Relationship between subjecting the qubit to dynamical decoupling and to a sequence of projective measurements

Abstract

We consider a qubit coupled to another system (its environment), and discuss the relationship between the effects of subjecting the qubit to either a dynamical decoupling sequence of unitary operations, or a sequence of projective measurements. We give a formal statement concerning equivalence of a sequence of coherent operations on a qubit, precisely operations from a minimal set {1 1Q,σx}, and a sequence of projective measurements ofσx observable. Using it we show that when the qubit is subjected to n such successive projective measurements at certain times, the expectation value of the last measurement can be expressed as a linear combination of expectation values ofσx observed after subjecting the qubit to dynamical decoupling sequences of π pulses, with k ≤ n of them applied at subsets of these times. Performing a sequence of measurements on the qubit gives then the same information about qubit decoherence and dynamics of environment as that contained in dynamical decoupling signal. Analysing the latter has been widely used to gain information about the environmental dynamics (perform so-called noise spectroscopy), so our result shows how all the resuts obtained with dynamical decoupling based protocols are related to those that can be obtained just by performing multiple measurements on the qubit. We also discuss in more detail the application of the general result to the case of the qubit undergoing pure dephasing, and outline possible extensions to higher-dimensional (a qudit or multiple qubits) systems.arXiv:1907.05165v2 [quant-ph]

Thermalization processes induced by quantum monitoring in multi-level systems

“…The study of sequence of quantum measurements, especially projective ones, is broad and covers several topics, ranging from fundamental quantum physics and quantum Zeno phenomena [8][9][10][11][12][13][14][15][16][17][18], quantum metrology and sensing [19][20][21][22][23][24] to quantum thermodynamics [25][26][27][28][29][30][31][32][33][34][35][36][37], both at the theoretical and experimental level. An active line of research focused on the characterization of the thermodynamics principles ruling the statistics of the measurement outcomes, with several contributions making use of quantum fluctuation theorems and Jarzynski relations [38][39][40][41][42][43][44].…”

The quantum Zeno and anti-Zeno effects with driving fields in the weak and strong coupling regimes

“…Both the QZE and the QAZE have gained considerable interest theoretically and experimentally due to their huge importance in the foundations of quantum mechanics as well as possible applications in quantum technologies. For example, the effect of repeated measurements can be used to infer properties of the environment of a quantum system, that is, noise sensing 37 – 39 . Generally speaking, so far, the main focus of the studies performed on QZE and the QAZE have been on the population decay model 24 – 29 , 40 – 45 and the dephasing model 30 (notable exceptions include Refs.…”

Statistics of projective measurement on a quantum probe as a witness of noncommutativity of algebra of a probed system

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