Adaptive characterization of coherent states

Akio Fujiwara, Hiroshi Nagaoka

Markku P. V. Stenberg, Kevin Pack, Frank K. Wilhelm

We present methods for efficient characterization of an optical coherent state $|\ensuremath{\alpha}\ensuremath{\rangle}$. We choose measurement settings adaptively and stochastically, based on data while it is collected. Our algorithm divides the estimation into two distinct steps: (i) before the first detection of a vacuum state, the probability of choosing a measurement setting is proportional to detecting vacuum with the setting, which makes using too similar measurement settings twice unlikely; and (ii) after the first detection of vacuum, we focus measurements in the region where vacuum is most likely to be detected. In step (i) [(ii)] the detection of vacuum (a photon) has a significantly larger effect on the shape of the posterior probability distribution of $\ensuremath{\alpha}$. Compared to nonadaptive schemes, our method makes the number of measurement shots required to achieve a certain level of accuracy smaller approximately by a factor proportional to the area describing the initial uncertainty of $\ensuremath{\alpha}$ in phase space. While this algorithm is not directly robust against readout errors, we make it such by introducing repeated measurements in step (i).

Jean-Pierre Antoine, Bagarello, Fabio, Jean‐Pierre Gazeau

Julio Guerrero, Antonio Sojo, Alberto Mayorgas +1 more

Abstract In this paper we study the entanglement in symmetric N-quDit systems. In particular we use generalizations to U(D) of spin U(2) coherent states (CSs) and their projections on definite parity c ∈ Z 2 D − 1 (multicomponent Schrödinger cat) states and we analyse their reduced density matrices when tracing out M < N quDits. The eigenvalues (or Schmidt coefficients) of these reduced density matrices are completely characterized, allowing to prove a theorem for the decomposition of a N-quDit Schrödinger cat state with a given parity c into a sum over all possible parities of tensor products of Schrödinger cat states of N − M and M particles. Diverse asymptotic properties of the Schmidt eigenvalues are studied and, in particular, for the (rescaled) double thermodynamic limit ( N , M → ∞ , M / N fixed), we reproduce and generalize to quDits known results for photon loss of parity adapted CSs of the harmonic oscillator, thus providing an unified Schmidt decomposition for both multi-quDits and (multi-mode) photons. These results allow to determine the entanglement properties of these states and also their decoherence properties under quDit loss, where we demonstrate the robustness of these states.

Yehuda Gavriel Roth

Abstract Coherence, the fundamental concept underlying quantum computers, is a complex phenomenon that limits their implementation. Coherent states can be non-stationary (i.e., not an eigenstate of the Hamiltonian), and system–environment interactions can cause decoherence. To adapt to environmental factors such as heat, the realization of quantum computers entails cold environments at temperatures close to absolute zero. Nonlinear dynamics can result from open systems (such as system–environment feedback interactions). Here we show that nonlinear maps characterized by a single attractor can cause mixed-density matrices to become pure and that implementing such nonlinear maps may provide a straightforward approach to realizing quantum computers.

G. M. D’Ariano, M. Vadacchino, Mario Rasetti