On Harmonic Polynomials      Invariant under Unitary Transformations

AbstractSo far, unconditional security in key distribution processes has been confined to quantum key distribution (QKD) protocols based on the no-cloning theorem of nonorthogonal bases. Recently, a completely different approach, the unconditionally secured classical key distribution (USCKD), has been proposed for unconditional security in the purely classical regime. Unlike QKD, both classical channels and orthogonal bases are key ingredients in USCKD, where unconditional security is provided by deterministic randomness via path superposition-based reversible unitary transformations in a coupled Mach–Zehnder interferometer. Here, the first experimental demonstration of the USCKD protocol is presented.

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Quantum Secret Sharing Protocol between Multiparty and Multiparty with Single Photons and Unitary Transformations

Chinese Physics Letters ◽

10.1088/0256-307x/25/4/007 ◽

2008 ◽

Vol 25 (4) ◽

pp. 1187-1190 ◽

Cited By ~ 33

Author(s):

Yan Feng-Li ◽

Gao Ting ◽

Li You-Cheng

Keyword(s):

Secret Sharing ◽

Quantum Secret Sharing ◽

Single Photons ◽

Unitary Transformations

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Time-optimal synthesis of unitary transformations in a coupled fast and slow qubit system

Physical Review A ◽

10.1103/physreva.77.032332 ◽

2008 ◽

Vol 77 (3) ◽

Cited By ~ 21

Author(s):

Robert Zeier ◽

Haidong Yuan ◽

Navin Khaneja

Keyword(s):

Optimal Synthesis ◽

Qubit System ◽

Unitary Transformations ◽

Time Optimal

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HYPER-SPHERICAL HARMONICS AND ANHARMONICS IN m-DIMENSIONAL SPACE

International Journal of Modern Physics E ◽

10.1142/s0218301308010398 ◽

2008 ◽

Vol 17 (06) ◽

pp. 1125-1130

Author(s):

M. R. SHOJAEI ◽

A. A. RAJABI ◽

H. HASANABADI

Keyword(s):

Quantum Mechanics ◽

General Theory ◽

Spherical Harmonics ◽

Interaction Potential ◽

Dimensional Space ◽

Harmonic Polynomials ◽

Central Importance ◽

Computational Tools ◽

Relative Coordinate

In quantum mechanics the hyper-spherical method is one of the most well-established and successful computational tools. The general theory of harmonic polynomials and hyper-spherical harmonics is of central importance in this paper. The interaction potential V is assumed to depend on the hyper-radius ρ only where ρ is the function of the Jacobi relative coordinate x1, x2,…, xn which are functions of the particles' relative positions.

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