The QS transformation

Li Yang, Chong Xiang, Bao Li

Several kinds of qubit-string-based(QS-based) bit commitment protocols are presented, and a definition of information-theoretic concealing is given. All the protocols presented here are proved to be secure under this definition. We suggest an attack algorithm to obtain the local unitary transformation introduced in no-go theorem, which is used to attack the binding condition, then study the security of our QS-based bit commitment protocols under this attack via introducing a new concept "physical security of protocol". At last we present a practical QS-based bit commitment scheme against channel loss and error.

Alwin Zulehner, Robert Wille

Fan Hong

We develop quantum mechanical Dirac ket-bra operator's integration theory in Q-ordering or P-ordering to multimode case, where Q-ordering means all Qs are to the left of all Ps and P-ordering means all Ps are to the left of all Qs. As their applications,we derive Q-ordered and P-ordered expansion formulas of multimode exponential operator e iPlΛlkQk. Application of the new formula in finding new general squeezing operators is demonstrated. The general exponential operator for coordinate representation transformation q1q2 → A B C D q1q2 is also derived. In this way, much more correpondence relations between classical coordinate transformations and their quantum mechanical images can be revealed.

Alwin Zulehner, Robert Wille

Alwin Zulehner, Robert Wille

V. P. Belavkin

We review the basic concepts of quantum probability and revise the classical and quantum stochastic (QS) calculus using the universal Itô B*-algebra approach. A non-commutative generalization of Lévy process is defined in Fock–Guichardet space in terms of the underlying B*-Itô modular algebra. The main notions and results of classical and QS analysis are reformulated in terms of the non-commutative but associative stochastic covariation of quantum integrals defined as sesquilinear forms adapted to a quantum Lévy process in Fock space. The general semi-Markov QS dynamics is defined in terms of a hemigroup of semi-morphic transformations as adjoints to a semiunitary hemigroup resolving a QS Schrödinger equation in Fock space. The corresponding semi-Markov hemigroup of completely positive contractions resolving a quantum master equation with generalized Lindblad generator as a non-commutative analogue of Feller–Kolmogorov equation is derived by taking vacuum conditional expectation in Fock space.