (CLP) patients. METHODS: A total of 123 UCLP patients and 215 non-CLP subjects were selected. The DCS of the left mandibular canine, premolar, and second molar in non-CLP subjects and on both cleft sides of UCLP patients were assessed utilizing the Demirjian method. CVMS was observed utilizing the Baccetti method. The results were analyzed by Spearman rank correlation, and the correlation coefficients were compared. RESULTS: There was a correlation between the CVMS and the DCS of the left mandibular canine, the first premolar, the second premolar, and the second molar in the non-CLP subjects and on both cleft sides of the UCLP patients (r=0.762-0.864, P<0.05; r=0.809-0.914, P<0.05, respectively). The correlation between the CVMS and the DCS of the mandibular first premolar was highest among the UCLP patients. Except for the first and the second premolars of UCLP females, the correlation between the DCS and the CVMS of the other teeth did not differ among the non-CLP subjects (P>0.05). CONCLUSIONS: DCS can be utilized as a biological index to determine the growth development statuses. The correlation between the CVMS and the DCS of the mandibular first premolar was the highest.