Quantum Information Theory

Information technologies are based on 1) the ability to identify objects, 2) efficient expression of information, and 3) correct transmission and processing of the information. These tasks are defined as the problems of signal detection, source coding, and channel coding, respectively and constitute the principal themes of information science. Quantum information theory demonstrates how these problems are generalized to the field of quantum mechanics and identifies the limits of new information transmission and processing methods, by utilizing the quantum effects.
On the other hand, the basic theorems of quantum information theory are given in very abstract forms, and only little has been known on physical implementation on them. So we put a particular emphasis on optical implementation of the basic theorems of quantum information theory. Theoretical studies along this line consists of the following three subjects.

Researchers: M. Sasaki, and M. Takeoka

 The main signal carriers in the optical communications are Guassian states, typically the coherent states, which exhibit the optimal transmission proparties through a lossy bosonic channel. Recent theoretical studies show the performance limits attained by Gaussian operations (linear optics, the squeezers, homodyne detections, and classical feedforward) on the Gaussian states. For example, quantum speedup of signal processing is impossible. The distillation of Gaussian entanglement is impossible either only by Gaussian local operations and classical communications (GLOCC).
In order to enjoy the potential benefit of quantum information processing one must go beyond the Gaussian operations. The non-Gaussian operations require the third or higher order Hamiltonians with respect to the optical fields. If one of such nonlinear processes would be applicable, then one can construct, in principle, arbitrary quantum operations by combining it with the Gaussian operations, constituting the universal gate set.
One of the plausible approach to implement such nonlinear gates is to use the nonlinear effect caused by the photon number measurement. The simplest example of such a non-Gaussian operation is shown in Fig. 1. A squeezed beam, which is a non-classical Gaussian state, is tapped off with a beam splitter with a small reflectance. The tapped beam is guided into a photon detector. Photon clicks are used to select the transmitted signal states. The output signal state thus conditioned results in "Schrdinger-cat-like state", which is a non-Gaussian state exhibiting a drastic quantum effect. The theoretical analysis of this scheme including wideband frequency characteristics of squeezed light source and various imperfections is given by

"Multimode theory theory of measurement-induced non-Gaussian operation on wideband squeezed light: Analytical formula," M. Sasaki and S. Suzuki, Phys. Rev. A to appear; quant-ph/0512073.


The extension of the above scheme into two beam provides a probabilistic entanglement distillation protocol for the two-mode squeezed state (Fig. 2). The output state is non-Gaussian. For practical photon detectors which fail the precise discrimination of photon numbers, the output state turn out a mixed state. The quantification of entanglement of such a state is highly non-trivial. Our recent results concern the quantification by the mutual information gain in the dense coding scheme as an operational measure (Fig. 3), and by the logarithmic negativity as an monotone measure without any external parameters but an intrinsic entanglement.
Typical numerical results are shown in Figs. 4 and 5. It was found that whenever the gain is seen in terms of the mutual information of the dense coding (smaller side of ), one can say that the intrinsic entanglement increases as measured by the logarithmic negativity. For further implications and discussions of our results can be seen on the following publications;

"Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to the dense coding scheme, " A. Kitagawa, M. Takeoka, K. Wakui, and M. Sasaki,
Phys. Rev. A 72, 022334 (2005); quant-ph/0503049.
"Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states," A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, Phys. Rev. A 73, 042310 (2006).