Verifying correlations within a quantum state is an important task in quantum state engineering, while realistic detectors with imperfect efficiency usually introduce errors into the detection results. With these detection errors, genuine multi-partite entanglement can be invisible. In this paper, we propose a simple method for correcting arbitrary uncorrelated detection errors. The method is based on the processing of data from repetitive experiments and can correct detection errors of any magnitude as long as the error magnitude is calibrated. The method is illustrated with its application in the detection of multi-partite entanglement from quantum state engineering.
Verifying correlations within a quantum state is an important task in quantum state engineering, while realistic detectors with imperfect efficiency usually introduce errors into the detection results. With these detection errors, genuine multi-partite entanglement can be invisible. In this paper, we propose a simple method for correcting arbitrary uncorrelated detection errors. The method is based on the processing of data from repetitive experiments and can correct detection errors of any magnitude as long as the error magnitude is calibrated. The method is illustrated with its application in the detection of multi-partite entanglement from quantum state engineering.
Standard procedures for entanglement detection assume that experimenters can exactly implement specific quantum measurements. Here, we depart from such idealizations and investigate, in both theory and experiment, the detection of genuine multipartite entanglement when measurements are subject to small imperfections. For arbitrary qubits number n, we construct multipartite entanglement witnesses where the detrimental influence of the imperfection is independent of n. In a tabletop four-partite photonic experiment, we demonstrate first how a small amount of alignment error can undermine the conclusions drawn from standard entanglement witnesses and then perform the correction analysis. Furthermore, since we consider quantum devices that are trusted but not perfectly controlled, we showcase advantages in terms of noise resilience as compared to device-independent models.
The accurate detection of small deviations in given density matrice is important for quantum information processing, which is a difficult task because of the intrinsic fluctuation in density matrices reconstructed using a limited number of experiments. We previously proposed a method for decoherence error detection using a machine-learning technique [S. Hara, T. Ono, R. Okamoto, T. Washio, and S. Takeuchi, Phys. Rev. A 89, 022104 (2014)]. However, the previous method is not valid when the errors are just changes in phase. Here, we propose a method that is valid for arbitrary errors in density matrices. The performance of the proposed method is verified using both numerical simulation data and real experimental data.
Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in an experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the experiment, namely, device independently. However, it is difficult to certify genuine entanglement of practical multipartite states in this way, and even more difficult to quantify it, due to the difficulty in identifying optimal multipartite Bell inequalities and protocols tolerant to state impurity. In this Letter, we explore a general and robust device-independent method that can be applied to various realistic multipartite quantum states in arbitrary finite dimension, while merely relying on bipartite Bell inequalities. Our method allows us both to certify the presence of genuine multipartite entanglement and to quantify it. Several important classes of entangled states are tested with this method, leading to the detection of genuinely entangled states. We also certify genuine multipartite entanglement in weakly entangled Greenberger-Horne-Zeilinger states, showing that the method applies equally well to less standard states.
The verification and quantification of experimentally created entanglement by simple measurements, especially between distant particles, is an important basic task in quantum processing. When composite systems are subjected to local measurements the measurement data will exhibit correlations, whether these systems are classical or quantum. Therefore, the observation of correlations in the classical measurement record does not automatically imply the presence of quantum correlations in the system under investigation. In this study, we explore the question of when correlations, or other measurement data, are sufficient to guarantee the existence of a certain amount of quantum correlations in the system and when additional information, such as the degree of purity of the system, is needed to do so. Various measurement settings are discussed, both numerically and analytically. Exact results and lower bounds on the least entanglement consistent with the observations are presented. The approach is suitable both for the bi-partite and the multi-partite setting.
Entanglement is one of the most fascinating features of quantum theory, as it fundamentally distinguishes quantum systems from classical systems. It not only might play a role in natural processes, but provides an especially powerful resource for a plethora of quantum information protocols, including quantum state teleportation, superdense coding as well as quantum computation schemes. However, for larger systems involving more than two parties, it is a challenging task to verify and characterize entanglement. In this thesis, efficient means for detecting genuine multipartite entanglement in multiqubit quantum systems will be derived, demonstrated, and discussed. Beyond that, methods for quantum state and process tomography will be introduced, which allow to analyze and investigate prepared multipartite states or even the performance of whole setups. Some typical obstacles for reliable state tomography will be pointed out, together with new means to understand experimentally obtained data. Finally, the measurement problem, which describes the unavoidable backaction of a measurement process to the quantum state under investigation, will be illustrated. Together with the discussion of different methods of quantum measurements, the optimal measurement instruments for binary qubit measurements will be derived. These optimal measurement instruments allow to perform a quantum measurement, providing a tunable amount of information about the quantum state, while avoiding any unnecessary disturbance to the state. This set of optimal instruments will be compared to other measurement schemes, such as measurements based on the optimal quantum cloning protocol.
Information processing based on the laws of quantum mechanics promises to be a revolutionary new avenue in information technology. This emerging field of quantum information processing (QIP) is however challenged by the fragile nature of the quantum bits (qubits) in which quantum information is stored and processed. An error in even a single qubit makes the quantum processor go off-track, corrupting the calculation as a whole. Therefore, the chance for an erroneous outcome increases with the number of qubits in the processor. Large-scale QIP thus hinges on the ability to correct for these errors. Classical information processing often uses error correction algorithms to identify errors by checking whether information is consistent in multiple copies. This strategy is unfortunately not applicable to QIP as quantum states cannot be copied. Moreover, direct measurements on qubits collapse their quantum states, reducing them to classical information. Fortunately, the theory of quantum error correction (QEC) overcomes these complications by encoding quantum information in entangled states of many qubits and performing parity measurements to identify errors in the system without destroying the encoded information. Implementing these codes is challenging as it requires many qubits and quick interleaving of operations and measurements. Moreover, to not introduce more errors in the system than QEC can solve for, these operations and measurements need to be of sufficient fidelity and speed...