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The quantum theory of measurement has been a matter of debate for over eighty years. Most of the discussion has focused on theoretical issues with the consequence that operational prescriptions, which are integral to experimental physics,…

A long-standing problem in quantum physics is to determine the minimal number of measurement bases required for the complete characterization of unknown quantum states, a question of particular relevance to high-dimensional quantum…

Experimental determination of an unknown quantum state usually requires several incompatible measurements. However, it is also possible to determine the full quantum state from a single, repeated measurement. For this purpose, the quantum…

Uncertainty principle is an inherent nature of quantum system that undermines the precise measurement of incompatible observables and hence the applications of quantum theory. Entanglement, another unique feature of quantum physics, was…

A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…

We prove the expected disturbance caused to a quantum system by a sequence of randomly ordered two-outcome projective measurements is upper bounded by the square root of the probability that at least one measurement in the sequence accepts.…

We investigate optimal encoding and retrieval of digital data, when the storage/communication medium is described by quantum mechanics. We assume an m-ary alphabet with arbitrary prior distribution, and an n-dimensional quantum system.…

Classical measurement strategies in many areas are approaching their maximum resolution and sensitivity levels, but these levels often still fall far short of the ultimate limits allowed by the laws of physics. To go further, strategies…

A central challenge in quantum metrology is identifying optimal measurements that saturate the quantum Cramer-Rao bound under realistic constraints, e.g., local measurements. We show that symmetries of the probe state provide a general…

We study the optimal way to estimate the quantum expectation value of a physical observable when a finite number of copies of a quantum pure state are presented. The optimal estimation is determined by minimizing the squared error averaged…

In consistent history quantum theory, a description of the time development of a quantum system requires choosing a framework or consistent family, and then calculating probabilities for the different histories which it contains. It is…

State discrimination is a useful test problem with which to clarify the power and limitations of different classes of measurement. We consider the problem of discriminating between given states of a bi-partite quantum system via sequential…

In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it…

Theory and experiment both demonstrate that an entangled quantum state of two subsystems is neither a superposition of states of its subsystems nor a superposition of composite states but rather a coherent superposition of nonlocal…

In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…

We propose a simple abstract formalisation of the act of observation, in which the system and the observer are assumed to be in a pure state and their interaction deterministically changes the states such that the outcome can be read from…

We provide optimal measurement schemes for estimating relative parameters of the quantum state of a pair of spin systems. We prove that the optimal measurements are joint measurements on the pair of systems, meaning that they cannot be…

We identify a universal structural principle underlying the smoothing of classical divergences: the optimizer of the smoothing problem is a clipped probability vector, independently of the specific divergence. This yields a…

The measurement process of observables in a quantum system comes out to be an unsovable problem which started in the early times of the development of the theory. In the present note we consider the measured system part of an open system…

A pivotal task in quantum metrology, and quantum parameter estimation in general, is to de- sign schemes that achieve the highest precision with given resources. Standard models of quantum metrology usually assume the dynamics is fixed, the…