Related papers: The "mean king's problem" with continuous variable…
The Mean King's problem asks to determine the outcome of a measurement that is randomly selected from a set of complementary observables. We review this problem and offer a combinatorial solution. More generally, we show that whenever an…
Mean king's problem is a kind of quantum state discrimination problems. In the problem, we try to discriminate eigenstates of noncommutative observables with the help of classical delayed information. The problem has been investigated from…
In quantum theory, the retrodiction problem is not as clear as its classical counterpart because of the uncertainty principle of quantum mechanics. In classical physics, the measurement outcomes of the present state can be used directly for…
The mean king problem is a quantum mechanical retrodiction problem, in which Alice has to name the outcome of an ideal measurement on a d-dimensional quantum system, made in one of (d+1) orthonormal bases, unknown to Alice at the time of…
In the King's Problem, a physicist is asked to prepare a d-state quantum system in any state of her choosing and give it to a king who measures one of (d+1) sets of mutually unbiased observables on it. The physicist is then allowed to make…
Conventional solutions to the (Mean) King's problem without using entanglement have been investigated by Aravind [P. K. Aravind, ``Best conventional solutions to the King's problem'', Z. Naturforsch. 58a, 682 (2003)]. We report that the…
The mean King problem is a conditional retrodiction problem. In this problem Alice prepares a two prime-dimensional particles state and avails one of the particles to the King who measures its state in one of mutually unbiased bases of his…
The predictive performance of any inferential model is critical to its practical success, but quantifying predictive performance is a subtle statistical problem. In this paper I show how the natural structure of any inferential problem…
The problem is that of sequential probability forecasting for finite-valued time series. The data is generated by an unknown probability distribution over the space of all one-way infinite sequences. It is known that this measure belongs to…
In 1987, Vaidman, Aharanov, and Albert put forward a puzzle called the Mean King's Problem (MKP) that can be solved only by harnessing quantum entanglement. Prime-powered solutions to the problem have been shown to exist, but they have not…
Selective inference is the problem of giving valid answers to statistical questions chosen in a data-driven manner. A standard solution to selective inference is simultaneous inference, which delivers valid answers to the set of all…
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…
The problem of inferring the outcome of a simultaneous measurement of two non-commuting observables is addressed. We show that for certain pairs with dense spectra, precise inferences of the measurement outcomes are possible in pre-and…
We study a generic principal-agent problem in continuous time on a finite time horizon. We introduce a framework in which the agent is allowed to employ measure-valued controls and characterise the continuation utility as a solution to a…
Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations…
The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required…
We consider the problem of predicting values of a random process or field satisfying a linear model $y(x)=\theta^\top f(x) + \varepsilon(x)$, where errors $\varepsilon(x)$ are correlated. This is a common problem in kriging, where the case…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
We show how one can ascertain the values of a complete set of mutually complementary observables of a prime degree of freedom.