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Copying information is an elementary operation in classical information processing. However, copying seems rather different in the quantum regime. Since the discovery of the universal quantum cloning machine, much has been found from the…

We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map…

If two parties share an unknown quantum state, one can ask how much quantum communication is needed for party A to send her share to party B. Recently, it was found that the number of qubits which should be sent is given by the conditional…

In his famous thought experiment, Wigner assigns an entangled state to the composite quantum system made up of Wigner's friend and her observed system. While the two of them have different accounts of the process, each Wigner and his friend…

Generically the probabilities of observational results depend upon both the quantum state and the rules for extracting the probabilities from it. It is often argued that inflation may make our observations independent of the quantum state.…

Although time is one of our most intuitive physical concepts, its understanding at the fundamental level is still an open question in physics. For instance, time in quantum mechanics and general relativity are two distinct and incompatible…

We consider state redistribution of a "hybrid" information source that has both classical and quantum components. The sender transmits classical and quantum information at the same time to the receiver, in the presence of classical and…

Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…

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…

It is argued that Feynman's rules for evaluating probabilities, combined with von Neumann's principle of psycho-physical parallelism, help avoid inconsistencies, often associated with quantum theory. The former allows one to assign…

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…

To maximize average information gain for a classical measurement, all outcomes of an observation must be equally likely. The condition of equally likely outcomes may be enforced in quantum theory by ensuring that one's state $\rho$ is…

We propose a new measure of quantum entanglement. Our measure is defined in terms of conditional information transmission for a Quantum Bayesian Net. We show that our measure is identically equal to the Entanglement of Formation in the case…

Two schemes for sharing an arbitrary two-qubit state based on entanglement swapping are proposed with Bell-state measurements and local unitary operations. One is based on the quantum channel with four Einstein-Podolsky-Rosen (EPR) pairs…

The breakthrough of quantum error correction brought with it the picture of quantum information as a sort of combination of two complementary types of classical information, "amplitude" and "phase". Here I show how this intuition can be…

The quantum decision theory is examined in its simplest form of two-condition two-choice setting. A set of inequalities to be satisfied by any quantum conditional probability describing the decision process is derived. Experimental data…

In quantum information theory it is generally accepted that quantum mutual information is an information-theoretic measure of total correlations of a bipartite quantum state. We argue that there exist quantum states for which quantum mutual…

It is widely known that `collapse of the wave function' on a quantum system A may be brought about by an interaction with another quantum system B. We will prove that this is not just a possible, but a necessary consequence of information…

This is an attempt to create a consistent and non-trivial extension of quantum theory, describing in detail the quantum measurement process. A tentative but concrete model is presented, based on the concept of multiple…

We analyze a quantum measurement where the apparatus is initially in a mixed state. We show that the amount of information gained in a measurement is not equal to the amount of entanglement between the system and the apparatus, but is…