Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum Information and Computation

Performance characterization of Pauli channels assisted by indefinite causal order and post-measurement

Francisco Delgado, Carlos Cardoso-Isidoro

Published Dec 1, 2020• 6 citations
Publisher

Abstract

Indefinite causal order has introduced disruptive procedures to improve the fidelity of quantum communication by introducing the superposition of { orders} on a set of quantum channels. It has been applied to several well characterized quantum channels as depolarizing, dephasing and teleportation. This work analyses the behavior of a parametric quantum channel for single qubits expressed in the form of Pauli channels. Combinatorics lets to obtain affordable formulas for the analysis of the output state of the channel when it goes through a certain imperfect quantum communication channel when it is deployed as a redundant application of it under indefinite causal order. In addition, the process exploits post-measurement on the associated control to select certain components of transmission. Then, the fidelity of such outputs is analysed to characterize the generic channel in terms of its parameters. As a result, we get notable enhancement in the transmission of information for well characterized channels due to the combined process: indefinite causal order plus post-measurement.

DOI
10.26421/qic20.15-16-1

Related papers

Performance of two redundant quantum channels for single qubits under indefinite causal order

Carlos Cardoso-Isidoro, Francisco Delgado

Abstract Indefinite causal order has introduced novel procedures to improve the quality of quantum communication. The superposition of paths on a set of consecutive quantum channels has demonstrated enhancement in communication on some of them. This work models a generic quantum channel for single qubits in terms of Kraus operators in the form of Pauli operators. The output state going through the channel can be obtained analytically to then analyse the quality by means of the quantum fidelity.

Journal of Physics Conference Series•Jan 1, 2021•1 citation

Symmetries in Teleportation Assisted by N-Channels under Indefinite Causal Order and Post-Measurement

Carlos Cardoso-Isidoro, Francisco Delgado

Quantum teleportation has had notorious advances in the last decade, being successfully deployed in the experimental domain. In other terrains, the understanding of indefinite causal order has demonstrated a valuable enhancement in quantum communication to correct channel imperfections. In this work, we address the symmetries underlying imperfect teleportation when it is assisted by indefinite causal order to correct the use of noisy entangled resources. In the strategy being presented, indefinite causal order introduces a control state to address the causal ordering. Then, by using post-selection, it fulfills the teleportation enhancement to recover the teleported state by constructive interference. By analysing primarily sequential teleportation under definite causal order, we perform a comparison basis for notable outcomes derived from indefinite causal order. After, the analysis is conducted by increasing the number of teleportation processes, thus suggesting additional alternatives to exploit the most valuable outcomes in the process by adding weak measurement as a complementary strategy. Finally, we discuss the current affordability for an experimental implementation.

Symmetry•Nov 20, 2020•8 citations

Symmetries of Quantum Fisher Information as Parameter Estimator for Pauli Channels under Indefinite Causal Order

Francisco Delgado

Quantum Fisher Information is considered in Quantum Information literature as the main resource to determine a bound in the parametric characterization problem of a quantum channel by means of probe states. The parameters characterizing a quantum channel can be estimated until a limited precision settled by the Cramér–Rao bound established in estimation theory and statistics. The involved Quantum Fisher Information of the emerging quantum state provides such a bound. Quantum states with dimension d=2, the qubits, still comprise the main resources considered in Quantum Information and Quantum Processing theories. For them, Pauli channels are an important family of parametric quantum channels providing the most faithful deformation effects of imperfect quantum communication channels. Recently, Pauli channels have been characterized when they are arranged in an Indefinite Causal Order. Thus, their fidelity has been compared with single or sequential arrangements of identical channels to analyse their induced transparency under a joint behaviour. The most recent characterization has exhibited important features for quantum communication related with their parametric nature. In this work, a parallel analysis has been conducted to extended such a characterization, this time in terms of their emerging Quantum Fisher Information to pursue the advantages of each kind of arrangement for the parameter estimation problem. The objective is to reach the arrangement stating the best estimation bound for each type of Pauli channel. A complete map for such an effectivity is provided for each Pauli channel under the most affordable setups considering sequential and Indefinite Causal Order arrangements, as well as discussing their advantages and disadvantages.

