Informationally complete measurements and group representation

D’Ariano, Giacomo Mauro; Perinotti, Paolo; Sacchi, Massimiliano F.

doi:10.1088/1464-4266/6/6/005

Cited by 106 publications

(110 citation statements)

References 25 publications

Supporting

Mentioning

105

Contrasting

Order By: Relevance

“…(6)(7)(8) and (13) that, if |ψ = d−1 r=0 ψ r |e r is a GP fiducial vector, then so is the vector |ψ * = d−1 r=0 ψ * r |e r obtained by complex conjugation. So to make the analysis complete we need to consider automorphisms of GP(d) which are generated by anti-unitary operators.…”

Section: The Extended Clifford Groupmentioning

confidence: 99%

See 1 more Smart Citation

Symmetric informationally complete–positive operator valued measures and the extended Clifford group

Appleby

2005

Journal of Mathematical Physics

257

463

View full text Add to dashboard Cite

We describe the structure of the extended Clifford Group (defined to be the group consisting of all operators, unitary and anti-unitary, which normalize the generalized Pauli group (or Weyl-Heisenberg group as it is often called)). We also obtain a number of results concerning the structure of the Clifford Group proper (i.e. the group consisting just of the unitary operators which normalize the generalized Pauli group). We then investigate the action of the extended Clifford group operators on symmetric informationally complete POVMs (or SIC-POVMs) covariant relative to the action of the generalized Pauli group. We show that each of the fiducial vectors which has been constructed so far (including all the vectors constructed numerically by Renes et al ) is an eigenvector of one of a special class of order 3 Clifford unitaries. This suggests a strengthening of a conjecture of Zauner's. We give a complete characterization of the orbits and stability groups in dimensions 2-7. Finally, we show that the problem of constructing fiducial vectors may be expected to simplify in the infinite

show abstract

Section: The Extended Clifford Groupmentioning

confidence: 99%

“…The concept of informational completeness is originally due to Prugovečki [5] (also see Busch [6], Busch et al [2], d'Ariano et al [7], Flammia et al [8], Finkelstein [9], and references cited therein). It has an obvious relevance to the problem of quantum state determination.…”

Section: Introductionmentioning

confidence: 99%

Symmetric informationally complete–positive operator valued measures and the extended Clifford group

Appleby

2005

Journal of Mathematical Physics

257

463

View full text Add to dashboard Cite

show abstract

“…(17) in this case can be detected by measuring d 2 − 1 observables via a local setting and classical processing of the measurement outcomes. Actually, a set of generalised Bell projectors can be written as follows [11] …”

mentioning

confidence: 99%

Detecting Lower Bounds to Quantum Channel Capacities

Macchiavello

Sacchi

2016

Phys. Rev. Lett.

View full text Add to dashboard Cite

We propose a method to detect lower bounds to quantum capacities of a noisy quantum communication channel by means of few measurements. The method is easily implementable and does not require any knowledge about the channel. We test its efficiency by studying its performance for most well known single qubit noisy channels and for the generalised Pauli channel in arbitrary finite dimension.arXiv:1510.00219v2 [quant-ph]

show abstract

“…We exploit the existence, proved in Ref. [28] for every dimension of the Hilbert space, of (rank-one) informationally complete measurements, that are POVMs whose elements form a basis for the operator space. In other words, there always exists a POVM {P i } i such that Tr[XP i ] = 0 for all i if and only if X = 0.…”

Section: Entanglement Of Formation and Approximate Channel Correctionmentioning

confidence: 99%

Entanglement measures and approximate quantum error correction

Buscemi

2008

Phys. Rev. A

View full text Add to dashboard Cite

It is shown that, if the loss of entanglement along a quantum channel is sufficiently small, then approximate quantum error correction is possible, thereby generalizing what happens for coherent information. Explicit bounds are obtained for the entanglement of formation and the distillable entanglement, and their validity naturally extends to other bipartite entanglement measures in between. Robustness of derived criteria is analyzed and their tightness compared. Finally, as a byproduct, we prove a bound quantifying how large the gap between entanglement of formation and distillable entanglement can be for any given finite dimensional bipartite system, thus providing a sufficient condition for distillability in terms of entanglement of formation.

show abstract

Informationally complete measurements and group representation

Cited by 106 publications

References 25 publications

Symmetric informationally complete–positive operator valued measures and the extended Clifford group

Symmetric informationally complete–positive operator valued measures and the extended Clifford group

Detecting Lower Bounds to Quantum Channel Capacities

Entanglement measures and approximate quantum error correction

Contact Info

Product

Resources

About