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

arXiv:2310.01637

Efficient Quantum Algorithm for Port-based Teleportation

Jiani Fei, Sydney Timmerman, Patrick M. Hayden

Published Oct 2, 2023• 1 citation
arXivHTMLPDF

Abstract

In this paper, we provide the first efficient algorithm for port-based teleportation, a unitarily equivariant version of teleportation useful for constructing programmable quantum processors and performing instantaneous nonlocal computation (NLQC). The latter connection is important in AdS/CFT, where bulk computations are realized as boundary NLQC. Our algorithm yields an exponential improvement to the known relationship between the amount of entanglement available and the complexity of the nonlocal part of any unitary that can be implemented using NLQC. Similarly, our algorithm provides the first nontrivial efficient algorithm for an approximate universal programmable quantum processor. The key to our approach is a generalization of Schur-Weyl duality we call twisted Schur-Weyl duality, as well as an efficient algorithm we develop for the twisted Schur transform, which transforms to a subgroup-reduced irrep basis of the partially transposed permutation algebra, whose dual is the $U^{\otimes n-k} \otimes (U^*)^{\otimes k}$ representation of the unitary group.

DOI
10.48550/arxiv.2310.01637

Related papers

Efficient quantum circuits for port-based teleportation

Dmitry Grinko, Adam Burchardt, Māris Ozols

Port-based teleportation (PBT) is a variant of quantum teleportation that, unlike the canonical protocol by Bennett et al., does not require a correction operation on the teleported state. Since its introduction by Ishizaka and Hiroshima in 2008, no efficient implementation of PBT was known. We close this long-standing gap by building on our recent results on representations of partially transposed permutation matrix algebras and mixed quantum Schur transform. We construct efficient quantum algorithms for probabilistic and deterministic PBT protocols on $n$ ports of arbitrary local dimension, both for EPR and optimized resource states. We describe two constructions based on different encodings of the Gelfand-Tsetlin basis for $n$ qudits: a standard encoding that achieves $\widetilde{O}(n)$ time and $O(n\log(n))$ space complexity, and a Yamanouchi encoding that achieves $\widetilde{O}(n^2)$ time and $O(\log(n))$ space complexity, both for constant local dimension and target error. We also describe efficient circuits for preparing the optimal resource states.

arXiv:2312.03188•Dec 5, 2023•2 citations

Asymptotic Performance of Port-Based Teleportation

Matthias Christandl, Felix Leditzky, Christian Majenz +3 more

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:1809.10751•Communications in Mathematical Physics•Nov 20, 2020•30 citations

Mixed Schur-Weyl duality in quantum information

Dmitry Grinko

This thesis explores the interplay between representation theory and quantum information. Specifically, we focus on mixed Schur–Weyl duality, which considers the action of the unitary group on mixed tensors. This setting naturally arises in quantum information tasks involving unitary-equivariant channels, such as port-based teleportation, quantum majority vote, and universal transposition of unitary operators. A key contribution of this thesis is an explicit derivation of the action of the generators of the partially transposed permutation matrix algebra—the commutant of the mixed unitary action—in the Gelfand–Tsetlin basis. As another key result of this thesis, we develop efficient quantum circuits for the mixed quantum Schur transform, a novel primitive in quantum information. The key ingredient of our construction is new efficient circuits for the dual Clebsch–Gordan transform of the unitary group. A significant application of our findings is the construction of efficient quantum algorithms for port-based teleportation, a variant of quantum teleportation that eliminates the need for corrective operations. Another application is a symmetry reduction of semidefinite optimisation problems with unitary equivariance symmetry. Finally, we study the extendibility of quantum states possessing unitary, mixed unitary, or orthogonal symmetry on the complete graph. We obtain analytically the exact maximum values for projections onto the maximally entangled state and the antisymmetric state for each of the three symmetry classes. This thesis demonstrates the usefulness of mixed Schur–Weyl duality in quantum information and computing. We expect that our tools will help address other problems in other areas of quantum information processing, such as communication, cryptography, and simulation.

