Asymptotic performance of port-based teleportation

Abstract

Quantum teleportation is one of the fundamental building blocks of quantum Shannon theory. While ordinary teleportation is simple and efficient, port-based teleportation (PBT) enables applications such as universal programmable quantum processors, instantaneous non-local quantum computation and attacks on position-based quantum cryptography. In this work, we determine the fundamental limit on the performance of PBT: for arbitrary fixed input dimension and a large number $N$ of ports, the error of the optimal protocol is proportional to the inverse square of $N$. We prove this by deriving an achievability bound, obtained by relating the corresponding optimization problem to the lowest Dirichlet eigenvalue of the Laplacian on the ordered simplex. We also give an improved converse bound of matching order in the number of ports. In addition, we determine the leading-order asymptotics of PBT variants defined in terms of maximally entangled resource states. The proofs of these results rely on connecting recently-derived representation-theoretic formulas to random matrix theory. Along the way, we refine a convergence result for the fluctuations of the Schur-Weyl distribution by Johansson, which might be of independent interest.

arXiv comment68 pages, 4 figures; comments welcome! v2: minor fixes, added plots comparing asymptotic expansions to exact formulas, code available at https://github.com/amsqi/port-based

References in corpus (33)

• Min- and Max- Relative Entropies and a New Entanglement Monotone
• Programmable quantum gate arrays
• Post-selection technique for quantum channels with applications to quantum cryptography
• Geometrical structure of Laplacian eigenfunctions
• The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
• Estimating the spectrum of a density operator
• Asymptotic teleportation scheme as a universal programmable quantum processor
• The Spectra of Density Operators and the Kronecker Coefficients of the Symmetric Group
• A Monogamy-of-Entanglement Game With Applications to Device-Independent Quantum Cryptography
• Simplified instantaneous non-local quantum computation with applications to position-based cryptography
• Fundamental limits to quantum channel discrimination
• On the Distributions of the Lengths of the Longest Monotone Subsequences in Random Words
• Approaches for approximate additivity of the Holevo information of quantum channels
• Quantum teleportation scheme by selecting one of multiple output ports
• Quantum universal variable-length source coding
• Position-Based Quantum Cryptography: Impossibility and Constructions
• On Nonzero Kronecker Coefficients and their Consequences for Spectra
• Port-based teleportation in arbitrary dimension
• Eigenvalue Distributions of Reduced Density Matrices
• Optimal Port-based Teleportation
• Approximate programmable quantum processors
• Compatible quantum correlations: on extension problems for Werner and isotropic states
• Resource Quantification for the No-Programming Theorem
• Generalized teleportation and entanglement recycling
• The Quantum Car
• Simplified formalism of the algebra of partially transposed permutation operators with applications
• Time gating of heralded single photons for atomic memories
• Higher-dimensional performance of port-based teleportation
• Optimality of programmable quantum measurements
• Recoupling coefficients and quantum entropies
• Fast protocols for local implementation of bipartite nonlocal unitaries
• Popescu-Rohrlich correlations imply efficient instantaneous nonlocal quantum computation
• Deduction of an upper bound on the success probability of port-based teleportation from the no-cloning theorem and the no-signaling principle

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• Complexity and entanglement in non-local computation and holography
• Efficient multi port-based teleportation schemes
• Multiport based teleportation -- transmission of a large amount of quantum information
• Optimality of the pretty good measurement for port-based teleportation
• Optimal Multi-port-based Teleportation Schemes
• On the Duality of Teleportation and Dense Coding
• Minimal Port-based Teleportation
• Infinite-Dimensional Programmable Quantum Processors
• Significance of Fidelity Deviation in Continuous Variable Teleportation
• Linear programming with unitary-equivariant constraints
• Continuous variable port-based teleportation
• Storage and retrieval of von Neumann measurements
• Optimal input states for quantifying the performance of continuous-variable unidirectional and bidirectional teleportation
• The Asymmetric Quantum Cloning Region
• Port-based entanglement teleportation via noisy resource states
• Teleportation of Post-Selected Quantum States
• Port-Based State Preparation and Applications
• Asymptotic teleportation schemes bridging between standard and port-based teleportation
• Port-based telecloning of an unknown quantum state
• From port-based teleportation to Frobenius reciprocity theorem: partially reduced irreducible representations and their applications
• On the distinguishability of geometrically uniform quantum states
• Square-root measurements and degradation of the resource state in port-based teleportation scheme
• A resource theory of asynchronous quantum information processing