Measurement of qutrits

Burlakov, A. V.; Krivitskii, L. A.; Kulik, S. P.; Maslennikov, Gleb; Chekhova, Maria V.

doi:10.1134/1.1576835

Cited by 24 publications

(18 citation statements)

References 15 publications

(11 reference statements)

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“…But these are distinct and commute only if R = Q 2 , in which case their product ͑P 2 I͒ contains a single identity factor, producing a contradiction. (2) No two generators of such a MCS may have compatible one-qutrit factors. This follows from point (1), noting that PQ and P 2 Q 2 appear in the same MCS but cannot be generators.…”

Section: B 4s-6b Theoremmentioning

confidence: 99%

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Mutually unbiased bases and trinary operator sets forNqutrits

Lawrence

2004

Phys. Rev. A

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A compete orthonormal basis of N-qutrit unitary operators drawn from the Pauli group consists of the identity and 9 N − 1 traceless operators. The traceless ones partition into 3 N + 1 maximally commuting subsets (MCS's) of 3 N − 1 operators each, whose joint eigenbases are mutually unbiased. We prove that Pauli factor groups of order 3 N are isomorphic to all MCS's and show how this result applies in specific cases. For two qutrits, the 80 traceless operators partition into 10 MCS's. We prove that 4 of the corresponding basis sets must be separable, while 6 must be totally entangled (and Bell-like). For three qutrits, 728 operators partition into 28 MCS's with less rigid structure, allowing for the coexistence of separable, partially entangled, and totally entangled (GHZ-like) bases. However a minimum of 16 GHZ-like bases must occur. Every basis state is described by an N-digit trinary number consisting of the eigenvalues of N observables constructed from the corresponding MCS.

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Section: B 4s-6b Theoremmentioning

confidence: 99%

“…Specific realizations for use in quantum communication protocols include biphotons [1,2], time-bin entangled photons [3], and photons with orbital angular momentum [4]. Qutrit quantum computation with trapped ions has been described theoretically [5], while one-qutrit gates have been demonstrated experimentally with deuterons [6].…”

Section: Introductionmentioning

confidence: 99%

Mutually unbiased bases and trinary operator sets forNqutrits

Lawrence

2004

Phys. Rev. A

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“…In this section, we assume that the unitary transformations to be applied to the system are limited to SO(3), the subgroup of rotations in 3D coordinate space. Examples of such systems are qutrits build from photon pairs [22].…”

Section: Overlap Function For Wigner D-matricesmentioning

confidence: 99%

Eigenvalue Determination for Mixed Quantum States using Overlap Statistics

Alonso,

Bermudez,

Gorin

2018

Preprint

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We consider the statistics of overlaps between a mixed state and its image under random unitary transformations. Choosing the transformations from the unitary group with its invariant (Haar) measure, the distribution of overlaps depends only on the eigenvalues of the mixed state. This allows one to estimate these eigenvalues from the overlap statistics. In the first part of this work, we present explicit results for qutrits, including a discussion of the expected uncertainties in the eigenvalue estimation. In the second part, we assume that the set of available unitary transformations is restricted to SO(3), realized as Wigner D-matrices. In that case, the overlap statistics does not depend only on the eigenvalues, but also on the eigenstates of the mixed state under scrutiny. The overlap distribution then shows a complicated pattern, which may be considered as a fingerprint of the mixed state. When using random transformations from the unitary group, the eigenvalues can be determined quite simply from the lower and the upper limit of the overlap statistics. This may still be possible in the SO(3) case, but only at the expense of a finite systematic uncertainty.

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“…Nonlinear optical parametric processes can produce nonclassical states of light 1 in many ways, some of which have been realized 2,3 . Research is continuing in promising directions aiming at controlling generation of these states [4][5][6] .…”

Section: Introductionmentioning

confidence: 99%

Generation of entangled polaritons in doped media

2013

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We developed a semiclassical theory of polariton excitations for the  -scheme of interaction realized in an yttrium orthosilicate crystal doped with Pr 59 atoms. The threshold optical pump power for efficient amplification of the probefield polaritons in a medium consisting of three-level atoms is determined. At the near-threshold conditions in the system the appearance of strong non-classical correlations (entanglement) between light and dark polaritons, similar to generation of biphotons in optics is predicted.

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Measurement of qutrits

Cited by 24 publications

References 15 publications

Mutually unbiased bases and trinary operator sets forNqutrits

Mutually unbiased bases and trinary operator sets forNqutrits

Eigenvalue Determination for Mixed Quantum States using Overlap Statistics

Generation of entangled polaritons in doped media

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