Related papers: Guesswork of a quantum ensemble
The quantum guesswork quantifies the minimum number of queries needed to guess the state of a quantum ensemble if one is allowed to query only one state at a time. Previous approaches to the computation of the guesswork were based on…
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…
The characterization of the quantum ensemble is a fundamental issue in quantum information theory and foundations. The ensemble is also useful for various quantum information processing. To characterize the quantum ensemble, in this…
What is the minimum number of guesses needed on average to correctly guess a realization of a random variable? The answer to this question led to the introduction of the notion of a quantity called guesswork by Massey in 1994, which can be…
The guesswork of a classical-quantum channel quantifies the cost incurred in guessing the state transmitted by the channel when only one state can be queried at a time, maximized over any classical pre-processing and minimized over any…
For a mixed quantum state with density matrix $\rho$ there are infinitely many ensembles of pure quantum states, which average to $\rho$. Starting from Laplace principle of insufficient reason (not to give \emph{a priori} preference to any…
Non-orthogonal quantum states pose a fundamental challenge in quantum information processing, as they cannot be distinguished with absolute certainty. Conventionally, the focus has been on minimizing error probability in quantum state…
The guesswork is an information-theoretic quantity which can be seen as an alternate security criterion to entropy. Recent work has established the theoretical framework for guesswork in the presence of quantum side information, which we…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to determine the states. This can be viewed as a kind of quantum state learning…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…
Error probability is a popular and well-studied optimization criterion in discriminating non-orthogonal quantum states. It captures the threat from an adversary who can only query the actual state once. However, when the adversary is able…
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are…
We consider the problem of determining the weights of a quantum ensemble. That is to say, given a quantum system that is in a set of possible known states according to an unknown probability law, we give strategies to estimate the…
The maximum-likelihood principle unifies inference of quantum states and processes from experimental noisy data. Particularly, a generic quantum process may be estimated simultaneously with unknown quantum probe states provided that…
We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a quantum measurement minimizing the…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…
We discuss single adaptive measurements for the estimation of mixed quantum states of qubits. The results are compared to the optimal estimation schemes using collective measurements. We also demonstrate that the advantage of collective…