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

Efficient multi-port teleportation schemes

Michał Studziński, Marek Mozrzymas, Piotr Kopszak, Michał Horodecki

Published Aug 3, 2020• 7 citations
OpenAlex

Abstract

In our work we propose a generalization of the port-based teleportation scheme, 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 the resource state is maximally entangled. It turns out that the new scheme gives better performance than the optimal PBT protocol with the respective larger dimension of the port. We exploit the same number of maximally entangled states in the resource state as in the ordinary port-based teleportation with a number of measurements scaling polynomially in the number of shared maximally entangled states. To obtain our results, i.e. explicit expressions for the performance of the new scheme, we deliver novel mathematical tools concerning representation theory of the algebra of partially transposed permutation operators, where the transposition acts on more than one subsystem.

Related papers

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

Optimal Multi-port-based Teleportation Schemes

Marek Mozrzymas, Michał Studziński, Piotr Kopszak

In this paper, we introduce optimal versions of a multi-port based teleportation scheme allowing to send a large amount of quantum information. We fully characterise probabilistic and deterministic case by presenting expressions for the average probability of success and entanglement fidelity. In the probabilistic case, the final expression depends only on global parameters describing the problem, such as the number of ports N , the number of teleported systems k , and local dimension d . It allows us to show square improvement in the number of ports with respect to the non-optimal case. We also show that the number of teleported systems can grow when the number N of ports increases as o(N) still giving high efficiency. In the deterministic case, we connect entanglement fidelity with the maximal eigenvalue of a generalised teleportation matrix. In both cases the optimal set of measurements and the optimal state shared between sender and receiver is presented. All the results are obtained by formulating and solving primal and dual SDP problems, which due to existing symmetries can be solved analytically. We use extensively tools from representation theory and formulate new results that could be of the separate interest for the potential readers.

arXiv:2011.09256•Quantum•Jun 17, 2021•14 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

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

Minimal port-based teleportation

Sergii Strelchuk, Michał Studziński

Abstract There are two types of port-based teleportation (PBT) protocols: deterministic—when the state always arrives to the receiver but is imperfectly transmitted and probabilistic—when the state reaches the receiver intact with high probability. We introduce the minimal set of requirements that define a feasible PBT protocol and construct a simple PBT protocol that satisfies these requirements: it teleports an unknown state of a qubit with success probability p succ = 1 − N + 2 2 N + 1 and fidelity 1 − O ( 1 N ) with the resource state consisting of N maximally entangled states. This protocol is not reducible from either the deterministic or probabilistic PBT protocol. We define the corresponding efficient superdense coding protocols which transmit more classical bits with fewer maximally entangled states. Furthermore, we introduce rigorous methods for comparing and converting between different PBT protocols.

arXiv:2111.05499•New Journal of Physics•Jun 1, 2023•6 citations

Quantum teleportation scheme by selecting one of multiple output ports

Satoshi Ishizaka, Tohya Hiroshima

The scheme of quantum teleportation, where Bob has multiple $(N)$ output ports and obtains the teleported state by simply selecting one of the $N$ ports, is thoroughly studied. We consider both the deterministic version and probabilistic version of the teleportation scheme aiming to teleport an unknown state of a qubit. Moreover, we consider two cases for each version: (i) the state employed for the teleportation is fixed to a maximally entangled state and (ii) the state is also optimized as well as Alice's measurement. We analytically determine the optimal protocols for all the four cases and show the corresponding optimal fidelity or optimal success probability. All these protocols can achieve the perfect teleportation in the asymptotic limit of $N\ensuremath{\rightarrow}\ensuremath{\infty}$. The entanglement properties of the teleportation scheme are also discussed.

arXiv:0901.2975•Physical Review A•Apr 3, 2009•101 citations
In our work we propose a generalization of the port-based teleportation scheme, 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 the resource state is maximally entangled. It turns out that the new scheme gives better performance than the optimal PBT protocol with the respective larger dimension of the port. We exploit the same number of maximally entangled states in the resource state as in the ordinary port-based teleportation with a number of measurements scaling polynomially in the number of shared maximally entangled states. To obtain our results, i.e. explicit expressions for the performance of the new scheme, we deliver novel mathematical tools concerning representation theory of the algebra of partially transposed permutation operators, where the transposition acts on more than one subsystem.
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.
In this paper, we introduce optimal versions of a multi-port based teleportation scheme allowing to send a large amount of quantum information. We fully characterise probabilistic and deterministic case by presenting expressions for the average probability of success and entanglement fidelity. In the probabilistic case, the final expression depends only on global parameters describing the problem, such as the number of ports N , the number of teleported systems k , and local dimension d . It allows us to show square improvement in the number of ports with respect to the non-optimal case. We also show that the number of teleported systems can grow when the number N of ports increases as o(N) still giving high efficiency. In the deterministic case, we connect entanglement fidelity with the maximal eigenvalue of a generalised teleportation matrix. In both cases the optimal set of measurements and the optimal state shared between sender and receiver is presented. All the results are obtained by formulating and solving primal and dual SDP problems, which due to existing symmetries can be solved analytically. We use extensively tools from representation theory and formulate new results that could be of the separate interest for the potential readers.
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, 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 There are two types of port-based teleportation (PBT) protocols: deterministic—when the state always arrives to the receiver but is imperfectly transmitted and probabilistic—when the state reaches the receiver intact with high probability. We introduce the minimal set of requirements that define a feasible PBT protocol and construct a simple PBT protocol that satisfies these requirements: it teleports an unknown state of a qubit with success probability p succ = 1 − N + 2 2 N + 1 and fidelity 1 − O ( 1 N ) with the resource state consisting of N maximally entangled states. This protocol is not reducible from either the deterministic or probabilistic PBT protocol. We define the corresponding efficient superdense coding protocols which transmit more classical bits with fewer maximally entangled states. Furthermore, we introduce rigorous methods for comparing and converting between different PBT protocols.
The scheme of quantum teleportation, where Bob has multiple (N)(N)(N) output ports and obtains the teleported state by simply selecting one of the NNN ports, is thoroughly studied. We consider both the deterministic version and probabilistic version of the teleportation scheme aiming to teleport an unknown state of a qubit. Moreover, we consider two cases for each version: (i) the state employed for the teleportation is fixed to a maximally entangled state and (ii) the state is also optimized as well as Alice's measurement. We analytically determine the optimal protocols for all the four cases and show the corresponding optimal fidelity or optimal success probability. All these protocols can achieve the perfect teleportation in the asymptotic limit of $N\ensuremath{\rightarrow}\ensuremath{\infty}$. The entanglement properties of the teleportation scheme are also discussed.