Related papers: Deriving quantum constraints and tight uncertainty…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
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…
Quantum mechanics traditionally places the observer outside of the system being studied and employs the Born interpretation. In this and related papers the observer is placed inside the system. To accomplish this, special rules are required…
Probabilities in quantum theory are traditionally given by Born's rule as the expectation values of projection operators. Here it is shown that Born's rule is insufficient in universes so large that they contain identical multiple copies of…
We show that the operational quantum formalism -- the Born rule, L\"uders state updating, quantum interference, non-Markovian effective dynamics, and Bell inequality violation at the Tsirelson bound $2\sqrt{2}$ -- arises within…
What does it take for real-deterministic c-valued (i.e., classical, commuting) variables to comply with the Heisenberg uncertainty principle? Here, we construct a class of real-deterministic c-valued variables out of the weak values…
We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all…
Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…
The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to…
The Born's rule introduces intrinsic randomness to the outcomes of a measurement performed on a quantum mechanical system. But, if the system is prepared in the eigenstate of an observable then the measurement outcome of that observable is…
The integral of the Wigner function over a subregion of the phase-space of a quantum system may be less than zero or greater than one. It is shown that for systems with one degree of freedom, the problem of determining the best possible…
For a pair of observables, they are called "incompatible", if and only if the commutator between them does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the…
We introduce a hierarchy of conditions necessarily satisfied by any distribution P(ab) representing the probabilities for two separate observers to obtain outcomes a and b when making local measurements on a shared quantum state. Each…
We propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum clock. This allows us to bypass some of the problems of previous proposals, and to obtain a Hermitian time of arrival operator whose probability…
Quantum decision theory is introduced here, and new basis for this theory is proposed. It is first based upon the author's general arguments for the Hilbert space formalism in quantum theory, next on arguments for the Born rule, that is,…
Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal…
If conscious observers are to be included in the quantum mechanical universe, we need to find the rules that engage observers with quantum mechanical systems. The author has proposed five rules that are discovered by insisting on empirical…
The Born rule assigns a probability to any possible outcome of a quantum measurement, but leaves open the question how these probabilities are to be interpreted and, in particular, how they relate to the outcome observed in an actual…
Consider the question: what statistical ensemble corresponds to minimal prior knowledge about a quantum system ? For the case where the system is in fact known to be in a pure state there is an obvious answer, corresponding to the unique…
In quantum mechanics, predictions are made by way of calculating expectation values of observables, which take the form of Hermitian operators. It is far less common to exploit non-Hermitian operators to perform measurements. Here, we show…