Laser Physics

Entanglement of qutrits

Alexander A. Klyachko, Barış Öztop, A.S. Shumovsky

Published Feb 1, 2007• 8 citations

Abstract

For two types of qutrits specified by the dynamical symmetry SU(3) and SU(2), we consider the difference in entanglement caused by the lack of quantum observables in the latter case. In particular, we show that the SU(2) qutrits can have specific separable entanglement caused by quantum correlations of intrinsic degrees of freedom in a single party without interparty correlations.

DOI: 10.1134/s1054660x07020302

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Laser Physics

Entanglement of qutrits

Alexander A. Klyachko, Barış Öztop, A.S. Shumovsky

Published Feb 1, 2007• 8 citations

Publisher

Abstract

DOI: 10.1134/s1054660x07020302

Related papers

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Otavio A. D. Molitor, Sergii Strelchuk, Michał Studziński

Collective noise can leave degrees of freedom unaffected, allowing them to store quantum information. Processing this information also requires physically available logical gates. We consider $r$ fundamental qutrits transforming under $U\in SU(3)$ and $s$ dual qutrits transforming under its complex conjugate $\overline U$ , with collective action $R_{r,s}(U)=U^{\otimes r}\otimes\overline U^{\otimes s}$ . Using the image of the walled Brauer algebra and Lie-algebra arguments, we show that adjacent exchanges within each qutrit type and one singlet-projector interaction between the two types generate any independently chosen family of special unitary gates on the noiseless subsystems by a finite pulse sequence, for every $r,s\geq1$ . This establishes semi-universality of this system. We illustrate the result with a numerically optimised sequence of 24 pulses for three fundamental qutrits and one dual qutrit. We then use the encoding and available logical corrections for qutrit teleportation under correlated Weyl noise. Under explicit assumptions on channel composition and which trials are retained, and allowing for baseline implementation errors, we identify noise ranges in which encoded teleportation exceeds the classical fidelity bound of $1/2$ , while the unencoded teleportation channel is entanglement breaking. We analyse fidelity on accepted trials separately from the transmission costs of the additional physical qutrits.Collective noise can leave degrees of freedom unaffected, allowing them to store quantum information. Processing this information also requires physically available logical gates. We consider $r$ fundamental qutrits transforming under $U\in SU(3)$ and $s$ dual qutrits transforming under its complex conjugate $\overline U$, with collective action $R_{r,s}(U)=U^{\otimes r}\otimes\overline U^{\otimes s}$. Using the image of the walled Brauer algebra and Lie-algebra arguments, we show that adjacent exchanges within each qutrit type and one singlet-projector interaction between the two types generate any independently chosen family of special unitary gates on the noiseless subsystems by a finite pulse sequence, for every $r,s\geq1$. This establishes semi-universality of this system. We illustrate the result with a numerically optimised sequence of 24 pulses for three fundamental qutrits and one dual qutrit. We then use the encoding and available logical corrections for qutrit teleportation under correlated Weyl noise. Under explicit assumptions on channel composition and which trials are retained, and allowing for baseline implementation errors, we identify noise ranges in which encoded teleportation exceeds the classical fidelity bound of $1/2$, while the unencoded teleportation channel is entanglement breaking. We analyse fidelity on accepted trials separately from the transmission costs of the additional physical qutrits.

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d=4

, which differs them significantly from the often used two-qubit model (

d=2

). New expressions for entanglement quantifiers of biphoton ququarts are derived and discussed. Rather simple procedures for a direct measurement of the degree of entanglement are described for both qutrits and ququarts.

Two-body control of noiseless subsystems with mixed

SU(3)

representations lifts teleportation above the classical fidelity limit

Collective noise can leave degrees of freedom unaffected, allowing them to store quantum information. Processing this information also requires physically available logical gates. We consider

r

fundamental qutrits transforming under

U\in SU(3)

and

s

dual qutrits transforming under its complex conjugate

\overline U

, with collective action

R_{r,s}(U)=U^{\otimes r}\otimes\overline U^{\otimes s}

. Using the image of the walled Brauer algebra and Lie-algebra arguments, we show that adjacent exchanges within each qutrit type and one singlet-projector interaction between the two types generate any independently chosen family of special unitary gates on the noiseless subsystems by a finite pulse sequence, for every

r,s\geq1

. This establishes semi-universality of this system. We illustrate the result with a numerically optimised sequence of 24 pulses for three fundamental qutrits and one dual qutrit. We then use the encoding and available logical corrections for qutrit teleportation under correlated Weyl noise. Under explicit assumptions on channel composition and which trials are retained, and allowing for baseline implementation errors, we identify noise ranges in which encoded teleportation exceeds the classical fidelity bound of

1/2

, while the unencoded teleportation channel is entanglement breaking. We analyse fidelity on accepted trials separately from the transmission costs of the additional physical qutrits.