Optimal Time-Reversal of Multi-phase Equatorial States

Even though the time-reversal is unphysical (it corresponds to the complex conjugation of the density matrix), for some restricted set of states it can be achieved unitarily, typically when there is a common de-phasing in a n-level system. However, in the presence of multiple phases (i. e. a different de-phasing for each element of an orthogonal basis occurs) the time reversal is no longer physically possible. In this paper we derive the channel which optimally approaches in fidelity the time-reversal of multi-phase equatorial states in arbitrary (finite) dimension. We show that, in contrast to the customary case of the Universal-NOT on qubits (or the universal conjugation in arbitrary dimension), the optimal phase covariant time-reversal for equatorial states is a nonclassical channel, which cannot be achieved via a measurement/preparation procedure. Unitary realizations of the optimal time-reversal channel are given with minimal ancillary dimension, exploiting the simplex structure of the optimal maps.Comment: 7 pages, minor change

On Quantum Algorithms

Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle) interferometers. We show how most known quantum algorithms, including quantum algorithms for factorising and counting, may be cast in this manner. Quantum searching is described as inducing a desired relative phase between two eigenvectors to yield constructive interference on the sought elements and destructive interference on the remaining terms.Comment: 15 pages, 8 figure

Quantum entanglement and classical communication through a depolarising channel

We analyse the role of entanglement for transmission of classical information through a memoryless depolarising channel. Using the isotropic character of this channel we prove analytically that the mutual information cannot be increased by encoding classical bits into entangled states of two qubits.Comment: 6 pages, 2 figures; contribution to special issue of JMO on the physics of quantum information; 2nd version: slight modifications and improved presentatio

Experimental Purification of Single Qubits

We report the experimental realization of the purification protocol for single qubits sent through a depolarization channel. The qubits are associated with polarization encoded photon particles and the protocol is achieved by means of passive linear optical elements. The present approach may represent a convenient alternative to the distillation and error correction protocols of quantum information.Comment: 10 pages, 2 figure

Entanglement production by quantum error correction in the presence of correlated environment

We analyze the effect of a quantum error correcting code on the entanglement of encoded logical qubits in the presence of a dephasing interaction with a correlated environment. Such correlated reservoir introduces entanglement between physical qubits. We show that for short times the quantum error correction interprets such entanglement as errors and suppresses it. However for longer time, although quantum error correction is no longer able to correct errors, it enhances the rate of entanglement production due to the interaction with the environment.Comment: 7 pages, 3 figures, published versio

Qubit channels with small correlations

We introduce a class of quantum channels with correlations acting on pairs of qubits, where the correlation takes the form of a shift operator onto a maximally entangled state. We optimise the output purity and show that below a certain threshold the optimum is achieved by partially entangled states whose degree of entanglement increases monotonically with the correlation parameter. Above this threshold, the optimum is achieved by the maximally entangled state characterizing the shift. Although, a full analysis can only be done for the 2-norm, both numerical and heuristic arguments indicate that this behavior and the optimal inputs are independent of p>1 when the optimal output purity is measured using the p-norm.Comment: 11 pages, 4 figures, 2 table

Universal and phase covariant superbroadcasting for mixed qubit states

We describe a general framework to study covariant symmetric broadcasting maps for mixed qubit states. We explicitly derive the optimal N to M superbroadcasting maps, achieving optimal purification of the single-site output copy, in both the universal and the phase covariant cases. We also study the bipartite entanglement properties of the superbroadcast states.Comment: 19 pages, 8 figures, strictly related to quant-ph/0506251 and quant-ph/051015

Dense coding with multipartite quantum states

We consider generalisations of the dense coding protocol with an arbitrary number of senders and either one or two receivers, sharing a multiparty quantum state, and using a noiseless channel. For the case of a single receiver, the capacity of such information transfer is found exactly. It is shown that the capacity is not enhanced by allowing the senders to perform joint operations. We provide a nontrivial upper bound on the capacity in the case of two receivers. We also give a classification of the set of all multiparty states in terms of their usefulness for dense coding. We provide examples for each of these classes, and discuss some of their properties.Comment: 14 pages, 1 figure, RevTeX

Phase covariant quantum cloning

We consider an N -> M quantum cloning transformation acting on pure two-level states lying on the equator of the Bloch sphere. An upper bound for its fidelity is presented, by establishing a connection between optimal phase covariant cloning and phase estimation. We give the explicit form of a cloning transformation that achieves the bound for the case N=1, M=2, and find a link between this case and optimal eavesdropping in the quantum cryptographic scheme BB84.Comment: 9 pages, 1 figur

Optimal estimation of multiple phases

We study the issue of simultaneous estimation of several phase shifts induced by commuting operators on a quantum state. We derive the optimal positive operator-valued measure corresponding to the multiple-phase estimation. In particular, we discuss the explicit case of the optimal detection of double phase for a system of identical qutrits and generalise these results to optimal multiple phase detection for d-dimensional quantum states.Comment: 6 page