arXiv subjects

Mark Hillery

Publications and source records attributed to Mark Hillery.

95 records · Page 6Linked to original sources

arXiv1997

Direct and indirect strategies for phase measurement

Recently, Torgerson and Mandel [Phys. Rev. Lett. 76, 3939 (1996)] have reported a disagreement between two schemes for measuring the phase difference of a pair of optical fields. We analyze these schemes and derive their associated phase-difference probability distributions, including both their strong and weak field limits. Our calculation confirms the main point of Torgerson and Mandel of the non-uniqueness of an operational definition of the phase distribution. We further discuss the role of postselection of data and argue that it cannot meaningfully improve the sensitivity.

quant-ph↗

arXiv1997

A Hamiltonian for quantum copying

We derive an explicit Hamiltonian for copying the basis up and down states of a quantum two-state system - a qubit - onto n "copy" qubits initially all prepared in the down state. In terms of spin components, for spin-1/2 particle spin states, the resulting Hamiltonian involves n- and (n+1)-spin interactions. The case n=1 also corresponds to a quantum-computing controlled-NOT gate.

quant-ph↗

arXiv1997

Quantum copying: Fundamental inequalities

How well one can copy an arbitrary qubit? To answer this question we consider two arbitrary vectors in a two-dimensional state space and an abstract copying transformation which will copy these two vectors. If the vectors are orthogonal, then perfect copies can be made. If they are not, then errors will be introduced. The size of the error depends on the inner product of the two original vectors. We derive a lower bound for the amount of noise induced by quantum copying. We examine both copying transformations which produce one copy and transformations which produce many, and show that the quality of each copy decreases as the number of copies increases.

quant-ph↗

arXiv1996

Quantized Fields in a Nonlinear Dielectric Medium: A Microscopic Approach

Theories which have been used to describe the quantized electromagnetic field interacting with a nonlinear dielectric medium are either phenomenological or derived by quantizing the macroscopic Maxwell equations. Here we take a different approach and derive a Hamiltonian describing interacting fields from one which contains both field and matter degrees of freedom. The medium is modelled as a collection of two-level atoms, and these interact with the electromagnetic field. The atoms are grouped into effective spins and the Holstein- Primakoff representation of the spin operators is used to expand them in one over the total spin. When the lowest-order term is combined with the free atomic and field Hamiltonians, a theory of noninteracting polaritons results. When higher-order terms are expressed in terms of polariton operators, standard nonlinear optical interactions emerge.

atom-ph↗

arXiv1996

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.

quant-ph↗