Related papers: No-Cloning in Reduced Power Algebras
It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…
We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural…
A generalized universal quantum cloning machine is proposed which allows the input to be arbitrary states in symmetric subspace. And it reduces to the universal quantum cloning machine (UQCM) if the input are identical pure states. The…
Non-Fock representations of the canonical commutation relations modeled over an infinite-dimensional nuclear space are constructed in an explicit form. The example of the nuclear space of smooth real functions of rapid decrease results in…
The algebra of constraints arising in the canonical quantization of N=1 supergravity in four dimensions is investigated. Using the holomorphic action, the structure functions of the algebra are given and it is shown that the algebra does…
The "Power of One Qubit" refers to a computational model that has access to only one pure bit of quantum information, along with n qubits in the totally mixed state. This model, though not as powerful as a pure-state quantum computer, is…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
Possibility of state cloning is analyzed in two types of generalizations of quantum mechanics with nonlinear evolution. It is first shown that nonlinear Hamiltonian quantum mechanics does not admit cloning without the cloning machine. It is…
The concept of a clone is central to many branches of mathematics, such as universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is a category with two objects such that one is a countably infinite power of the other.…
The quantum analogs of the N-dimensional Cayley-Klein spaces with different combinations of quantum and Cayley-Klein structures are described for non-minimal multipliers, which include the first and the second powers of contraction…
The topic area of this paper parameterized quantum circuits (quantum neural networks) which are trained to estimate a given function, specifically the type of circuits proposed by Mitarai et al. (Phys. Rev. A, 2018). The input is encoded…
Amplitudes are the major logical object in Quantum Theory. Despite this fact they presents no physical reality and in consequence only observables can be experimetally checked. We discuss the possibility of a theory of Quantum Probabilities…
For a quiver with potential, we can associate a vanishing cycle to each representation space. If there is a nice torus action on the potential, the vanishing cycles can be expressed in terms of truncated Jacobian algebras. We study how…
A number of noncontextual models exist which reproduce different subsets of quantum theory and admit a no-cloning theorem. Therefore, if one chooses noncontextuality as one's notion of classicality, no-cloning cannot be regarded as a…
Quantum control is traditionally expressed through bilinear models and their associated Lie algebra controllability criteria. But, the first order approximation are not always sufficient and higher order developpements are used in recent…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classical case, both the measures and the positive definite kernels…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…