Related papers: No-Cloning in Reduced Power Algebras
The no-cloning principle tells us that non-orthogonal quantum states cannot be cloned, but it does not tell us that orthogonal states can always be cloned. We suggest a situation where the cloning transformations are restricted, leading to…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
A brief review of various numerical techniques used in loop quantum cosmology and results is presented. These include the way extensive numerical simulations shed insights on the resolution of classical singularities, resulting in the key…
Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
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…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…
Two of the fundamental no-go theorems of quantum information are the no-cloning theorem (that it is impossible to make copies of general quantum states) and the no-teleportation theorem (the prohibition on telegraphing, or sending quantum…
Today's quantum processors composed of fifty or more qubits have allowed us to enter a computational era where the output results are not easily simulatable on the world's biggest supercomputers. What we have not seen yet, however, is…
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…
Refactoring is a crucial technique for improving the efficiency and maintainability of software by restructuring its internal design while preserving its external behavior. While classical programs have benefited from various refactoring…
We examine the toy model of modal quantum theory (MQT), an analogue of actual quantum theory based on finite fields. In particular, we investigate how several essential ``no-go'' results (for cloning, deleting and hiding processes) work in…
Linearity and unitarity are two fundamental tenets of quantum theory. Any consequence that follows from these must be respected in the quantum world. The no-cloning theorem and the no-deleting theorem are the consequences of the linearity…
Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the…
Clifford algebras are used for definition of spinors. Because of using spin-1/2 systems as an adequate model of quantum bit, a relation of the algebras with quantum information science has physical reasons. But there are simple mathematical…
The impossibility of perfectly copying (or cloning) an arbitrary quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate cloning have been found in many cases.…
Standard quantum mechanics employs complex Hilbert spaces, but whether complex numbers are fundamental or merely convenient has long been debated. For decades, real-valued equivalents were considered mathematically possible but cumbersome.…
Arbitrary quantum states cannot be copied. In fact, to make a copy we must provide complete information about the system. However, can a quantum system self-replicate? This is not answered by the no-cloning theorem. In the classical…
we envisage a novel quantum cloning machine, which takes an input state and produces an output state whose success branch can exist in a linear superposition of multiple copies of the input state and the failure branch exist in a…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…