Square-root measurements and degradation of the resource state in port-based teleportation scheme

• URL: http://arxiv.org/abs/2105.14886v4
• Date: Mon, 29 Aug 2022 10:26:11 GMT
• Title: Square-root measurements and degradation of the resource state in port-based teleportation scheme
• Authors: Micha{\l} Studzi\'nski, Marek Mozrzymas, Piotr Kopszak
• Abstract summary: Port-based teleportation (PBT) is a protocol of quantum teleportation in which a receiver does not have to apply correction to the transmitted state. We analyse for the first time the recycling protocol for the deterministic PBT beyond the qubit case.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Port-based teleportation (PBT) is a protocol of quantum teleportation in which a receiver does not have to apply correction to the transmitted state. In this protocol two spatially separated parties can teleport an unknown quantum state only by exploiting joint measurements on number of shared $d-$dimensional maximally entangled states (resource state) together with a state to be teleported and one way classical communication. In this paper we analyse for the first time the recycling protocol for the deterministic PBT beyond the qubit case. In the recycling protocol the main idea is to re-use the remaining resource state after one or many rounds of PBT for further processes of teleportation. The key property is to learn how much the underlying resource state degrades after every round of the teleportation process. We measure this by evaluating quantum fidelity between respective resource states. To do so we first present analysis of the square-root measurements used by the sender in PBT by exploiting the symmetries of the system. In particular, we show how to effectively evaluate their square-roots and composition. These findings allow us to present the explicit formula for the recycling fidelity involving only group-theoretic parameters describing irreducible representations in the Schur-Weyl duality. For the first time, we also analyse the degradation of the resource state for the optimal PBT scheme and show its degradation for all $d\geq 2$. In the both versions, the qubit case is discussed separately resulting in compact expression for fidelity, depending only on the number of shared entangled pairs.

Related papers

• Sample-Optimal Quantum State Tomography for Structured Quantum States in One Dimension [25.333797381352973]
  We study whether the number of state copies can saturate the information theoretic bound (i.e., $O(n)$) using physical quantum measurements. We propose a projected gradient descent (PGD) algorithm to solve the constrained least-squares problem and show that it can efficiently find an estimate with bounded recovery error.
  arXiv  Detail & Related papers  (2024-10-03T15:26:26Z)
• Optimal quantum state tomography with local informationally complete measurements [25.33379738135298]
  We study whether a general MPS/MPDO state can be recovered with bounded errors using only a number of state copies in the number of qubits. We provide a positive answer for a variety of common many-body quantum states, including typical short-range entangled states, random MPS/MPDO states, and thermal states of one-dimensional Hamiltonians.
  arXiv  Detail & Related papers  (2024-08-13T17:58:02Z)
• Efficient Algorithms for All Port-Based Teleportation Protocols [10.720038857779135]
  Port-based teleportation (PBT) is a form of quantum teleportation in which no corrective unitary is required. We provide algorithms in all four regimes for qudits tackling the two deterministic cases for qudits. Our approach to the implementation of the square-root measurement in PBT can be directly generalised to other highly symmetric state ensembles.
  arXiv  Detail & Related papers  (2023-11-20T18:49:16Z)
• Quantum State Tomography for Matrix Product Density Operators [28.799576051288888]
  Reconstruction of quantum states from experimental measurements is crucial for the verification and benchmarking of quantum devices. Many physical quantum states, such as states generated by noisy, intermediate-scale quantum computers, are usually structured. We establish theoretical guarantees for the stable recovery of MPOs using tools from compressive sensing and the theory of empirical processes.
  arXiv  Detail & Related papers  (2023-06-15T18:23:55Z)
• The SWAP Imposter: Bidirectional Quantum Teleportation and its Performance [6.345523830122166]
  Bidirectional quantum teleportation is a fundamental protocol for exchanging quantum information between two parties. We develop two different ways of quantifying the error of nonideal bidirectional teleportation. We obtain semidefinite programming lower bounds on the error of nonideal bidirectional teleportation.
  arXiv  Detail & Related papers  (2022-10-19T20:43:57Z)
• Quantifying the performance of approximate teleportation and quantum error correction via symmetric two-PPT-extendibility [5.192118773220603]
  In practice, the ideal realization of quantum teleportation relies on having access to a maximally entangled state. We present a method to quantify the performance of approximate teleportation when using an arbitrary resource state.
  arXiv  Detail & Related papers  (2022-07-14T13:53:50Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• Quantifying the performance of bidirectional quantum teleportation [6.345523830122166]
  Bidirectional teleportation is a fundamental protocol for exchanging quantum information between two parties. We develop two ways of quantifying the simulation error of unideal bidirectional teleportation. We find semi-definite programming lower bounds on the simulation error of unideal bidirectional teleportation.
  arXiv  Detail & Related papers  (2020-10-15T17:36:17Z)
• Optimality of the pretty good measurement for port-based teleportation [7.106986689736826]
  Port-based teleportation (PBT) is a protocol in which Alice teleports an unknown quantum state to Bob. We give an explicit proof that the so-called pretty good measurement, or square-root measurement, is optimal for the PBT protocol.
  arXiv  Detail & Related papers  (2020-08-25T17:50:23Z)
• Gaussian conversion protocols for cubic phase state generation [104.23865519192793]
  Universal quantum computing with continuous variables requires non-Gaussian resources. The cubic phase state is a non-Gaussian state whose experimental implementation has so far remained elusive. We introduce two protocols that allow for the conversion of a non-Gaussian state to a cubic phase state.
  arXiv  Detail & Related papers  (2020-07-07T09:19:49Z)
• Simulation of Thermal Relaxation in Spin Chemistry Systems on a Quantum Computer Using Inherent Qubit Decoherence [53.20999552522241]
  We seek to take advantage of qubit decoherence as a resource in simulating the behavior of real world quantum systems. We present three methods for implementing the thermal relaxation. We find excellent agreement between our results, experimental data, and the theoretical prediction.
  arXiv  Detail & Related papers  (2020-01-03T11:48:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.