Related papers: Past observable dynamics of a continuously monitor…

Weak quantum measurements enable real-time tracking and control of dynamical quantum systems, producing quantum trajectories -- evolutions of the quantum state of the system conditioned on measurement outcomes. For classical systems, the…

Tracking the dynamics of a quantum system is conventionally achieved by monitoring the system continuously in time and filtering the information contained in measurement records via the causal quantum trajectory approach. However, in…

Noisy unsharp measurements incorporated in quantum information protocols may hinder performance, reducing the quantum advantage. However, we show that, unlike projective measurements which completely destroy quantum correlations between…

We consider a quantum system continuously monitored in time which in turn is coupled to an arbitrary dissipative classical system (diagonal reduced density matrix). The quantum and classical dynamics can modify each other, being described…

We analyze the information that one can learn about the state of a quantum two-level system, i.e. a qubit, when probed weakly by a nearby detector. In particular, we focus on the case when the qubit Hamiltonian and the qubit's operator…

Extracting information efficiently from quantum systems is a major component of quantum information processing tasks. Randomized measurements, or classical shadows, enable predicting many properties of arbitrary quantum states using few…

Smoothing is an estimation method whereby a classical state (probability distribution for classical variables) at a given time is conditioned on all-time (both past and future) observations. Here we define a smoothed quantum state for a…

We present a new scheme to detect and visualize oscillations of a single quantum system in real time. The scheme is based upon a sequence of very weak generalized measurements, distinguished by their low disturbance and low information…

A generic qubit unitary operator affected by depolarizing noise is duplicated and inserted in a quantum switch process realizing a superposition of causal orders. The characterization of the resulting switched quantum channel is worked out…

Quantum instruments describe both the classical outcome and the updated state associated with a quantum measurement. We ask whether these processes can be simulated using only a natural subset of resources, namely projective measurements on…

The estimation of multi-qubit observables is a key task in quantum information science. The standard approach is to decompose a multi-qubit observable into a weighted sum of Pauli strings. The observable can then be estimated from…

Stationary quantum information sources emit sequences of correlated qudits -- that is, structured quantum stochastic processes. If an observer performs identical measurements on a qudit sequence, the outcomes are a realization of a…

A generic qubit unitary operator affected by quantum noise is duplicated and inserted in a coherently superposed channel, superposing two paths offered to a probe qubit across the noisy unitary, and driven by a control qubit. A…

The measurement of a quantum two-level system, or a qubit in modern terminology, often involves an electromagnetic field that interacts with the qubit, before the field is measured continuously and the qubit state is inferred from the noisy…

We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic processes with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary…

Learning problems involving quantum data are natural candidates for demonstrating an advantage in quantum machine learning. Recent results indicate that, for certain tasks and under noiseless conditions, coherent processing of quantum data…

Randomised measurements can efficiently characterise many-body quantum states by learning the expectation values of observables with low Pauli weights. In this paper, we generalise the theoretical tools of classical shadow tomography to the…

We investigate what can be concluded about a quantum system when sequential quantum measurements of its observable -- a prominent example of the so-called quantum stochastic process -- fulfill the Kolmogorov consistency condition and thus…

We analyze the problem of estimating past quantum states of a monitored system from a mathematical perspective in order to ensure self-consistency with the principle of quantum non-demolition. Despite several claims of ``measuring…

The quantum measurement process by a single-electron transistor or a quantum point contact coupled to a quantum bit is studied. We find a unified description of the statistics of the monitored quantity, the current, in the regime of strong…