Tight informationally complete quantum measurements
@article{Scott2006TightIC, title={Tight informationally complete quantum measurements}, author={A. J. Scott}, journal={Journal of Physics A}, year={2006}, volume={39}, pages={13507-13530} }
We introduce a class of informationally complete positive-operator-valued measures which are, in analogy with a tight frame, 'as close as possible' to orthonormal bases for the space of quantum states. These measures are distinguished by an exceptionally simple state-reconstruction formula which allows 'painless' quantum state tomography. Complete sets of mutually unbiased bases and symmetric informationally complete positive-operator-valued measures are both members of this class, the latter…
210 Citations
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References
SHOWING 1-10 OF 83 REFERENCES
Symmetric informationally complete quantum measurements
- Mathematics
- 2003
It is conjecture that a particular kind of group-covariant SIC–POVM exists in arbitrary dimensions, providing numerical results up to dimension 45 to bolster this claim.
Informationally complete measurements and group representation
- Mathematics
- 2004
Informationally complete measurements on a quantum system allow one to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that…
Quantum Measurements and Finite Geometry
- Mathematics, Physics
- 2004
A complete set of mutually unbiased bases for a Hilbert space of dimension N is analogous in some respects to a certain finite geometric structure, namely, an affine plane. Another kind of quantum…
Minimal Informationally Complete Measurements for Pure States
- Mathematics
- 2005
We consider measurements, described by a positive-operator-valued measure (POVM), whose outcome probabilities determine an arbitrary pure state of a D-dimensional quantum system. We call such a…
Informationally complete measurements on bipartite quantum systems: Comparing local with global measurements
- Mathematics
- 2005
Informationally complete measurements allow the estimation of expectation values of any operator on a quantum system, by changing only the data processing of the measurement outcomes. In particular,…
On approximately symmetric informationally complete positive operator-valued measures and related systems of quantum states
- Mathematics, Computer Science
- 2005
This work addresses the problem of constructing positive operator-valued measures in finite dimension n consisting of n2 operators of rank one which have an inner product close to uniform and presents two constructions of approximate versions of SIC-POVMs, where a small deviation from uniformity of the inner products is allowed.
Mutually unbiased bases are complex projective 2-designs
- MathematicsProceedings. International Symposium on Information Theory, 2005. ISIT 2005.
- 2005
It is demonstrated that maximal sets of MUBs come with a rich combinatorial structure by showing that they actually are the same objects as the complex projective 2-designs with angle set {0, 1/d}.
Optimal tight frames and quantum measurement
- PhysicsIEEE Trans. Inf. Theory
- 2002
The well-known canonical frame is shown to be proportional to the ULSF and to coincide with the CLSF with a certain scaling and frame-theoretical analogs of various quantum-mechanical concepts and results are developed.
Reexamination of optimal quantum state estimation of pure states (5 pages)
- Mathematics
- 2005
A direct derivation is given for the optimal mean fidelity of quantum state estimation of a d-dimensional unknown pure state with its N copies given as input, which was first obtained by Hayashi in…
A de Finetti representation for finite symmetric quantum states
- Mathematics
- 2005
Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally…