Approach to the quantum phase transition of spin chains in terms of pair-wise entanglement

Kaoru Shimizu and Akira Kawaguchi,*Physics Letters A* 355 (2006) 176-179

The Lewenstein-Sanpera decomposition of a two-qubit density matrix *r* provides us with a clear understanding of the entanglement properties in S=1/2 quantum Ising spin chains undergoing quantum phase transition(QPT).
By decomposing *r* into a separable part *Lr*_{s} and an inseparable part **(1-***L*)*r*_{e}, we can evaluate the concurrence *C*(*r*), a measure of pair-wise entanglement
as a product of **(1-***L*) and the concurrence *C*(*r*_{e}). By analyzing **(1-***L*) and *C*(*r*_{e}), we can interpret the reported singular behavior of *C*(*r*)
in the conventional QPT framework. The behavior of *C*(*r*_{e}) and **(1-***L*) at the critical point indicates the singular maximization of quantum spin fluctuation and the divergence in the spin correlation length,
respectively.

Communication channels analogous to one out of two oblivious transfers based on quantum uncertainty.

II. Closing EPR-type loopholes

Kaoru Shimizu and Nobuyuki Imoto, *Physical Review A* **67**, 034301 (2003)

In a recent proposal for a quantum cryptographic scheme analogous to one out of two oblivious transfers [Phys.Rev A 66, 052316 (2002)], a sender, Bob, can encode two bits of information (*X*,*Y*) in a quantum carrier but a receiver,
Alice, can decode only either *X* or *Y* dependent on her choice. Although Bob can discover her choice whenever he desires, she can detect this with a 50% probability. This paper clarifies the amount of information that Bob can expect to
obtain from Alice without being detected by her by means of an Einstein-Podolsky-Rosen(EPR) type of attack. We can show that Bob inevitably fails to discover her choice with a 50% probability even though he can always completely escape her detection.

Communication channels analogous to one out of two oblivious transfers based on quantum uncertainty

Kaoru Shimizu and Nobuyuki Imoto, *Physical Review A* **66**, 052316(2002)

This paper proposes a cryptographic quantum communication scheme analogous to one out of two oblivious transfers based on quantum conjugate coding defined in a four-dimensional Hilbert space. The quantum uncertainty principle ensures that our scheme
can satisfy the following two conditions:(i) a sender, Bob, can encode two bits of information *X*= 0 or 1 and *Y*= 0 or 1, but a receiver, Alice, can only obtain either *X* or *Y* dependent on her choice; and (ii) honest Bob, who
attempts to encode (*X*,*Y*), cannot reveal Alice's choice. By contrast, when malicious Bob tries to reveal her choice, honest Alice can detect malicious Bob with a finite probability. Moreover, by using our proposed scheme many times, we can
construct a protocol for "cheat-sensitive" quantum bit commitment (Cheat-Sensitive QBC) from Alice to Bob. Contrary to common berief, the security of our QBC protocol may not be violated by the well-known no-go theorem of QBC. This is because our QBC
protocol does not meet the assumptions ("perfect concealing") in which the no-go theorem holds.