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Discrete Phase-Space Structures and Mutually Unbiased Bases

A. B. Klimov, José Luis Romero, Gunnar G. Bjork +1 more

Lecture notes in computer scienceSep 20, 20071 citation

Structure of the sets of mutually unbiased bases for N qubits (8 pages)

José Luis Romero

Physical Review AJan 1, 20051 citation

Generating mutually unbiased bases and discrete Wigner functions for three-qubit system

Mojtaba Aliakbarzadeh, Hishamuddin B Zainuddin

It is known that there exists 2N+ 1 mutually unbiased bases for N qubits system. Between the different MUB construction algorithms of the three-qubit case, we focus on Wootters method with discrete phase space that leads naturally to a complete set of 2N+ 1 mutually unbiased bases for the state space. We construct discrete Wigner function using mutually unbiased bases from the discrete phase space for three-qubit system by explicitly calculating the Wigner functions for exemplary three-qubit pure states such as the GHZ state, the W state and the embedded Bell state. We also highlight some quasi-probability characteristics of these entangled states.It is known that there exists 2N+ 1 mutually unbiased bases for N qubits system. Between the different MUB construction algorithms of the three-qubit case, we focus on Wootters method with discrete phase space that leads naturally to a complete set of 2N+ 1 mutually unbiased bases for the state space. We construct discrete Wigner function using mutually unbiased bases from the discrete phase space for three-qubit system by explicitly calculating the Wigner functions for exemplary three-qubit pure states such as the GHZ state, the W state and the embedded Bell state. We also highlight some quasi-probability characteristics of these entangled states.

Jan 1, 20140 citations

Quantum Coherence of Qubit States with respect to Mutually Unbiased Bases

Ming-Yang Shen, Yi-Hao Sheng, Yuan-Hong Tao +2 more

International Journal of Theoretical PhysicsNov 4, 20206 citations

Mutually unbiased bases in discrete phase space

A. B. Klimov, J. L. Romero, Gunnar G. Bjork +1 more

We work out the phase-space structure for a system of n qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field GF(2 n) and investigate the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We provide a simple classification of such curves and study in detail the four- and eight-dimensional cases, analyzing also the effect of local transformations. In this way, we provide a comprehensive phase-space approach to the construction of mutually unbiased bases for n qubits.We work out the phase-space structure for a system of n qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field GF(2 n) and investigate the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We provide a simple classification of such curves and study in detail the four- and eight-dimensional cases, analyzing also the effect of local transformations. In this way, we provide a comprehensive phase-space approach to the construction of mutually unbiased bases for n qubits.

Jun 4, 20080 citations

Generation of all sets of mutually unbiased bases for three-qubit systems

Iulia Ghiu

We propose a new method of finding the mutually unbiased bases for three qubits. The key element is the construction of the table of striation-generating curves in the discrete phase space. We derive a system of equations in the Galois field GF(8) and show that the solutions of these equations are sufficient for the construction of the general sets of complete mutually unbiased bases. A few examples are presented in order to show how our algorithm works in the following cases: striation table with three and two axes, and one and no axis in the discrete phase space.We propose a new method of finding the mutually unbiased bases for three qubits. The key element is the construction of the table of striation-generating curves in the discrete phase space. We derive a system of equations in the Galois field GF(8) and show that the solutions of these equations are sufficient for the construction of the general sets of complete mutually unbiased bases. A few examples are presented in order to show how our algorithm works in the following cases: striation table with three and two axes, and one and no axis in the discrete phase space.

arXiv:1312.2875Physica ScriptaMar 1, 201314 citations

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