TY - JOUR

T1 - Convex resource theory of non-Gaussianity

AU - Takagi, Ryuji

AU - Zhuang, Quntao

N1 - Funding Information:
The authors thank Daniel Gottesman, Jeffrey H. Shapiro, Yasunari Suzuki, and Seth Lloyd for fruitful discussions. R.T. acknowledges the support of the Takenaka scholarship foundation. Q.Z. is supported by the Air Force Office of Scientific Research Grant No. FA9550-14-1-0052. Q.Z. also acknowledges the Claude E. Shannon Research Assistantship.
Funding Information:
R.T. acknowledges the support of the Takenaka scholarship foundation. Q.Z. is supported by the Air Force Office of Scientific Research Grant No. FA9550-14-1-0052. Q.Z. also acknowledges the Claude E. Shannon Research Assistantship.
Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/6/25

Y1 - 2018/6/25

N2 - Continuous-variable systems realized in quantum optics play a major role in quantum information processing, and it is also one of the promising candidates for a scalable quantum computer. We introduce a resource theory for continuous-variable systems relevant to universal quantum computation. In our theory, easily implementable operations - Gaussian operations combined with feed-forward - are chosen to be the free operations, making the convex hull of the Gaussian states the natural free states. Since our free operations and free states cannot perform universal quantum computation, genuine non-Gaussian states - states not in the convex hull of Gaussian states - are the necessary resource states for universal quantum computation together with free operations. We introduce a monotone to quantify the genuine non-Gaussianity of resource states, in analogy to the stabilizer theory. A direct application of our resource theory is to bound the conversion rate between genuine non-Gaussian states. Finally, we give a protocol that probabilistically distills genuine non-Gaussianity - increases the genuine non-Gaussianity of resource states - only using free operations and postselection on Gaussian measurements, where our theory gives an upper bound for the distillation rate. In particular, the same protocol allows the distillation of cubic phase states, which enable universal quantum computation when combined with free operations.

AB - Continuous-variable systems realized in quantum optics play a major role in quantum information processing, and it is also one of the promising candidates for a scalable quantum computer. We introduce a resource theory for continuous-variable systems relevant to universal quantum computation. In our theory, easily implementable operations - Gaussian operations combined with feed-forward - are chosen to be the free operations, making the convex hull of the Gaussian states the natural free states. Since our free operations and free states cannot perform universal quantum computation, genuine non-Gaussian states - states not in the convex hull of Gaussian states - are the necessary resource states for universal quantum computation together with free operations. We introduce a monotone to quantify the genuine non-Gaussianity of resource states, in analogy to the stabilizer theory. A direct application of our resource theory is to bound the conversion rate between genuine non-Gaussian states. Finally, we give a protocol that probabilistically distills genuine non-Gaussianity - increases the genuine non-Gaussianity of resource states - only using free operations and postselection on Gaussian measurements, where our theory gives an upper bound for the distillation rate. In particular, the same protocol allows the distillation of cubic phase states, which enable universal quantum computation when combined with free operations.

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U2 - 10.1103/PhysRevA.97.062337

DO - 10.1103/PhysRevA.97.062337

M3 - Article

AN - SCOPUS:85049414500

SN - 2469-9926

VL - 97

JO - Physical Review A

JF - Physical Review A

IS - 6

M1 - 062337

ER -