Related papers: Estimating Pre- and Post-Selected Ensembles
Vaidman has proposed a controversial criterion for determining the past of a single quantum particle based on the "weak trace" it leaves. We here consider more general examples of entangled systems and analyze the past of single, as well as…
The projected ensemble -- an ensemble of pure states on a subsystem conditioned on projective measurement outcomes on its complement -- provides a finer probe of ergodicity and information structure than the reduced density matrix of the…
Monitored quantum circuits host a rich variety of exotic non-equilibrium phases. Among the most representative examples are measurement-induced phase transitions between distinct area-law entangled states. However, because these transitions…
We present a description of the measurement process based on the parametric representation with environmental coherent states. This representation is specifically tailored for studying quantum systems whose environment needs being…
Statistical postprocessing is used to translate ensembles of raw numerical weather forecasts into reliable probabilistic forecast distributions. In this study, we examine the use of permutation-invariant neural networks for this task. In…
Given an arbitrary measurement over a system of interest, the outcome of a posterior measurement can be used for improving the statistical estimation of the system state after the former measurement. Here, we realize an…
Smoothing is a technique for estimating the state of an imperfectly monitored open system by combining both prior and posterior measurement information. In the quantum regime, current approaches to smoothing either give unphysical outcomes,…
In this paper, we present a thought experiment that demonstrates that the equivalence of quantum reduced states and statistical mixed states of ensembles is not merely a simple mathematical formulation in quantum mechanics, but rather…
Throughout quantum mechanics there is statistical balance, in the collective response of an ensemble of systems to differing measurement types. Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical…
We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…
What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a…
The evolution of a measured system and an experimental apparatus is presented in an unified form. Conditions under which the state of such a total system forms, evaluates and declines from a superposition of states are defined. The problem…
In this article, we present a detailed analysis of two famous delayed choice experiments: Wheeler's classic gedanken-experiment and the delayed quantum eraser. Our analysis shows that the outcomes of both experiments can be fully explained…
Quantum technology has the potential to revolutionize how we acquire and process experimental data to learn about the physical world. An experimental setup that transduces data from a physical system to a stable quantum memory, and…
Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this…
We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias…
The guesswork quantifies the minimum cost incurred in guessing the state of an ensemble, when only one state can be queried at a time. In the classical case, it is well known that the optimal strategy trivially consists of querying the…
We explore the possibility of using "weak measurements" without "weak value" for quantum state estimation. Since for weak measurements the disturbance caused during each measurement is small, we can rescue the state, unlike for the case of…
We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically…
In former work, we showed that a quantum algorithm is the sum over the histories of a classical algorithm that knows in advance 50% of the information about the solution of the problem - each history is a possible way of getting the…