Yoshiyuki Tsuda

Accuracy of quantum-state estimation utilizing Akaike's information criterion

We experimentally analyzed the statistical errors in quantum-state estimation and examined whether their lower bound, which is derived from the Cramer-Rao inequality, can be truly attained or not. In the experiments, polarization states of bi-photons produced via spontaneous parametric down-conversion were estimated employing tomographic measurements. Using a new estimation strategy based on Akaikes information criterion, we demonstrated that the errors actually approach the lower bound, while they fail to approach it using the conventional estimation strategy.We report our theoretical and experimental investigations into errors in quantum-state estimation, putting a special emphasis on their asymptotic behavior. Tomographic measurements and maximum likelihood estimation are used for estimating several kinds of identically prepared quantum states (biphoton polarization states) produced via spontaneous parametric down-conversion. Excess errors in the estimation procedures are eliminated by introducing an estimation strategy utilizing Akaikes information criterion. We make a quantitative comparison between the errors of the experimentally estimated states and their asymptotic lower bounds, which are derived from the Cramer-Rao inequality. Our results reveal the influence of entanglement on the errors in the estimation. An alternative measurement strategy employing inseparable measurements is also discussed, and its performance is numerically explored.

Hypothesis testing for an entangled state produced by spontaneous parametric down-conversion

Generation and characterization of entanglement are crucial tasks in quantum information processing. A hypothesis testing scheme for entanglement has been formulated. Three designs were proposed to test the entangled photon states created by the spontaneous parametric down conversion. The time allocations between the measurement vectors were designed to consider the anisotropic deviation of the generated photon states from the maximally entangled states. The designs were evaluated in terms of the

Experimental investigation of pulsed entangled photons and photonic quantum channels

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Quantum estimation for non-differentiable models

value based on the observed data. It has been experimentally demonstrated that the optimal time allocation between the coincidence and anticoincidence measurement vectors improves the entanglement test. A further improvement is also experimentally demonstrated by optimizing the time allocation between the anticoincidence vectors. Analysis on the data obtained in the experiment verified the advantage of the entanglement test designed by the optimal time allocation.

Bhattacharyya inequality for quantum state estimation

The development of key devices and systems in quantum information technology, such as entangled particle sources, quantum gates and quantum cryptographic systems, requires a reliable and well-established method for characterizing how well the devices or systems work. We report our recent work on experimental characterization of pulsed entangled photonic states and photonic quantum channels, using the methods of state and process tomography. By using state tomography, we could reliably evaluate the states generated from a two-photon source under development and develop a highly entangled pulsed photon source. We are also devoted to characterization of single-qubit and two-qubit photonic quantum channels. Characterization of typical single-qubit decoherence channels has been demonstrated using process tomography. Characterization of two-qubit channels, such as classically correlated channels and quantum mechanically correlated channels is under investigation. These characterization techniques for quantum states and quantum processes will be useful for developing photonic quantum devices and for improving their performances.

A study of LOCC-detection of a maximally entangled state using hypothesis testing

State estimation is a classical problem in quantum information. In optimization of an estimation scheme, to find a lower bound to the error of the estimator is a very important step. So far, all the proposed tractable lower bounds use a derivative of the density matrix. However, sometimes, we are interested in quantities with singularity, e.g. concurrence etc. In this paper, lower bounds to a mean square error of an estimator are derived for a quantum estimation problem without smoothness assumptions. Our main idea is to replace the derivative by difference, as is done in classical estimation theory. We applied the inequalities to several examples, and derived an optimal estimator for some of them.

Hypothesis testing for a maximally entangled state

Using a higher order derivative with respect to the parameter, we will give lower bounds for variance of unbiased estimators in quantum estimation problems. This is a quantum version of the Bhattacharyya inequality in the classical statistical estimation. Because of the non-commutativity of operator multiplication, we obtain three different types of lower bounds: Type S, Type R and Type L. If the parameter is a real number, the Type S bound is useful. If the parameter is complex, the Type R and L bounds are useful. As an application, we will consider estimation of polynomials of the complex amplitude of the quantum Gaussian state. For the case where the amplitude lies in the real axis, a uniformly optimum estimator for the square of the amplitude will be derived using the Type S bound. It will be shown that there is no unbiased estimator uniformly optimum as a polynomial of annihilation and/or creation operators for the cube of the amplitude. For the case where the amplitude does not necessarily lie in the real axis, uniformly optimum estimators for holomorphic, antiholomorphic and real-valued polynomials of the amplitude will be derived. Those estimators for the holomorphic and real-valued cases attain the Type R bound, and those for the antiholomorphic and real-valued cases attain the Type L bound. This paper clarifies what is the best method to measure the energy of a laser.