Symmetry•Sep 1, 2022•5 citations

An Architecture Superposing Indefinite Causal Order and Path Superposition Improving Pauli Channels’ Parameter Estimation

Carlos Cardoso-Isidoro, Francisco Delgado

Quantum Parameter Estimation (QPE) is commonly led using quantum probe states for the characterization of quantum systems. For these purposes, Quantum Fisher Information (QFI) plays a crucial role by imposing a lower bound for the parametric estimation of quantum channels. Several schemes for obtaining QFI lower bounds have been proposed, particularly for Pauli channels regarding qubits. Those schemes commonly employ either the individual channel, multiple copies of it, or arrangements including communication architectures. The present work aims to propose an architecture involving path superposition and causal indefinite order in superposition. Thus, by controlling the symmetry balance of this superposition, it reaches notable improvements in quantum parameter estimation. The proposed architecture has been tested to find the best possible QPE bounds for a representative and emblematic set of Pauli channels. Further, for the most reluctant channels, it was revisited testing the architecture again under a primary path superposition (using double teleportation) and also using entangled probe states to recombine their outputs with the original undisturbed state. Notable outcomes practically near zero were found for the QPE bounds, stating a hierarchy between the approaches, but anyway reaching a perfect theoretical QPE, particularly for the last path superposition including the proposed architecture.

Symmetry•Jan 5, 2024•1 citation

Parametric Symmetries in Architectures Involving Indefinite Causal Order and Path Superposition for Quantum Parameter Estimation of Pauli Channels

Francisco Delgado

Parameter estimation for devices containing or supporting quantum systems is a field of quantum metrology using quantum probe states to reach their characterization. Pauli channels are ideal structures where qubits are transmitted or contained, commonly altering them with specific fingerprints. The ultimate limit imposed on such estimation is addressed using the quantum Fisher information, stating a lower bound for it. Although the most simple scheme suggests performing such an estimation directly using the individual channel, other approaches have shown improved outcomes by repeating identical copies of the channel for the characterization, or otherwise those connected inside of specific circuit arrangements. These connections commonly include path superposition or causal indefinite architectures. In addition, other improvements have been observed in concrete channels when complementary unitary controls are included. The current research analyses the complete set of Pauli channels under some of those architectures in a comparative approach to reach a better estimation, thus stating hierarchies. It is observed that the use of those unitary controls notably improves previous outcomes by several orders of magnitude.

Symmetry•May 16, 2023•4 citations

Communication Enhancement through Quantum Coherent Control of N Channels in an Indefinite Causal-Order Scenario

Lorenzo M. Procopio, Francisco Delgado, Marco Enríquez +2 more

In quantum Shannon theory, transmission of information is enhanced by quantum features. Up to very recently, the trajectories of transmission remained fully classical. Recently, a new paradigm was proposed by playing quantum tricks on two completely depolarizing quantum channels i.e., using coherent control in space or time of the two quantum channels. We extend here this control to the transmission of information through a network of an arbitrary number N of channels with arbitrary individual capacity i.e., information preservation characteristics in the case of indefinite causal order. We propose a formalism to assess information transmission in the most general case of N channels in an indefinite causal order scenario yielding the output of such transmission. Then, we explicitly derive the quantum switch output and the associated Holevo limit of the information transmission for N = 2 , N = 3 as a function of all involved parameters. We find in the case N = 3 that the transmission of information for three channels is twice that of transmission of the two-channel case when a full superposition of all possible causal orders is used.

