Practical implementation of mutually unbiased bases using quantum circuits
arXiv:1412.4358 · doi:10.1103/PhysRevA.91.032102
Abstract
The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work out a simple and efficient method based on cyclic generation of mutually unbiased bases. The basic generator requires only Hadamard and controlled-phase gates, which are available in most practical realizations of these systems. We show how complete sets of mutually unbiased bases with different entanglement structures can be realized for three and four qubits. We also analyze the quantum circuits implementing the various entanglement classes.
5 pages, 2 color figures. Comments welcome!
References in corpus (39)
- 14-qubit entanglement: creation and coherence
- Quantum state tomography via compressed sensing
- Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
- Unknown Quantum States and Operations, a Bayesian View
- On mutually unbiased bases
- Efficient quantum state tomography
- A new proof for the existence of mutually unbiased bases
- Observation of eight-photon entanglement
- Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
- Quantum phase estimation with lossy interferometers
- Optimal states and almost optimal adaptive measurements for quantum interferometry
- Entanglement detection via mutually unbiased bases
- Permutationally invariant quantum tomography
- Characterizing the entanglement of symmetric many-particle spin-1/2 systems
- Classical and quantum communication without a shared reference frame
- Mutually unbiased binary observable sets on N qubits
- Permutationally invariant state reconstruction
- Constructing Mutually Unbiased Bases in Dimension Six
- Scalable reconstruction of density matrices
- Entanglement in mutually unbiased bases
- Maximal Sets of Mutually Unbiased Quantum States in Dimension Six
- On the structure of the sets of mutually unbiased bases for N qubits
- Spin tomography
- Six-qubit permutation-based decoherence-free orthogonal basis
- Multicomplementary operators via finite Fourier transform
- Mutually unbiased bases in dimension six: The four most distant bases
- Numerical evidence for the maximum number of mutually unbiased bases in dimension six
- Mutually Unbiased Bases and Trinary Operator Sets for N Qutrits
- Mutually unbiased phase states, phase uncertainties, and Gauss sums
- Rank-based model selection for multiple ions quantum tomography
- Practical learning method for multi-scale entangled states
- Informational completeness of continuous-variable measurements
- Optimal quantum tomography of permutationally invariant qubits
- Entanglement Patterns in Mutually Unbiased Basis Sets for N Prime-state Particles
- Construction of mutually unbiased bases with cyclic symmetry for qubit systems
- Sizing up entanglement in mutually unbiased bases with Fisher information
- Complete sets of cyclic mutually unbiased bases in even prime power dimensions
- Structure of the sets of mutually unbiased bases with cyclic symmetry
- Ordered Measurements of Permutationally-Symmetric Qubit Strings