G. Mauro D'Ariano

Quantum Communication, Computing, and Measurement 2

Based on the Fourth International Conference on Quantum Communication, Measurement and Computing, this volume brings together scientists working in the interdisciplinary fields of quantum communication science and technology. Topics include quantum information theory, quantum computing, stochastic processes and filtering, and quantum measurement theory

Using Entanglement Improves the Precision of Quantum Measurements

We show how entanglement can be used to improve the estimation of an unknown transformation. Using entanglement is always of benefit in improving either the precision or the stability of the measurement. Examples relevant for applications are illustrated, for either qubits or continuous variables.

Quorum of observables for universal quantum estimation

Quantum tomography is the process of reconstructing the ensemble average of an arbitrary operator (observable or not, including the density matrix), which may not be directly accessible by feasible detection schemes, starting from the measurement of a complete set of observables i.e. a quorum. The measurement of a quorum thus represents a complete characterization of the quantum state. The operator expression in terms of a quorum corresponds to an expansion on an irreducible set of operators in the Liouville space. We give two general characterizations of these sets, and show that all the known quantum tomographies can be described in this framework. New operatorial resolutions are also given that may be used in novel reconstruction schemes.

Quantum tomography as a tool for the characterization of optical devices

We describe a novel tool for the quantum characterization of optical devices. The experimental set-up involves a stable reference state that undergoes an unknown quantum transformation and is then revealed by balanced homodyne detection. Through tomographic analysis of the homodyne data we are able to characterize the signal and to estimate parameters of the interaction, such as the loss of an optical component or the gain of an amplifier. We present experimental results for coherent signals, with application to the estimation of losses introduced by simple optical components, and show how these results can be extended to the characterization of more general optical devices.

Minimax discrimination of two Pauli channels

We consider the problem of optimally discriminating two Pauli channels in the minimax strategy, maximizing the smallest of the probabilities of correct identification of the channel. We find the optimal input state at the channel and show the conditions under which using entanglement strictly enhances distinguishability. We finally compare the minimax strategy with the Bayesian one.

Added noise in homodyne measurement of field observables

Abstract Homodyne tomography provides a way for measuring generic field operators. Here we analyze the determination of the most relevant quantities: intensity, field, amplitude and phase. We show that tomographic measurements are affected by additional noise in comparison with the direct detection of each observable by itself. The case of coherent states has been analyzed in detail and earlier estimations of tomographic precision are critically discussed.

Physical realizations of quantum operations

Quantum operations (QOs) describe any state change allowed in quantum mechanics, such as the evolution of an open system or the state change due to a measurement. We address the problem of which unitary transformations and which observables can be used to achieve a QO with generally different input and output Hilbert spaces. We classify all unitary extensions of a QO and give explicit realizations in terms of free-evolution direct-sum dilations and interacting tensor-product dilations. In terms of Hilbert space dimensionality the free-evolution dilations minimize the physical resources needed to realize the QO, and for this case we provide bounds for the dimension of the ancilla space versus the rank of the QO. The interacting dilations on the other hand, correspond to the customary ancilla-system interaction realization, and for these we derive a majorization relation which selects the allowed unitary interactions between system and ancilla.

Optimal quantum estimation of the coupling between two bosonic modes

We address the problem of the optimal quantum estimation of the coupling parameter of a bilinear interaction, such as the transmittivity of a beamsplitter or the internal phase-shift of an interferometer. The optimal measurement scheme confirms Heisenberg scaling of precision versus the total energy as an unsurpassable bound, but with a largely reduced multiplicative constant.

Optimal phase estimation in quantum networks

We address the problem of estimating the phase ! given N copies of the phase rotation u! within an array of quantum operations in finite dimensions. We first consider the special case where the array consists of an arbitrary input state followed by any arrangement of the N phase rotations, and ending with a POVM. We optimize the POVM for a given input state and fixed arrangement. Then we also optimize the input state for some specific cost functions. In all cases, the optimal POVM is equivalent to a quantum Fourier transform in an appropriate basis. Examples and applications are given.

Functional quantum computing: An optical approach

Recent theoretical investigations treat quantum computations as functions, quantum processes which operate on other quantum processes, rather than circuits. Much attention has been given to the