On measurements of the parameters of a quantum random process

Scott Roger Shepard

Олексій Нарєжній, Daniel Jancarczyk, І.Д. Горбенко +2 more

The object of research is the process of mutual synchronization of quantum random number generators (QRNG) in the group standard of quantum noise. A method for generating random numbers is proposed, which relates to the methods of group standardization of the QRNG, and is used to increase the speed and reliability of the random number formation The paper substantiates the mathematical model of quantum phase noise of the QRNG group, which are in a mutual synchronization mode. The method is based on solving the problem of identifying parameters of a group of the same type to the QRNG in the mutual synchronization mode. The solution to this problem requires the availability of reliable and operational data when calculating the Kalman filter parameters necessary for estimating the synchronization parameters of quantum measures of phase noise. The results of experimental studies presented in the article are an example of building a QRNG with a given level of reliability and speed. A feature of the proposed QRNG quantum phase noise measurement system is the synchronization of processing time using GPS signals (Ll C/A).

Aleksei M. Aleshin, Nikitin, Vladimir V., P. I. Pronin

In quantum mechanics, randomness is postulated as a separate axiom. De Broglie's theory allows one to reproduce quantum phenomena from completely deterministic formalism. But the question of the quantum randomness emergency in the de Broglie-Bohm theory needs special attention. In the work [G. Tastevin, F. Laloë, Comptes Rendus. Physique, 2021, 22, 1, pp. 99-116], it was shown that it arises as a result of the device microscopic state influence on the measurement result. In our work, we investigate the genesis of the quantum randomness in the de Broglie's theory in more details. Namely, we investigate the target system and the device behaviour in the decoherence process and model the measurement of canonical-conjugate observables. We propose a thought experiment which tests the opportunity of the information transition using beable-parameters violating the uncertainty relation. We show that in the measurement process, the strong stochastic fluctuations of beable parameters arise randomising the system in accordance with the uncertainty relation. Nevertheless, we find anomalous models of measurement in which these fluctuations can be neglected. These special models require further investigation.

Z. Ficek, R. Tanaś

Shawn Geller, Tongyu Zhao, Alex Kwiatkowski +3 more

A common problem with physical qubits is that the state can leak outside the computational subspace. To characterize the problem, it is desirable to measure both the leakage probability and the fidelity of gates inside the computational subspace. Randomized benchmarking is a readily accessible method for estimating average gate fidelities and can be modified to account for leakage. However, in the presence of state preparation and measurement errors (SPAM) there are parameter degeneracies, and fidelities and leakage become underdetermined. We study the example of qudits with any number of leakage levels under the assumption of gate-independent noise. We show that randomized benchmarking sequences with leakage level decoherence can be analyzed as a Markov process with noisy classical preparations and measurements. This result generalizes to randomized benchmarking with random gates from an arbitrary group that contains a phase-decohering subgroup. We characterize the parameter degeneracy in inferring the Markov process, preparations and measurements. Based on this characterization we develop a measurement and inference method taking advantage of known conservative bounds on SPAM to constrain fidelity, leakage and other parameters of the Markov process, state preparations and measurements. As part of our study, we experimentally implemented the measurement method for a qubit defined on the one-excitation subspace of two transmons, for which there are two leakage levels. We determined confidence intervals accounting for parameter degeneracy for a number of performance parameters of the system. For leakage and fidelity, we compare these intervals to those obtained for several conventional methods for leakage benchmarking.

Martin Varbanov, Todd A. Brun

One of the abstract concepts of measurement in quantum information theory is the \\textit{generalized measurement}, a special subclass of which is the \\textit{positive-operator value measurements}. A different paradigm of measurement comes from Quantum Optics, when one considers measurements continuous in time. Their natural description involves the concept of \\textit{a stochastic process}--a time-dependent random variable. In this paper we construct a \\textit{continuous} stochastic process to simulate any generalized measurement--in the long time limit it gives the same outcomes with the right probabilities as the measurement being simulated. This stochastic evolution takes the form of a random walk in a space of measurement parameters, and the continuous measurement process must in general take into account the outcomes of earlier measurements.