Antoni Wojcik

Unmodulated spin chains as universal quantum wires

We study a quantum state transfer between two qubits interacting with the ends of a quantum wire consisting of linearly arranged spins coupled by an excitation conserving, time-independent Hamiltonian. We show that, if we control the coupling between the source and the destination qubits and the ends of the wire, the evolution of the system can lead to an almost perfect transfer even in the case in which all nearest-neighbour couplings between the internal spins of the wire are equal.

Comment on “Quantum dense key distribution”

In this Comment we question the security of the recently proposed scheme of a quantum dense key distribution by Degiovanni et al. [Phys. Rev. A 69, 032310 (2004)].

Symmetric scheme for superdense coding between multiparties

Recently Liu, Long, Tong, and Li [Phys. Rev. A 65, 022304 (2002)] proposed a scheme for superdense coding between multiparties. This scheme seems to be highly asymmetric in the sense that only one sender effectively exploits entanglement. We show that this scheme can be modified in order to allow more senders to benefit from the entanglement-enhanced information transmission.

Trapping a particle of a quantum walk on the line

We observe that changing a phase at a single point in a discrete quantum walk results in a rather surprising localization effect. For certain values of this phase change the possibility of localization strongly depends on the internal coin-state of the walker.

Quantum walks on cycles

We consider asymptotic behaviour of a Hadamard walk on a cycle. For the walk which starts with a state in which all the probability is concentrated on one node, we find the explicit formula for the limiting distribution and discuss its asymptotic behaviour when the length of the cycle tends to infinity. We also demonstrate that for a carefully chosen initial state, the limiting distribution of a quantum walk on cycle can lie further away from the uniform distribution than its initial state.

Creating a Superposition of Unknown Quantum States

The superposition principle is one of the landmarks of quantum mechanics. The importance of quantum superpositions provokes questions about the limitations that quantum mechanics itself imposes on the possibility of their generation. In this work, we systematically study the problem of the creation of superpositions of unknown quantum states. First, we prove a no-go theorem that forbids the existence of a universal probabilistic quantum protocol producing a superposition of two unknown quantum states. Second, we provide an explicit probabilistic protocol generating a superposition of two unknown states, each having a fixed overlap with the known referential pure state. The protocol can be applied to generate coherent superposition of results of independent runs of subroutines in a quantum computer. Moreover, in the context of quantum optics it can be used to efficiently generate highly nonclassical states or non-Gaussian states.

Entanglement in the Majumdar-Ghosh model

We present an analysis of the entanglement characteristics in the Majumdar-Ghosh (MG) or J{sub 1}-J{sub 2} Heisenberg model. For a system consisting of up to 28 spins, there is a deviation from the scaling behavior of the entanglement entropy characterizing the unfrustrated Heisenberg chain above J{sub 2}{approx_equal}0.25. This feature can be used as an indicator of the dimer phase transition occurring in this model. Additionally, we also consider entanglement at the MG point J{sub 2}=0.5J{sub 1}.

Quantum walk as a generalized measuring device.

We show that a one-dimensional discrete time quantum walk can be used to implement a generalized measurement in terms of a positive operator value measure (POVM) on a single qubit. More precisely, we show that for a single qubit any set of rank 1 and rank 2 POVM elements can be generated by a properly engineered quantum walk. In such a scenario the measurement of a particle at a position x=i corresponds to a measurement of a POVM element E_{i} on a qubit. Since the idea of quantum walks originates from the von Neumann model of measurement, in which the change of the position of the pointer depends on the state of the system that is being measured, we argue that von Neumann measurements can be naturally extended to POVMs if one includes the internal evolution of the system in the model.

How to encode the states of two non-entangled qubits in one qutrit

A new scheme of quantum coding is presented. The scheme concerns the quantum states to which Schumachers compression does not apply. It is shown that two qubits can be encoded in a single qutrit in such a way that one can faithfully reconstruct the state of one qubit. Decision on which of these two qubits is to be reconstructed can be made long after the encoding took place. The scheme succeeds with the average probability of 2/3.

EXAMPLES OF NON-UNIFORM LIMITING DISTRIBUTIONS FOR THE QUANTUM WALK ON EVEN CYCLES

We present three different types of the evolution of a time-averaged probability distribution of the quantum walk on even cycles. We concentrate on initial states which lead to non-uniform limiting distributions.