Related papers: No-Cloning in Reduced Power Algebras
A large number of physicists now admit that quantum mechanics is a non local theory. The EPR argument and the many experiments (including recent loop-hole free tests) showing the violation of Bell's inequalities seem to have confirmed…
We propose a notion of quantum control in a quantum programming language which permits the superposition of finitely many quantum operations without performing a measurement. This notion takes the form of a conditional construct similar to…
The power and expressivity of deep classical neural networks can be attributed to non-linear input-output relations. Such non-linearities are at the heart of many computational tasks, such as data classification and pattern recognition.…
Lie groups and quantum algebras are connected through their common universal enveloping algebra. The adjoint action of Lie group on its algebra is naturally extended to related q-algebra and q-coalgebra. In such a way, quantum structure can…
It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded…
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…
In Shannon information theory the capacity of a memoryless communication channel cannot be increased by the use of feedback. In quantum information theory the no-cloning theorem means that noiseless copying and feedback of quantum…
Analogue computers use continuous properties of physical system for modeling. In the paper is described possibility of modeling by analogue quantum computers for some model of data analysis. It is analogue associative memory and a formal…
We prove generic versions of the no-cloning and no-broadcasting theorems, applicable to essentially {\em any} non-classical finite-dimensional probabilistic model that satisfies a no-signaling criterion. This includes quantum theory as well…
We study the non-singlet sectors of matrix quantum mechanics (MQM) through an operator algebra which generates the spectrum. The algebra is a nonlinear extension of the W_\infty algebra where the nonlinearity comes from the angular part of…
Quantum non-locality is normally defined via violations of Bell's inequalities that exclude certain classical hidden variable theories from explaining quantum correlations. Another definition of non-locality refers to the wave-function…
Boundedness and compactness properties of multiplication operators on quantum (non-commutative) function spaces are investigated. For endomorphic multiplication operators these properties can be characterized in the setting of quantum…
One perspective on quantum algorithms is that they are classical algorithms having access to a special kind of memory with exotic properties. This perspective suggests that, even in the case of quantum algorithms, the control flow notions…
We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
The no-cloning theorem asserts that, unlike classical information, quantum information cannot be copied. This seemingly undesirable phenomenon is harnessed in quantum cryptography. Uncloneable cryptography studies settings in which the…
An interesting concept in quantum computation is that of global control (GC), where there is no need to manipulate qubits individually. One can implement a universal set of quantum gates on a one-dimensional array purely via signals that…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability…
In spite of their evident logical character, particle statistics symmetries are not among the inherently quantum features exploited in quantum computation. A difficulty may be that, being a constant of motion of a unitary evolution, a…