Efficient multi port-based teleportation schemes

Abstract

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.

References in corpus (32)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Quantum Teleportation is a Universal Computational Primitive
• Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolski-Rosen Channels
• Advances in Quantum Teleportation
• Novel schemes for measurement-based quantum computation
• One-and-a-half quantum de Finetti theorems
• Asymptotic teleportation scheme as a universal programmable quantum processor
• Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality
• Separability properties of tripartite states with UxUxU-symmetry
• An introduction to measurement based quantum computation
• Simplified instantaneous non-local quantum computation with applications to position-based cryptography
• Fundamental limits to quantum channel discrimination
• Quantum teleportation scheme by selecting one of multiple output ports
• Reversing Unknown Quantum Transformations: Universal Quantum Circuit for Inverting General Unitary Operations
• Enhanced symmetries of gauge theory and resolving the spectrum of local operators
• Optimal probabilistic storage and retrieval of unitary channels
• Quantum communication complexity advantage implies violation of a Bell inequality
• Port-based teleportation in arbitrary dimension
• Optimal Port-based Teleportation
• Asymptotic performance of port-based teleportation
• Generalized teleportation and entanglement recycling
• Free particles from Brauer algebras in complex matrix models
• Simplified formalism of the algebra of partially transposed permutation operators with applications
• Characterising port-based teleportation as a universal simulator of qubit channels
• Structure and properties of the algebra of partially transposed permutation operators
• Multiport based teleportation -- transmission of a large amount of quantum information
• Higher-dimensional performance of port-based teleportation
• On a family of a linear maps from $M_n(\mathbb{C})$ to $M_{n^2}(\mathbb{C})$
• Characterization of equivariant maps and application to entanglement detection
• Temperley-Lieb quantum channels
• Continuum Limit of gl(M/N) Spin Chains
• Commutant structuture of Ux...xUxU* transformations

Cited by in corpus (17)

• Reversing Unknown Qubit-Unitary Operation, Deterministically and Exactly
• Dimension-free entanglement detection in multipartite Werner states
• Optimality of the pretty good measurement for port-based teleportation
• Optimal universal quantum circuits for unitary complex conjugation
• Minimal Port-based Teleportation
• Linear programming with unitary-equivariant constraints
• Optimal input states for quantifying the performance of continuous-variable unidirectional and bidirectional teleportation
• Port-based entanglement teleportation via noisy resource states
• Universal adjointation of isometry operations using conversion of quantum supermaps
• Teleportation of Post-Selected Quantum States
• $\mathcal{N}=4$ SYM, (super)-polynomial rings and emergent quantum mechanical symmetries
• From port-based teleportation to Frobenius reciprocity theorem: partially reduced irreducible representations and their applications
• Asymptotic teleportation schemes bridging between standard and port-based teleportation
• Port-based telecloning of an unknown quantum state
• Quantum Advantage in Storage and Retrieval of Isometry Channels
• Iterative construction of ${\mathfrak{S}}_p\times {\mathfrak{S}}_p$ group-adapted irreducible matrix units for the walled Brauer algebra
• A resource theory of asynchronous quantum information processing