skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: The SWAP imposter: Bidirectional quantum teleportation and its performance
Bidirectional quantum teleportation is a fundamental protocol for exchanging quantum information between two parties. Specifically, two individuals make use of a shared resource state as well as local operations and classical communication (LOCC) to swap quantum states. In this work, we concisely highlight the contributions of our companion paper [A. U. Siddiqui and M. M. Wilde, arXiv:2010.07905 (2020)]. We develop two different ways of quantifying the error of nonideal bidirectional teleportation by means of the normalized diamond distance and the channel infidelity. We then establish that the values given by both metrics are equal for this task. Additionally, by relaxing the set of operations allowed from LOCC to those that completely preserve the positivity of the partial transpose, we obtain semidefinite programing lower bounds on the error of nonideal bidirectional teleportation. We evaluate these bounds for some key examples—isotropic states and when there is no resource state at all. In both cases, we find an analytical solution. The second example establishes a benchmark for classical versus quantum bidirectional teleportation. Another example that we investigate consists of two Bell states that have been sent through a generalized amplitude damping channel. For this scenario, we find an analytical expression for the error, as well as a numerical solution that agrees with the former up to numerical precision.  more » « less
Award ID(s):
1852454
PAR ID:
10484642
Author(s) / Creator(s):
;
Publisher / Repository:
American Institute of Physics
Date Published:
Journal Name:
AVS Quantum Science
Volume:
5
Issue:
1
ISSN:
2639-0213
Page Range / eLocation ID:
011407
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; (, Reports on Progress in Physics)
    Abstract Secret-key distillation from quantum states and channels is a central task of interest in quantum information theory, as it facilitates private communication over a quantum network. Here, we study the task of secret-key distillation from bipartite states and point-to-point quantum channels using local operations and one-way classical communication (one-way LOCC). We employ the resource theory of unextendible entanglement to study the transformation of a bipartite state under one-way LOCC, and we obtain several efficiently computable upper bounds on the number of secret bits that can be distilled from a bipartite state using one-way LOCC channels; these findings apply not only in the one-shot setting but also in some restricted asymptotic settings. We extend our formalism to private communication over a quantum channel assisted by forward classical communication. We obtain efficiently computable upper bounds on the one-shot forward-assisted private capacity of a channel, thus addressing a question in the theory of quantum-secured communication that has been open for some time now. Our formalism also provides upper bounds on the rate of private communication when using a large number of channels in such a way that the error in the transmitted private data decreases exponentially with the number of channel uses. Moreover, our bounds can be computed using semidefinite programs, thus providing a computationally feasible method to understand the limits of private communication over a quantum network. 
    more » « less
  2. ; ; ; ; (, Physical Review Research)
    We study the problem of implementing arbitrary permutations of qubits under interaction constraints in quantum systems that allow for arbitrarily fast local operations and classical communication (LOCC). In particular, we show examples of speedups over swap-based and more general unitary routing methods by distributing entanglement and using LOCC to perform quantum teleportation. We further describe an example of an interaction graph for which teleportation gives a logarithmic speedup in the worst-case routing time over swap-based routing. We also study limits on the speedup afforded by quantum teleportation—showing an O ( N log N ) upper bound on the separation in routing time for any interaction graph—and give tighter bounds for some common classes of graphs. Published by the American Physical Society2024 
    more » « less
  3. ; ; (, New Journal of Physics)
    Abstract To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum channels to characterize and quantify the quantum ‘magic’ or non-stabilizerness of noisy quantum circuits. For qudit quantum computing with odd dimensiond, it is known that quantum states with non-negative Wigner function can be efficiently simulated classically. First, inspired by this observation, we introduce a resource theory based on completely positive-Wigner-preserving quantum operations as free operations, and we show that they can be efficiently simulated via a classical algorithm. Second, we introduce two efficiently computable magic measures for quantum channels, called the mana and thauma of a quantum channel. As applications, we show that these measures not only provide fundamental limits on the distillable magic of quantum channels, but they also lead to lower bounds for the task of synthesizing non-Clifford gates. Third, we propose a classical algorithm for simulating noisy quantum circuits, whose sample complexity can be quantified by the mana of a quantum channel. We further show that this algorithm can outperform another approach for simulating noisy quantum circuits, based on channel robustness. Finally, we explore the threshold of non-stabilizerness for basic quantum circuits under depolarizing noise. 
    more » « less
  4. ; ; (, Quantum)
    A powerful operational paradigm for distributed quantum information processing involves manipulating pre-shared entanglement by local operations and classical communication (LOCC). The LOCC round complexity of a given task describes how many rounds of classical communication are needed to complete the task. Despite some results separating one-round versus two-round protocols, very little is known about higher round complexities. In this paper, we revisit the task of one-shot random-party entanglement distillation as a way to highlight some interesting features of LOCC round complexity. We first show that for random-party distillation in three qubits, the number of communication rounds needed in an optimal protocol depends on the entanglement measure used; for the same fixed state some entanglement measures need only two rounds to maximize whereas others need an unbounded number of rounds. In doing so, we construct a family of LOCC instruments that require an unbounded number of rounds to implement. We then prove explicit tight lower bounds on the LOCC round number as a function of distillation success probability. Our calculations show that the original W-state random distillation protocol by Fortescue and Lo is essentially optimal in terms of round complexity. 
    more » « less
  5. ; ; ; ; ; ; (, PRX Quantum)
    Geometric locality is an important theoretical and practical factor for quantum low-density parity-check (qLDPC) codes that affects code performance and ease of physical realization. For device architectures restricted to two-dimensional (2D) local gates, naively implementing the high-rate codes suitable for low-overhead fault-tolerant quantum computing incurs prohibitive overhead. In this work, we present an error-correction protocol built on a bilayer architecture that aims to reduce operational overheads when restricted to 2D local gates by measuring some generators less frequently than others. We investigate the family of bivariate-bicycle qLDPC codes and show that they are well suited for a parallel syndrome-measurement scheme using fast routing with local operations and classical communication (LOCC). Through circuit-level simulations, we find that in some parameter regimes, bivariate-bicycle codes implemented with this protocol have logical error rates comparable to the surface code while using fewer physical qubits. Published by the American Physical Society2025 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email