•Jan 1, 2025•0 citations

Efficient Multi Port-Based Teleportation Schemes

Michał Studziński, Marek Mozrzymas, Piotr Kopszak +1 more

In this manuscript we analyse generalised port-based teleportation (PBT) schemes, allowing for transmitting more than one unknown quantum state (or a composite quantum state) in one go, where the state ends up in several ports at Bob’s side. We investigate the efficiency of our scheme discussing both deterministic and probabilistic case, where parties share maximally entangled states. It turns out that the new scheme gives better performance than various variants of the optimal PBT protocol used for the same task. All the results are presented in group-theoretic manner depending on such quantities like dimensions and multiplicities of irreducible representations in the Schur-Weyl duality. The presented analysis was possible by considering the algebra of permutation operators acting on$n$systems distorted by the action of partial transposition acting on more than one subsystem. Considering its action on the$n-$fold tensor product of the Hilbert space with finite dimension, we present construction of the respective irreducible matrix representations, which are in fact matrix irreducible representations of the Walled Brauer Algebra. I turns out that the introduced formalism, and symmetries beneath it, appears in many aspects of theoretical physics and mathematics - theory of anti ferromagnetism, aspects of gravity theory or in the problem of designing quantum circuits for special task like for example inverting an unknown unitary.

arXiv:2008.00984•IEEE Transactions on Information Theory•Jul 5, 2022•22 citations

Port-based teleportation in arbitrary dimension

Michał Studziński, Sergii Strelchuk, Marek Mozrzymas +1 more

Port-based teleportation (PBT), introduced in 2008, is a type of quantum teleportation protocol which transmits the state to the receiver without requiring any corrections on the receiver's side. Evaluating the performance of PBT was computationally intractable and previous attempts succeeded only with small systems. We study PBT protocols and fully characterize their performance for arbitrary dimensions and number of ports. We develop new mathematical tools to study the symmetries of the measurement operators that arise in these protocols and belong to the algebra of partially transposed permutation operators. First, we develop the representation theory of the mentioned algebra which provides an elegant way of understanding the properties of subsystems of a large system with general symmetries. In particular, we introduce the theory of the partially reduced irreducible representations which we use to obtain a simpler representation of the algebra of partially transposed permutation operators and thus explicitly determine the properties of any port-based teleportation scheme for fixed dimension in polynomial time.

arXiv:1612.09260•Scientific Reports•Sep 1, 2017•49 citations

A simple proof of unitary parallelization via port-based teleportation

Anurag Anshu, Quynh T. Nguyen

Port-based teleportation (PBT) is a variant of quantum teleportation that does not require corrections on the teleported state: starting with $N$ shared EPR states, Alice can teleport a qudit to Bob by performing a measurement on her system and informing Bob which of his $N$ `ports' to retrieve the state, up to infidelity decaying with $N$. Existing efficient quantum circuits of PBT rely on representation theory tools such as the Schur transform. In this note, we report an elementary efficient circuit for PBT, which has depth $\operatorname{polylog}(N,d)$. As a corollary, this gives a simple proof that all $n$-qubit unitaries can be parallelized to $\operatorname{poly}(n)$ depth, recovering a recent result due to Nehoran--Slote--Yuen and OpenAI.

