Tools for the Analysis of Quantum Protocols Requiring State Generation Within a Time Window
Quantum protocols commonly require a certain number of quantum resource states to be available simultaneously. An important class of examples is quantum network protocols that require a certain number of entangled pairs. Here, we consider a setting in which a process generates a quantum resource sta...
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2024-01-01
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| Series: | IEEE Transactions on Quantum Engineering |
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| Online Access: | https://ieeexplore.ieee.org/document/10417724/ |
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| author | Bethany Davies Thomas Beauchamp Gayane Vardoyan Stephanie Wehner |
| author_facet | Bethany Davies Thomas Beauchamp Gayane Vardoyan Stephanie Wehner |
| author_sort | Bethany Davies |
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| description | Quantum protocols commonly require a certain number of quantum resource states to be available simultaneously. An important class of examples is quantum network protocols that require a certain number of entangled pairs. Here, we consider a setting in which a process generates a quantum resource state with some probability <inline-formula><tex-math notation="LaTeX">$p$</tex-math></inline-formula> in each time step and stores it in a quantum memory that is subject to time-dependent noise. To maintain sufficient quality for an application, each resource state is discarded from the memory after <inline-formula><tex-math notation="LaTeX">$w$</tex-math></inline-formula> time steps. Let <inline-formula><tex-math notation="LaTeX">$s$</tex-math></inline-formula> be the number of desired resource states required by a protocol. We characterize the probability distribution <inline-formula><tex-math notation="LaTeX">$X_{(w,s)}$</tex-math></inline-formula> of the ages of the quantum resource states, once <inline-formula><tex-math notation="LaTeX">$s$</tex-math></inline-formula> states have been generated in a window <inline-formula><tex-math notation="LaTeX">$w$</tex-math></inline-formula>. Combined with a time-dependent noise model, knowledge of this distribution allows for the calculation of fidelity statistics of the <inline-formula><tex-math notation="LaTeX">$s$</tex-math></inline-formula> quantum resources. We also give exact solutions for the first and second moments of the waiting time <inline-formula><tex-math notation="LaTeX">$\tau _{(w,s)}$</tex-math></inline-formula> until <inline-formula><tex-math notation="LaTeX">$s$</tex-math></inline-formula> resources are produced within a window <inline-formula><tex-math notation="LaTeX">$w$</tex-math></inline-formula>, which provides information about the rate of the protocol. Since it is difficult to obtain general closed-form expressions for statistical quantities describing the expected waiting time <inline-formula><tex-math notation="LaTeX">$\mathbb {E}(\tau _{(w,s)})$</tex-math></inline-formula> and the distribution <inline-formula><tex-math notation="LaTeX">$X_{(w,s)}$</tex-math></inline-formula>, we present two novel results that aid their computation in certain parameter regimes. The methods presented in this work can be used to analyze and optimize the execution of quantum protocols. Specifically, with an example of a blind quantum computing protocol, we illustrate how they may be used to infer <inline-formula><tex-math notation="LaTeX">$w$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$p$</tex-math></inline-formula> to optimize the rate of successful protocol execution. |
| format | Article |
| id | doaj-art-1bb4800d063e469a8cf8faca43e6aab9 |
| institution | Kabale University |
| issn | 2689-1808 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
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| series | IEEE Transactions on Quantum Engineering |
| spelling | doaj-art-1bb4800d063e469a8cf8faca43e6aab92025-01-28T00:02:31ZengIEEEIEEE Transactions on Quantum Engineering2689-18082024-01-01512010.1109/TQE.2024.335867410417724Tools for the Analysis of Quantum Protocols Requiring State Generation Within a Time WindowBethany Davies0https://orcid.org/0009-0006-5422-1388Thomas Beauchamp1https://orcid.org/0000-0001-7480-3728Gayane Vardoyan2https://orcid.org/0000-0002-6005-8138Stephanie Wehner3https://orcid.org/0000-0002-8433-0730QuTech, Delft University of Technology, Delft, The NetherlandsQuTech, Delft University of Technology, Delft, The NetherlandsQuTech, Delft University of Technology, Delft, The NetherlandsQuTech, Delft University of Technology, Delft, The NetherlandsQuantum protocols commonly require a certain number of quantum resource states to be available simultaneously. An important class of examples is quantum network protocols that require a certain number of entangled pairs. Here, we consider a setting in which a process generates a quantum resource state with some probability <inline-formula><tex-math notation="LaTeX">$p$</tex-math></inline-formula> in each time step and stores it in a quantum memory that is subject to time-dependent noise. To maintain sufficient quality for an application, each resource state is discarded from the memory after <inline-formula><tex-math notation="LaTeX">$w$</tex-math></inline-formula> time steps. Let <inline-formula><tex-math notation="LaTeX">$s$</tex-math></inline-formula> be the number of desired resource states required by a protocol. We characterize the probability distribution <inline-formula><tex-math notation="LaTeX">$X_{(w,s)}$</tex-math></inline-formula> of the ages of the quantum resource states, once <inline-formula><tex-math notation="LaTeX">$s$</tex-math></inline-formula> states have been generated in a window <inline-formula><tex-math notation="LaTeX">$w$</tex-math></inline-formula>. Combined with a time-dependent noise model, knowledge of this distribution allows for the calculation of fidelity statistics of the <inline-formula><tex-math notation="LaTeX">$s$</tex-math></inline-formula> quantum resources. We also give exact solutions for the first and second moments of the waiting time <inline-formula><tex-math notation="LaTeX">$\tau _{(w,s)}$</tex-math></inline-formula> until <inline-formula><tex-math notation="LaTeX">$s$</tex-math></inline-formula> resources are produced within a window <inline-formula><tex-math notation="LaTeX">$w$</tex-math></inline-formula>, which provides information about the rate of the protocol. Since it is difficult to obtain general closed-form expressions for statistical quantities describing the expected waiting time <inline-formula><tex-math notation="LaTeX">$\mathbb {E}(\tau _{(w,s)})$</tex-math></inline-formula> and the distribution <inline-formula><tex-math notation="LaTeX">$X_{(w,s)}$</tex-math></inline-formula>, we present two novel results that aid their computation in certain parameter regimes. The methods presented in this work can be used to analyze and optimize the execution of quantum protocols. Specifically, with an example of a blind quantum computing protocol, we illustrate how they may be used to infer <inline-formula><tex-math notation="LaTeX">$w$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$p$</tex-math></inline-formula> to optimize the rate of successful protocol execution.https://ieeexplore.ieee.org/document/10417724/Performance analysisquantum networksscan statistics |
| spellingShingle | Bethany Davies Thomas Beauchamp Gayane Vardoyan Stephanie Wehner Tools for the Analysis of Quantum Protocols Requiring State Generation Within a Time Window IEEE Transactions on Quantum Engineering Performance analysis quantum networks scan statistics |
| title | Tools for the Analysis of Quantum Protocols Requiring State Generation Within a Time Window |
| title_full | Tools for the Analysis of Quantum Protocols Requiring State Generation Within a Time Window |
| title_fullStr | Tools for the Analysis of Quantum Protocols Requiring State Generation Within a Time Window |
| title_full_unstemmed | Tools for the Analysis of Quantum Protocols Requiring State Generation Within a Time Window |
| title_short | Tools for the Analysis of Quantum Protocols Requiring State Generation Within a Time Window |
| title_sort | tools for the analysis of quantum protocols requiring state generation within a time window |
| topic | Performance analysis quantum networks scan statistics |
| url | https://ieeexplore.ieee.org/document/10417724/ |
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