arXiv:1902.01807•Entropy•Oct 18, 2019•69 citations
Indefinite causal order has introduced disruptive procedures to improve the fidelity of quantum communication by introducing the superposition of { orders} on a set of quantum channels. It has been applied to several well characterized quantum channels as depolarizing, dephasing and teleportation. This work analyses the behavior of a parametric quantum channel for single qubits expressed in the form of Pauli channels. Combinatorics lets to obtain affordable formulas for the analysis of the output state of the channel when it goes through a certain imperfect quantum communication channel when it is deployed as a redundant application of it under indefinite causal order. In addition, the process exploits post-measurement on the associated control to select certain components of transmission. Then, the fidelity of such outputs is analysed to characterize the generic channel in terms of its parameters. As a result, we get notable enhancement in the transmission of information for well characterized channels due to the combined process: indefinite causal order plus post-measurement.
Quantum teleportation has had notorious advances in the last decade, being successfully deployed in the experimental domain. In other terrains, the understanding of indefinite causal order has demonstrated a valuable enhancement in quantum communication to correct channel imperfections. In this work, we address the symmetries underlying imperfect teleportation when it is assisted by indefinite causal order to correct the use of noisy entangled resources. In the strategy being presented, indefinite causal order introduces a control state to address the causal ordering. Then, by using post-selection, it fulfills the teleportation enhancement to recover the teleported state by constructive interference. By analysing primarily sequential teleportation under definite causal order, we perform a comparison basis for notable outcomes derived from indefinite causal order. After, the analysis is conducted by increasing the number of teleportation processes, thus suggesting additional alternatives to exploit the most valuable outcomes in the process by adding weak measurement as a complementary strategy. Finally, we discuss the current affordability for an experimental implementation.
Quantum Fisher Information is considered in Quantum Information literature as the main resource to determine a bound in the parametric characterization problem of a quantum channel by means of probe states. The parameters characterizing a quantum channel can be estimated until a limited precision settled by the Cramér–Rao bound established in estimation theory and statistics. The involved Quantum Fisher Information of the emerging quantum state provides such a bound. Quantum states with dimension d=2, the qubits, still comprise the main resources considered in Quantum Information and Quantum Processing theories. For them, Pauli channels are an important family of parametric quantum channels providing the most faithful deformation effects of imperfect quantum communication channels. Recently, Pauli channels have been characterized when they are arranged in an Indefinite Causal Order. Thus, their fidelity has been compared with single or sequential arrangements of identical channels to analyse their induced transparency under a joint behaviour. The most recent characterization has exhibited important features for quantum communication related with their parametric nature. In this work, a parallel analysis has been conducted to extended such a characterization, this time in terms of their emerging Quantum Fisher Information to pursue the advantages of each kind of arrangement for the parameter estimation problem. The objective is to reach the arrangement stating the best estimation bound for each type of Pauli channel. A complete map for such an effectivity is provided for each Pauli channel under the most affordable setups considering sequential and Indefinite Causal Order arrangements, as well as discussing their advantages and disadvantages.
Quantum Parameter Estimation (QPE) is commonly led using quantum probe states for the characterization of quantum systems. For these purposes, Quantum Fisher Information (QFI) plays a crucial role by imposing a lower bound for the parametric estimation of quantum channels. Several schemes for obtaining QFI lower bounds have been proposed, particularly for Pauli channels regarding qubits. Those schemes commonly employ either the individual channel, multiple copies of it, or arrangements including communication architectures. The present work aims to propose an architecture involving path superposition and causal indefinite order in superposition. Thus, by controlling the symmetry balance of this superposition, it reaches notable improvements in quantum parameter estimation. The proposed architecture has been tested to find the best possible QPE bounds for a representative and emblematic set of Pauli channels. Further, for the most reluctant channels, it was revisited testing the architecture again under a primary path superposition (using double teleportation) and also using entangled probe states to recombine their outputs with the original undisturbed state. Notable outcomes practically near zero were found for the QPE bounds, stating a hierarchy between the approaches, but anyway reaching a perfect theoretical QPE, particularly for the last path superposition including the proposed architecture.
Parameter estimation for devices containing or supporting quantum systems is a field of quantum metrology using quantum probe states to reach their characterization. Pauli channels are ideal structures where qubits are transmitted or contained, commonly altering them with specific fingerprints. The ultimate limit imposed on such estimation is addressed using the quantum Fisher information, stating a lower bound for it. Although the most simple scheme suggests performing such an estimation directly using the individual channel, other approaches have shown improved outcomes by repeating identical copies of the channel for the characterization, or otherwise those connected inside of specific circuit arrangements. These connections commonly include path superposition or causal indefinite architectures. In addition, other improvements have been observed in concrete channels when complementary unitary controls are included. The current research analyses the complete set of Pauli channels under some of those architectures in a comparative approach to reach a better estimation, thus stating hierarchies. It is observed that the use of those unitary controls notably improves previous outcomes by several orders of magnitude.
In quantum Shannon theory, transmission of information is enhanced by quantum features. Up to very recently, the trajectories of transmission remained fully classical. Recently, a new paradigm was proposed by playing quantum tricks on two completely depolarizing quantum channels i.e., using coherent control in space or time of the two quantum channels. We extend here this control to the transmission of information through a network of an arbitrary number N of channels with arbitrary individual capacity i.e., information preservation characteristics in the case of indefinite causal order. We propose a formalism to assess information transmission in the most general case of N channels in an indefinite causal order scenario yielding the output of such transmission. Then, we explicitly derive the quantum switch output and the associated Holevo limit of the information transmission for N = 2 , N = 3 as a function of all involved parameters. We find in the case N = 3 that the transmission of information for three channels is twice that of transmission of the two-channel case when a full superposition of all possible causal orders is used.