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Our Focus Of Interest

(For an introductory level description of our research, please go to the undergraduate intro in the LITERATURE section.)
(Our group publications list are available here.)

Quantum information processing seeks to perform tasks which are impossible or not effective with the use of conventional classical information processing, by using systems described by quantum mechanics. Quantum computation, quantum cryptography, and quantum communication have been proposed and this new field of quantum information processing has developed rapidly especially over the last 10 years. Entanglement is nonlocal correlation that appears in certain types of quantum states (non-separable states) and has been considered as the fundamental resource for quantum information processing. In our group, we are investigating new properties of multiparticle and multi-level entanglement and the use of these properties as resources for quantum information processing. Our current projects are the following:

Entanglement convertibility for infinite dimensional pure bipartite states:

It is shown that the order property of pure bipartite states under SLOCC (stochastic local operations and classical communications) changes radically when dimensionality shifts from finite to infinite. In contrast to finite dimensional systems where there is no pure comparable state, the existence of infinitely many mutually SLOCC incomparable states is shown for infinite dimensional systems even under the bounded energy and finite information exchange condition. These results show that the effect of the infinite dimensionality of Hilbert space, the ``infinite workspace'' property, remains even in physically relevant infinite dimensional systems.

Local copying and its relationship to local discrimination:

We obtain the necessary and sufficient conditions of a set of maximally entangled bipartite states in prime dimensional systems for creating two copies of a given unknown maximally entangled state drawn from the set only using a known maximally entangled state and local operations and classical communications (LOCC). In the prime dimensional systems, the set of the locally copiable maximally entangled states is equivalent to a subset of the canonical Bell states which are decomposable by simultaneous Schmidt decomposition. As the result, we show that local copying of the maximally entangled states is more difficult than local discrimination at least in prime dimensional systems.

Asymmetric qubit information sharing between two parties:

The necessary and sufficient conditions for deterministic extraction of qubit information encoded in bipartite states using only LOCC are presented. The conditions indicate that there is a way to asymmetrically share qubit information between two parties where one party's qubit can be only used as a remote "quantum key" to fully recover the original qubit information at the other party. A communication protocol which allows conditional transmission of qubit information using the non-copyable quantum key is proposed.

Local state discrimination and multipartite entanglement measures:

We present necessary conditions for the local, perfect discrimination of general multipartite states in terms of the global robustness of entanglement, the relative entropy of entanglement and the geometric measure. These lead to an upper bound to the number of orthogonal multipartite states that can be locally discriminated exactly. The bound is explicitly found for pure biparitite states and is shown to be tight for a set of generalized m-party GHZ states, adding evidence that W-states are more `powerfully' entangled than GHZ states for this kind of task. Some known results are proved in a unified way.

The transition to infinite dimensions:

We study how and when large spin systems can indeed be treated as bosonic systems by approaching from finite to infinite dimensions. The mathematical basis of this transition is group contraction. Many theoretical tools exist for infinite dimensional systems, which do not exist for large spin systems. We hope to use this to develop rigorous analogy of homodyne measurements and other continuous variable operations for spin systems and see when a system really behaves as infinite dimensional.

One-way quantum computation and graph states:

In the one-way computer the computation, the computation carried out is defined by the set of measurement commands, and the graphs state. We investigate the relationship between the set of possible computations and the graph state and find a set of necessary conditions that the graph must satisfy to be consistent with a unitary computation. We hope to use this result to show how graph states can be used in cryptographic protocols.

Last updated 07 April 2006.
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