quant-pharXiv:2610.30761•Oct 23, 2026•0 citations
In this paper, we provide the first efficient algorithm for port-based teleportation, a unitarily equivariant version of teleportation useful for constructing programmable quantum processors and performing instantaneous nonlocal computation (NLQC). The latter connection is important in AdS/CFT, where bulk computations are realized as boundary NLQC. Our algorithm yields an exponential improvement to the known relationship between the amount of entanglement available and the complexity of the nonlocal part of any unitary that can be implemented using NLQC. Similarly, our algorithm provides the first nontrivial efficient algorithm for an approximate universal programmable quantum processor. The key to our approach is a generalization of Schur-Weyl duality we call twisted Schur-Weyl duality, as well as an efficient algorithm we develop for the twisted Schur transform, which transforms to a subgroup-reduced irrep basis of the partially transposed permutation algebra, whose dual is the U⊗n−k⊗(U∗)⊗kU^{\otimes n-k} \otimes (U^*)^{\otimes k}U⊗n−k⊗(U∗)⊗k representation of the unitary group.
Port-based teleportation (PBT) is a variant of quantum teleportation that, unlike the canonical protocol by Bennett et al., does not require a correction operation on the teleported state. Since its introduction by Ishizaka and Hiroshima in 2008, no efficient implementation of PBT was known. We close this long-standing gap by building on our recent results on representations of partially transposed permutation matrix algebras and mixed quantum Schur transform. We construct efficient quantum algorithms for probabilistic and deterministic PBT protocols on nnn ports of arbitrary local dimension, both for EPR and optimized resource states. We describe two constructions based on different encodings of the Gelfand-Tsetlin basis for nnn qudits: a standard encoding that achieves O~(n)\widetilde{O}(n)O(n) time and O(nlog⁡(n))O(n\log(n))O(nlog(n)) space complexity, and a Yamanouchi encoding that achieves O~(n2)\widetilde{O}(n^2)O(n2) time and O(log⁡(n))O(\log(n))O(log(n)) space complexity, both for constant local dimension and target error. We also describe efficient circuits for preparing the optimal resource states.
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.
This thesis explores the interplay between representation theory and quantum information. Specifically, we focus on mixed Schur–Weyl duality, which considers the action of the unitary group on mixed tensors. This setting naturally arises in quantum information tasks involving unitary-equivariant channels, such as port-based teleportation, quantum majority vote, and universal transposition of unitary operators. A key contribution of this thesis is an explicit derivation of the action of the generators of the partially transposed permutation matrix algebra—the commutant of the mixed unitary action—in the Gelfand–Tsetlin basis. As another key result of this thesis, we develop efficient quantum circuits for the mixed quantum Schur transform, a novel primitive in quantum information. The key ingredient of our construction is new efficient circuits for the dual Clebsch–Gordan transform of the unitary group. A significant application of our findings is the construction of efficient quantum algorithms for port-based teleportation, a variant of quantum teleportation that eliminates the need for corrective operations. Another application is a symmetry reduction of semidefinite optimisation problems with unitary equivariance symmetry. Finally, we study the extendibility of quantum states possessing unitary, mixed unitary, or orthogonal symmetry on the complete graph. We obtain analytically the exact maximum values for projections onto the maximally entangled state and the antisymmetric state for each of the three symmetry classes. This thesis demonstrates the usefulness of mixed Schur–Weyl duality in quantum information and computing. We expect that our tools will help address other problems in other areas of quantum information processing, such as communication, cryptography, and simulation.
In this manuscript we analyse generalised port-based teleportation (PBT) schemes, allowing for transmitting more than one unknown quantum state (or a composite quantum state) in one go, where the state ends up in several ports at Bob’s side. We investigate the efficiency of our scheme discussing both deterministic and probabilistic case, where parties share maximally entangled states. It turns out that the new scheme gives better performance than various variants of the optimal PBT protocol used for the same task. All the results are presented in group-theoretic manner depending on such quantities like dimensions and multiplicities of irreducible representations in the Schur-Weyl duality. The presented analysis was possible by considering the algebra of permutation operators acting onnnnsystems distorted by the action of partial transposition acting on more than one subsystem. Considering its action on then−n-n−fold tensor product of the Hilbert space with finite dimension, we present construction of the respective irreducible matrix representations, which are in fact matrix irreducible representations of the Walled Brauer Algebra. I turns out that the introduced formalism, and symmetries beneath it, appears in many aspects of theoretical physics and mathematics - theory of anti ferromagnetism, aspects of gravity theory or in the problem of designing quantum circuits for special task like for example inverting an unknown unitary.
Port-based teleportation (PBT), introduced in 2008, is a type of quantum teleportation protocol which transmits the state to the receiver without requiring any corrections on the receiver's side. Evaluating the performance of PBT was computationally intractable and previous attempts succeeded only with small systems. We study PBT protocols and fully characterize their performance for arbitrary dimensions and number of ports. We develop new mathematical tools to study the symmetries of the measurement operators that arise in these protocols and belong to the algebra of partially transposed permutation operators. First, we develop the representation theory of the mentioned algebra which provides an elegant way of understanding the properties of subsystems of a large system with general symmetries. In particular, we introduce the theory of the partially reduced irreducible representations which we use to obtain a simpler representation of the algebra of partially transposed permutation operators and thus explicitly determine the properties of any port-based teleportation scheme for fixed dimension in polynomial time.
Port-based teleportation (PBT) is a variant of quantum teleportation that does not require corrections on the teleported state: starting with NNN shared EPR states, Alice can teleport a qudit to Bob by performing a measurement on her system and informing Bob which of his NNN `ports' to retrieve the state, up to infidelity decaying with NNN. Existing efficient quantum circuits of PBT rely on representation theory tools such as the Schur transform. In this note, we report an elementary efficient circuit for PBT, which has depth polylog⁡(N,d)\operatorname{polylog}(N,d)polylog(N,d). As a corollary, this gives a simple proof that all nnn-qubit unitaries can be parallelized to poly⁡(n)\operatorname{poly}(n)poly(n) depth, recovering a recent result due to Nehoran--Slote--Yuen and OpenAI.