Structure of the sets of mutually unbiased bases with cyclic symmetry
arXiv:1404.3035 · doi:10.1088/1751-8113/47/45/455303
Abstract
Mutually unbiased bases that can be cyclically generated by a single unitary operator are of special interest, since they can be readily implemented in practice. We show that, for a system of qubits, finding such a generator can be cast as the problem of finding a symmetric matrix over the field equipped with an irreducible characteristic polynomial of a given Fibonacci index. The entanglement structure of the resulting complete sets is determined by two additive matrices of the same size.
arXiv comment20 pages
References in corpus (46)
- Good Quantum Error-Correcting Codes Exist
- A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
- Quantum Error Correction and Orthogonal Geometry
- On mutually unbiased bases
- A new proof for the existence of mutually unbiased bases
- Quantum cryptography with 3-state systems
- Discrete phase space based on finite fields
- Evenly distributed unitaries: on the structure of unitary designs
- Higher-dimensional orbital angular momentum based quantum key distribution with mutually unbiased bases
- Equiangular lines, mutually unbiased bases, and spin models
- Mutually unbiased binary observable sets on N qubits
- On SIC-POVMs and MUBs in Dimension 6
- Constructing Mutually Unbiased Bases in Dimension Six
- Entanglement in mutually unbiased bases
- Entanglement assisted random access codes
- Maximal Sets of Mutually Unbiased Quantum States in Dimension Six
- On the structure of the sets of mutually unbiased bases for N qubits
- The mean king's problem: Prime degrees of freedom
- Quantum Secret Sharing with Multi-level Mutually (Un-)Biased Bases
- Mutually Unbiased Bases and Finite Projective Planes
- Multicomplementary operators via finite Fourier transform
- Qubits in phase space: Wigner function approach to quantum error correction and the mean king problem
- Mutually unbiased bases in dimension six: The four most distant bases
- Unconditionally Secure Key Distribution In Higher Dimensions By Depolarization
- Numerical evidence for the maximum number of mutually unbiased bases in dimension six
- Security bound of two-bases quantum key-distribution protocols using qudits
- Mean king's problem with mutually unbiased bases and orthogonal Latin squares
- A SU(2) recipe for mutually unbiased bases
- Mutually Unbiased Bases and Trinary Operator Sets for N Qutrits
- Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models
- The mean king's problem: Spin 1
- Generation of mutually unbiased bases as powers of a unitary matrix in 2-power dimensions
- MUBs inequivalence and affine planes
- Solution to the Mean King's problem with mutually unbiased bases for arbitrary levels
- SIC-POVMs and MUBs: Geometrical Relationships in Prime Dimension
- Solution to the King's Problem in prime power dimensions
- Channel kets, entangled states, and the location of quantum information
- Graph-state formalism for mutually unbiased bases
- Construction of mutually unbiased bases with cyclic symmetry for qubit systems
- General Quantum Key Distribution in Higher Dimension
- Maximal Entanglement, Collective Coordinates and Tracking the King
- Sizing up entanglement in mutually unbiased bases with Fisher information
- Complete sets of cyclic mutually unbiased bases in even prime power dimensions
- New Tales of the Mean King
- Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture
- Affine Constellations Without Mutually Unbiased Counterparts
Cited by in corpus (5)
- States that are far from being stabilizer states
- Galois Unitaries, Mutually Unbiased Bases, and MUB-balanced states
- Practical implementation of mutually unbiased bases using quantum circuits
- Cyclic measurements and simplified quantum state tomography
- Construction of Structured Incoherent Unit Norm Tight Frames