TY - JOUR

T1 - Impossibility to produce arbitrary non-Gaussian states using zero-mean Gaussian states and partial photon number resolving detection

AU - Gagatsos, Christos N.

AU - Guha, Saikat

N1 - Funding Information:
C.N.G. was supported by Xanadu Quantum Technologies. C.N.G. and S.G. acknowledge Xanadu Quantum Technologies and Linran Fan for multiple useful discussions on this topic. C.N.G. also acknowledges partial funding support from the National Science Foundation, FET, Award No. 2122337.
Publisher Copyright:
© 2021 authors. Published by the American Physical Society.

PY - 2021/12

Y1 - 2021/12

N2 - Gaussian states and measurements collectively are not powerful-enough resources for quantum computing, as any Gaussian dynamics can be simulated efficiently, classically. However, it is known that any one non-Gaussian resource - a state, a unitary operation, or a measurement - together with Gaussian unitaries, makes for universal quantum resources. Photon number resolving (PNR) detection, a readily realizable non-Gaussian measurement, has been a popular tool to try and engineer non-Gaussian states for universal quantum processing. In this paper, we consider PNR detection of a subset of the modes of a zero-mean pure multimode Gaussian state as a means to herald a target non-Gaussian state on the undetected modes. This is motivated from the ease of scalable preparation of Gaussian states that have zero mean, using squeezed vacuum and passive linear optics. We calculate upper bounds on the fidelity between the actual heralded state and the target state. We find that this fidelity upper bound is 1/2 when the target state is a multimode coherent cat-basis cluster state, a resource sufficient for universal quantum computing. This proves that there exist non-Gaussian states that are not producible by this method. Our fidelity upper bound is a simple expression that depends only on the target state represented in the photon-number basis, which could be applied to other non-Gaussian states of interest.

AB - Gaussian states and measurements collectively are not powerful-enough resources for quantum computing, as any Gaussian dynamics can be simulated efficiently, classically. However, it is known that any one non-Gaussian resource - a state, a unitary operation, or a measurement - together with Gaussian unitaries, makes for universal quantum resources. Photon number resolving (PNR) detection, a readily realizable non-Gaussian measurement, has been a popular tool to try and engineer non-Gaussian states for universal quantum processing. In this paper, we consider PNR detection of a subset of the modes of a zero-mean pure multimode Gaussian state as a means to herald a target non-Gaussian state on the undetected modes. This is motivated from the ease of scalable preparation of Gaussian states that have zero mean, using squeezed vacuum and passive linear optics. We calculate upper bounds on the fidelity between the actual heralded state and the target state. We find that this fidelity upper bound is 1/2 when the target state is a multimode coherent cat-basis cluster state, a resource sufficient for universal quantum computing. This proves that there exist non-Gaussian states that are not producible by this method. Our fidelity upper bound is a simple expression that depends only on the target state represented in the photon-number basis, which could be applied to other non-Gaussian states of interest.

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U2 - 10.1103/PhysRevResearch.3.043182

DO - 10.1103/PhysRevResearch.3.043182

M3 - Article

AN - SCOPUS:85122517013

VL - 3

JO - Physical Review Research

JF - Physical Review Research

SN - 2643-1564

IS - 4

M1 - 043182

ER -