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The problem of quantum state reduction in the process of measurement has attracted attention of almost everyone who created, developed or explained quantum physics to the students. Absence of a solution is the basis for the statement that…

We analyze to what extent it is possible to copy arbitrary states of a two-level quantum system. We show that there exists a "universal quantum copying machine", which approximately copies quantum mechanical states in such a way that the…

A physicists' explanation of why thou shalt not clone one bit gives a stronger version of Conway and Kochen's theorem.

A family of quantum cloning machines is introduced that produce two approximate copies from a single quantum bit, while the overall input-to-output operation for each copy is a Pauli channel. A no-cloning inequality is derived, describing…

We discuss the possibility of creating money that is physically impossible to counterfeit. Of course, "physically impossible" is dependent on the theory that is a faithful description of nature. Currently there are several proposals for…

It is well known that (non-orthogonal) pure states cannot be cloned so one may ask: how much or what kind of additional (quantum) information is needed to supplement one copy of a quantum state in order to be able to produce two copies of…

Quantum cloning is a fundamental protocol of quantum information theory. Perfect universal quantum cloning is prohibited by the laws of quantum mechanics, only imperfect copies being reachable. Symmetric quantum cloning is concerned with…

It is shown that any quantum operation that perfectly clones the entanglement of all maximally-entangled qubit pairs cannot preserve separability. This ``entanglement no-cloning'' principle naturally suggests that some approximate cloning…

We introduce an approach to quantum cloning based on spin networks and we demonstrate that phase covariant cloning can be realized using no external control but only with a proper design of the Hamiltonian of the system. In the 1 -> 2…

We review a possible framework for (non)linear quantum theories, into which linear quantum mechanics fits as well, and discuss the notion of ``equivalence'' in this setting. Finally, we draw the attention to persisting severe problems of…

We develop a theory of the algorithmic information in bits contained in an individual pure quantum state. This extends classical Kolmogorov complexity to the quantum domain retaining classical descriptions. Quantum Kolmogorov complexity…

The paper has been withdrawn by the author due to unhappy mistake in the initial scope of the work.

Cloning machines, that is, transformations that achieve the best approximate copying of a quantum state compatible with the no-cloning theorem, have been a fundamental research topic over the last five years. This study is of particular…

We propose the concept of pseudorandom states and study their constructions, properties, and applications. Under the assumption that quantum-secure one-way functions exist, we present concrete and efficient constructions of pseudorandom…

Incompatibility is a feature of quantum theory that sets it apart from classical theory, and the inability to clone an unknown quantum state is one of the most fundamental instances. The no-hiding theorem is another such instance that…

Since its origins, Quantum mechanics has presented problems with the concept of individuality. It is argued that quantum particles do not have individuality, and so, one can speak about "entities without identity". On the contrary, we claim…

No-Cloning and No-Deleting theorems are verified with the constraint on local state transformations via the existence of incomparable states. Assuming the existence of exact cloning or deleting operation defined on a minimum number of two…

Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM

In a recent paper [2], Chang et al. have proposed studying "Quantum $\mathbb{F}_{un}$": the $q \mapsto 1$ limit of Modal Quantum Theories over finite fields $\mathbb{F}_q$, motivated by the fact that such limit theories can be naturally…

A family of asymmetric cloning machines for $N$-dimensional quantum states is introduced. These machines produce two imperfect copies of a single state that emerge from two distinct Heisenberg channels. The tradeoff between the quality of…