Related papers: The Prime state and its quantum relatives

We propose a quantum circuit that creates a pure state corresponding to the quantum superposition of all prime numbers less than 2^n, where n is the number of qubits of the register. This Prime state can be built using Grover's algorithm,…

Large series of prime numbers can be superposed on a single quantum register and then analyzed in full parallelism. The construction of this Prime state is efficient, as it hinges on the use of a quantum version of any efficient primality…

The states of the qubit, the basic unit of quantum information, are $2 \times 2$ positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of…

We explore the connection between quantum entanglement and the exchange symmetry of the states of N identical particles. Each particle has n-levels. The N particles span the nN dimensional Hilbert space. We shall call the general state of…

We provide a group-theoretical classification of the entangled states of N identical particles. The connection between quantum entanglement and the exchange symmetry of the states of N identical particles is made explicit using the duality…

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 develop a representation of an n-qubit register that parameterizes its statevector as a series of nested entanglements. We show that the recursive substructure of this representation provides a natural framework for automating the…

Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…

We present a mapping which associates pure N-qubit states with a polynomial. The roots of the polynomial characterize the state completely. Using the properties of the polynomial we construct a way to determine the separability and the…

We develop an approach where the quantum system states and quantum observables are described as in classical statistical mechanics -- the states are identified with probability distributions and observables, with random variables. An…

We introduce the notions of quantum characteristic and quantum flatness for arbitrary rings. More generally, we develop the theory of quantum integers in a ring and show that the hypothesis of quantum flatness together with positive quantum…

Quantum entanglement and its paradoxical properties hold the key to an information processing revolution. Much attention has focused recently on the challenging problem of characterizing entanglement. Entanglement for a two qubit system is…

In a recent paper it has been shown how to create a quantum state related to the prime number sequence using Grover's algorithm. Moreover, its multiqubit entanglement was analyzed. In the present work, we compare the multiqubit entanglement…

It is shown that generic N-party pure quantum states (with equidimensional subsystems) are uniquely determined by their reduced states of just over half the parties; in other words, all the information in almost all N-party pure states is…

If a pure state of a qubit pair is developed over the four basis states, it is known that an equality between the four coefficients of that development exists if and only if that state is unentangled. This paper considers an arbitrary pure…

The cluster state model for quantum computation [Phys. Rev. Lett. 86, 5188] outlines a scheme that allows one to use measurement on a large set of entangled quantum systems in what is known as a cluster state to undertake quantum…

The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state is defined as the minimum average entanglement of an ensemble of pure…

The quantum orthogonal arrays define remarkable classes of multipartite entangled states called $k$-uniform states whose every reductions to $k$ parties are maximally mixed. We present constructions of quantum orthogonal arrays of strength…

A statistical analysis of the prime numbers indicates possible traces of quantum chaos. We have computed the nearest neighbor spacing distribution, number variance, skewness, and excess for sequences of the first N primes for various values…

A fundamental step of any quantum algorithm is the preparation of qubit registers in a suitable initial state. Often qubit registers represent a discretization of continuous variables and the initial state is defined by a multivariate…