Aspects of mutually unbiased bases in odd prime power dimensions

We rephrase the Wootters-Fields construction [Ann. Phys., {\bf 191}, 363 (1989)] of a full set of mutually unbiased bases in a complex vector space of dimensions $N=p^r$, where $p$ is an odd prime, in terms of the character vectors of the cyclic group $G$ of order $p$. This form may be useful in explicitly writing down mutually unbiased bases for $N=p^r$.Comment: 3 pages, latex, no figure

Quantum-Matter-Spacetime : Peter Mittelstaedt's Contributions to Physics and Its Foundations

In a period of over 50 years, Peter Mittelstaedt has made substantial and lasting contributions to several fields in theoretical physics as well as the foundations and philosophy of physics. Here we present an overview of his achievements in physics and its foundations which may serve as a guide to the bibliography (printed in this Festschrift) of his publications. An appraisal of Peter Mittelstaedt's work in the philosophy of physics is given in a separate contribution by B. Falkenburg

Comment on "Quantitative wave-particle duality in multibeam interferometers"

In a recent paper [Phys. Rev. {\bf A64}, 042113 (2001)] S. D\"urr proposed an interesting multibeam generalization of the quantitative formulation of interferometric wave-particle duality, discovered by Englert for two-beam interferometers. The proposed generalization is an inequality that relates a generalized measure of the fringe visibility, to certain measures of the maximum amount of which-way knowledge that can be stored in a which-way detector. We construct an explicit example where, with three beams in a pure state, the scheme proposed by D\"{u}rr leads to the possibility of an ideal which-way detector, that can achieve a better path-discrimination, at the same time as a better fringe visibility. In our opinion, this seems to be in contrast with the intuitive idea of complementarity, as it is implemented in the two-beams case, where an increase in path discrimination always implies a decrease of fringe visibility, if the beams and the detector are in pure states.Comment: 4 pages, 1 encapsulated figure. In press on Phys. Rev.

A single photon produces general W state of N qubits and its application

Based on the Wu's scheme[1], We prepare the general N-qubit W state. We find that the concurrence of two qubits in general N-qubit W state is only related to their coefficients and we successfully apply the general N-qubit W state to quantum state transfer and quantum state prepare like that in two-qubit system

Quantum State Reconstruction of Many Body System Based on Complete Set of Quantum Correlations Reduced by Symmetry

We propose and study a universal approach for the reconstruction of quantum states of many body systems from symmetry analysis. The concept of minimal complete set of quantum correlation functions (MCSQCF) is introduced to describe the state reconstruction. As an experimentally feasible physical object, the MCSQCF is mathematically defined through the minimal complete subspace of observables determined by the symmetry of quantum states under consideration. An example with broken symmetry is analyzed in detail to illustrate the idea.Comment: 10 pages, n figures, Revte

Entanglement sharing among qudits

Consider a system consisting of n d-dimensional quantum particles (qudits), and suppose that we want to optimize the entanglement between each pair. One can ask the following basic question regarding the sharing of entanglement: what is the largest possible value Emax(n,d) of the minimum entanglement between any two particles in the system? (Here we take the entanglement of formation as our measure of entanglement.) For n=3 and d=2, that is, for a system of three qubits, the answer is known: Emax(3,2) = 0.550. In this paper we consider first a system of d qudits and show that Emax(d,d) is greater than or equal to 1. We then consider a system of three particles, with three different values of d. Our results for the three-particle case suggest that as the dimension d increases, the particles can share a greater fraction of their entanglement capacity.Comment: 4 pages; v2 contains a new result for 3 qudits with d=

Mutually unbiased binary observable sets on N qubits

The Pauli operators (tensor products of Pauli matrices) provide a complete basis of operators on the Hilbert space of N qubits. We prove that the set of 4^N-1 Pauli operators may be partitioned into 2^N+1 distinct subsets, each consisting of 2^N-1 internally commuting observables. Furthermore, each such partitioning defines a unique choice of 2^N+1 mutually unbiased basis sets in the N-qubit Hilbert space. Examples for 2 and 3 qubit systems are discussed with emphasis on the nature and amount of entanglement that occurs within these basis sets.Comment: 5 pages, 5 figures. Replacement - expanded introduction and conclusions; added reference

Multi-output programmable quantum processor

By combining telecloning and programmable quantum gate array presented by Nielsen and Chuang [Phys.Rev.Lett. 79 :321(1997)], we propose a programmable quantum processor which can be programmed to implement restricted set of operations with several identical data outputs. The outputs are approximately-transformed versions of input data. The processor successes with certain probability.Comment: 5 pages and 2 PDF figure

Distributed Relay Protocol for Probabilistic Information-Theoretic Security in a Randomly-Compromised Network

We introduce a simple, practical approach with probabilistic information-theoretic security to mitigate one of quantum key distribution's major limitations: the short maximum transmission distance (~200 km) possible with present day technology. Our scheme uses classical secret sharing techniques to allow secure transmission over long distances through a network containing randomly-distributed compromised nodes. The protocol provides arbitrarily high confidence in the security of the protocol, with modest scaling of resource costs with improvement of the security parameter. Although some types of failure are undetectable, users can take preemptive measures to make the probability of such failures arbitrarily small.Comment: 12 pages, 2 figures; added proof of verification sub-protocol, minor correction

Quantum Copying: Beyond the No-Cloning Theorem

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 quality of its output does not depend on the input. We also examine a machine which combines a unitary transformation with a selective measurement to produce good copies of states in a neighborhood of a particular state. We discuss the problem of measurement of the output states.Comment: RevTex, 26 pages, to appear in Physical Review