Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Computer and Systems Sciences International

Computations on quantum computers based on non-classic probability theory

N. N. Popov, Владимир Иванович Цурков

Published Nov 1, 2014• 1 citation
Publisher

Abstract

Principal concepts of quantum probability theory are considered. Some properties of a priori and a posteriori quantum probabilities are studied. Concepts of regular and nondestructive measurement procedures are analyzed. Effects associated with compatibility and lack of correlation of quantum procedures are studied. Markov sequences of quantum procedures for quantum systems with finite or countable number of states is defined. The computation process on the n -qubit quantum computer is showed to represent operations that obey laws of quantum probability theory.

DOI
10.1134/s1064230714060100

Related papers

Quantum computations and non-classical Markov processes

В. Ю. Игнатьев, Мороз Ирина Игоревна, N. N. Popov +1 more

Random quantum processes with a countable set of elementary orthogonal events that govern the operation of a quantum computer are discussed. For the case of pure states, expressions for a posteriori quantum probabilities are derived. For stationary and nonstationary random quantum processes with the countable set of states, properties of transition quantum probabilities are investigated. A method for finding a posteriori quantum probabilities is proposed. An analog of the Kolmogorov equation for random quantum processes is presented.

Journal of Computer and Systems Sciences International•Mar 1, 2015•0 citations

Conditional Probability and A Posteriori States in Quantum Mechanics

Masanao Ozawa

In order to develop a statistical theory of quantum measurements including continuous observables, a concept of a posteriori states is introduced, which generalizes the notion of regular conditional probability distributions in classical probability theory. Its statistical interpretation in measuring processes is discussed and its existence is proved. As an application, we also give a complete proof of the Davies-Lewis conjecture that there are no (weakly) repeatable instruments for non-discrete observables in the standard formulation of quantum mechanics, using the notion of a posteriori states.

Publications of the Research Institute for Mathematical Sciences•Apr 30, 1985•99 citations

Introduction to Quantum Algorithms

Santanu Pattanayak

In 1981 Richard Feynman proposed the idea that a computer built of quantum mechanical elements obeying quantum mechanical laws can perform efficient simulations of quantum systems. Quantum computing works on the laws of quantum mechanical properties such as superposition, entanglement, and interference. Unlike in classical computing, in quantum computers a register can exist in all possible states at once due to its superposition properties. It is only when a quantum system is measured that we observe one of the possible states. Such a system is advantageous since, when measured, each state can appear with a certain probability encoded in the state prior to the measurement. Quantum computing works by increasing the probability of the desired state to a sufficiently high value so that the desired state can be obtained with high confidence with a minimal number of measurements. In this regard, quantum interference, which results from quantum superposition, plays a big role since it allows probability amplitudes corresponding to a given state to interfere and cancel each other. This property of quantum interference biases the measurement to a set of states that we desire as the outcome of quantum algorithms. Similarly, quantum entanglement allows one to create a strong correlation between quantum objects, especially qubits, to the advantage of quantum algorithms, as you will see throughout this chapter.

Apress eBooks•Jan 1, 2021•1 citation

Quantum probability and quantum decision making

Vyacheslav I. Yukalov, Didier Sornette

A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary.

arXiv:1601.02480•Jan 11, 2016•0 citations

Constructor theory of information

David Deutsch, Chiara Marletto

We propose a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible—i.e. in constructor-theoretic terms. It includes conjectured, exact laws of physics expressing the regularities that allow information to be physically instantiated. Although these laws are directly about information, independently of the details of particular physical instantiations, information is not regarded as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone. This theory solves a problem at the foundations of existing information theory, namely that information and distinguishability are each defined in terms of the other. It also explains the relationship between classical and quantum information, and reveals the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, including the lack of in-principle distinguishability of some states, the impossibility of cloning, the existence of pairs of variables that cannot simultaneously have sharp values, the fact that measurement processes can be both deterministic and unpredictable, the irreducible perturbation caused by measurement, and locally inaccessible information (as in entangled systems).

arXiv:1405.5563•Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences•Dec 17, 2014•112 citations

Quantum Probability and Quantum Decision Making

Vyacheslav I. Yukalov, Didier Sornette

A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary.

•Jan 11, 2016•1 citation
Principal concepts of quantum probability theory are considered. Some properties of a priori and a posteriori quantum probabilities are studied. Concepts of regular and nondestructive measurement procedures are analyzed. Effects associated with compatibility and lack of correlation of quantum procedures are studied. Markov sequences of quantum procedures for quantum systems with finite or countable number of states is defined. The computation process on the n -qubit quantum computer is showed to represent operations that obey laws of quantum probability theory.
Random quantum processes with a countable set of elementary orthogonal events that govern the operation of a quantum computer are discussed. For the case of pure states, expressions for a posteriori quantum probabilities are derived. For stationary and nonstationary random quantum processes with the countable set of states, properties of transition quantum probabilities are investigated. A method for finding a posteriori quantum probabilities is proposed. An analog of the Kolmogorov equation for random quantum processes is presented.
In order to develop a statistical theory of quantum measurements including continuous observables, a concept of a posteriori states is introduced, which generalizes the notion of regular conditional probability distributions in classical probability theory. Its statistical interpretation in measuring processes is discussed and its existence is proved. As an application, we also give a complete proof of the Davies-Lewis conjecture that there are no (weakly) repeatable instruments for non-discrete observables in the standard formulation of quantum mechanics, using the notion of a posteriori states.
In 1981 Richard Feynman proposed the idea that a computer built of quantum mechanical elements obeying quantum mechanical laws can perform efficient simulations of quantum systems. Quantum computing works on the laws of quantum mechanical properties such as superposition, entanglement, and interference. Unlike in classical computing, in quantum computers a register can exist in all possible states at once due to its superposition properties. It is only when a quantum system is measured that we observe one of the possible states. Such a system is advantageous since, when measured, each state can appear with a certain probability encoded in the state prior to the measurement. Quantum computing works by increasing the probability of the desired state to a sufficiently high value so that the desired state can be obtained with high confidence with a minimal number of measurements. In this regard, quantum interference, which results from quantum superposition, plays a big role since it allows probability amplitudes corresponding to a given state to interfere and cancel each other. This property of quantum interference biases the measurement to a set of states that we desire as the outcome of quantum algorithms. Similarly, quantum entanglement allows one to create a strong correlation between quantum objects, especially qubits, to the advantage of quantum algorithms, as you will see throughout this chapter.
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary.
We propose a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible—i.e. in constructor-theoretic terms. It includes conjectured, exact laws of physics expressing the regularities that allow information to be physically instantiated. Although these laws are directly about information, independently of the details of particular physical instantiations, information is not regarded as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone. This theory solves a problem at the foundations of existing information theory, namely that information and distinguishability are each defined in terms of the other. It also explains the relationship between classical and quantum information, and reveals the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, including the lack of in-principle distinguishability of some states, the impossibility of cloning, the existence of pairs of variables that cannot simultaneously have sharp values, the fact that measurement processes can be both deterministic and unpredictable, the irreducible perturbation caused by measurement, and locally inaccessible information (as in entangled systems).
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary.