Theory of Quantum System Certification

Kliesch, Martin; Roth, Ingo

doi:10.1103/prxquantum.2.010201

Cited by 110 publications

(84 citation statements)

References 120 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A broad review of multipronged modern methods of certification as well as benchmarking of quantum states and processes can be found in the recent paper 4 . For a more introductory tutorial to the theory of system certification we refer the reader to 5 . Verification of quantum processes is often studied in the context of specific elements of quantum information processing tasks.…”

Section: Introductionmentioning

confidence: 99%

Excluding false negative error in certification of quantum channels

Krawiec

Pawela

Puchała

2021

Sci Rep

View full text Add to dashboard Cite

Certification of quantum channels is based on quantum hypothesis testing and involves also preparation of an input state and choosing the final measurement. This work primarily focuses on the scenario when the false negative error cannot occur, even if it leads to the growth of the probability of false positive error. We establish a condition when it is possible to exclude false negative error after a finite number of queries to the quantum channel in parallel, and we provide an upper bound on the number of queries. On top of that, we found a class of channels which allow for excluding false negative error after a finite number of queries in parallel, but cannot be distinguished unambiguously. Moreover, it will be proved that parallel certification scheme is always sufficient, however the number of steps may be decreased by the use of adaptive scheme. Finally, we consider examples of certification of various classes of quantum channels and measurements.

show abstract

Section: Introductionmentioning

confidence: 99%

Excluding false negative error in certification of quantum channels

Krawiec

Pawela

Puchała

2021

Sci Rep

View full text Add to dashboard Cite

show abstract

“…However, a rigorous conclusion about the comparison between different efficient schemes for general entangled states still requires sophisticated calculations. On the other hand, there have been remarkable advances in the certification of intermediatescale quantum systems [63], such as the classical shadows method [64][65][66][67] and quantum overlapping tomography [68]. The incorporation of the spectrum-estimation-based scheme into these advanced schemes may shed light on the investigation of multipartite coherence.…”

Section: Discussionmentioning

confidence: 99%

The Tightness of Multipartite Coherence from Spectrum Estimation

Ding

Fang

2021

Entropy

View full text Add to dashboard Cite

Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems. Along this line of research, several efficient procedures have been proposed to detect multipartite quantum coherence without quantum state reconstruction, among which the spectrum-estimation-based method is suitable for various coherence measures. Here, we first generalize the spectrum-estimation-based method for the geometric measure of coherence. Then, we investigate the tightness of the estimated lower bound of various coherence measures, including the geometric measure of coherence, the l1-norm of coherence, the robustness of coherence, and some convex roof quantifiers of coherence multiqubit GHZ states and linear cluster states. Finally, we demonstrate the spectrum-estimation-based method as well as the other two efficient methods. We observe that the spectrum-estimation-based method outperforms other methods in various coherence measures, which significantly enhances the accuracy of estimation.

show abstract

“…[ 73 ] Considering this in terms of frame theory in quantum measurement, [ 22,75 ] consider this discrete Q function as a frame, where the dual frame is then the P function kernel, such that

\begin{matrix} true \\ right M & = & left A_{2}^{false(- 1 false)} = \frac{1}{2} double-struck1 + \frac{1}{2 \sqrt{3}} (() σ^{sans-serifz} + σ^{sans-serify} + σ^{sans-serify}) \end{matrix}

\begin{matrix} true \\ right \tilde{M} & = & left 3 A_{2}^{false(- 1 false)} - double-struck1 = \frac{1}{2} double-struck1 + \frac{\sqrt{3}}{2} (() σ^{sans-serifz} + σ^{sans-serify} + σ^{sans-serify}) = A_{2}^{false(1 false)} \end{matrix}

More generally we can transform between any of these kernels by

{scriptA}_{2}^{(s_{2})} = 3^{\frac{1}{2} false(s 2 - s 1 false)} {scriptA}_{2}^{(s_{1})} + \frac{1 - 3^{\frac{1}{2} false(s 2 - s 1 false)}}{2} 1

By understanding these phase‐space functions in these terms, they can prove to be powerful tools for verification of quantum states, for example ref. [76] which we will discuss further in Section 4.…”

Section: Phase‐space Formulation Of Finite Quantum Systemsmentioning

confidence: 99%

“…This allows a direct comparison to verification and fidelity estimation protocols, for example, refs. [76, 147] and the fidelity estimation results in Section 4.1.…”

Section: Quantum Technologies In Phase Spacementioning

confidence: 99%

Overview of the Phase Space Formulation of Quantum Mechanics with Application to Quantum Technologies

Rundle

Everitt

2021

Adv Quantum Tech

View full text Add to dashboard Cite

The phase‐space formulation of quantum mechanics has recently seen increased use in testing quantum technologies, including methods of tomography for state verification and device validation. Here, an overview of quantum mechanics in phase space is presented. The formulation to generate a generalized phase‐space function for any arbitrary quantum system is shown, such as the Wigner and Weyl functions along with the associated Q and P functions. Examples of how these different formulations are used in quantum technologies are provided, with a focus on discrete quantum systems, qubits in particular. Also provided are some results that, to the authors' knowledge, have not been published elsewhere. These results provide insight into the relation between different representations of phase space and how the phase‐space representation is a powerful tool in understanding quantum information and quantum technologies.

show abstract

Theory of Quantum System Certification

Cited by 110 publications

References 120 publications

Excluding false negative error in certification of quantum channels

Excluding false negative error in certification of quantum channels

The Tightness of Multipartite Coherence from Spectrum Estimation

Overview of the Phase Space Formulation of Quantum Mechanics with Application to Quantum Technologies

Contact Info

Product

Resources

About