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.
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.
Port-based teleportation (PBT) is a form of quantum teleportation in which no corrective unitary is required on the part of the receiver. Two primary regimes exist—deterministic PBT in which teleportation is always successful, but is imperfect, and probabilistic PBT, in which teleportation succeeds with probability less than one, but teleportation is perfect upon a success. Two further regimes exist within each of these, in which the resource state used for the teleportation is fixed to a maximally entangled state or free to be optimized. Recent works have resolved the long-standing problem of efficiently implementing port-based teleportation, tackling the two deterministic cases for qudits. Here, we provide algorithms in all four regimes for qubits. Emphasis is placed on the practicality of these algorithms, where we give polynomial improvements in the known gate complexity for PBT, as well as an exponential improvement in the required number of ancillas (albeit in separate protocols). Our approach to the implementation of the square-root measurement in PBT can be directly generalized to other highly symmetric state ensembles. For certain families of states, such a framework yields efficient algorithms in the case in which the Petz-recovery algorithm for the square-root measurement runs in exponential time. Published by the American Physical Society 2024
Port-based teleportation (PBT) is a teleportation scheme such that the teleported state appears in one of receiver's multiple output ports without any correcting operation on the output port. In this paper, we make some remarks on PBT. Those include the possibility of recoverable PBT (a hybrid protocol between PBT and the standard teleportation scheme), the possibility of port-based superdense coding (a dual protocol to PBT), and the fidelily upper bound expected from the entanglement monogamy relation in asymmetric universal cloning.
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 O(n) time and O(nlog(n)) space complexity, and a Yamanouchi encoding that achieves O(n2) 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.
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.
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.
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 onnsystems distorted by the action of partial transposition acting on more than one subsystem. Considering its action on then−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.