Optimality of the pretty good measurement for port-based teleportation

• URL: http://arxiv.org/abs/2008.11194v2
• Date: Tue, 20 Sep 2022 12:20:36 GMT
• Title: Optimality of the pretty good measurement for port-based teleportation
• Authors: Felix Leditzky
• Abstract summary: 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.
• Score: 7.106986689736826
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Port-based teleportation (PBT) is a protocol in which Alice teleports an unknown quantum state to Bob using measurements on a shared entangled multipartite state called the port state and forward classical communication. In this paper, we give an explicit proof that the so-called pretty good measurement, or square-root measurement, is optimal for the PBT protocol with independent copies of maximally entangled states as the port state. We then show that the very same measurement remains optimal even when the port state is optimized to yield the best possible PBT protocol. Hence, there is one particular pretty good measurement achieving the optimal performance in both cases. The following well-known facts are key ingredients in the proofs of these results: (i) the natural symmetries of PBT, leading to a description in terms of representation-theoretic data; (ii) the operational equivalence of PBT with certain state discrimination problems, which allows us to employ duality of the associated semidefinite programs. Along the way, we rederive the representation-theoretic formulas for the performance of PBT protocols proved in [Studzi\'nski et al., 2017] and [Mozrzymas et al., 2018] using only standard techniques from the representation theory of the unitary and symmetric groups. Providing a simplified derivation of these beautiful formulas is one of the main goals of this paper.

Related papers

• 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)
• Robust and efficient verification of graph states in blind measurement-based quantum computation [52.70359447203418]
  Blind quantum computation (BQC) is a secure quantum computation method that protects the privacy of clients. It is crucial to verify whether the resource graph states are accurately prepared in the adversarial scenario. Here, we propose a robust and efficient protocol for verifying arbitrary graph states with any prime local dimension.
  arXiv  Detail & Related papers  (2023-05-18T06:24:45Z)
• Byzantine-Robust Federated Learning with Optimal Statistical Rates and Privacy Guarantees [123.0401978870009]
  We propose Byzantine-robust federated learning protocols with nearly optimal statistical rates. We benchmark against competing protocols and show the empirical superiority of the proposed protocols. Our protocols with bucketing can be naturally combined with privacy-guaranteeing procedures to introduce security against a semi-honest server.
  arXiv  Detail & Related papers  (2022-05-24T04:03:07Z)
• Data post-processing for the one-way heterodyne protocol under composable finite-size security [62.997667081978825]
  We study the performance of a practical continuous-variable (CV) quantum key distribution protocol. We focus on the Gaussian-modulated coherent-state protocol with heterodyne detection in a high signal-to-noise ratio regime. This allows us to study the performance for practical implementations of the protocol and optimize the parameters connected to the steps above.
  arXiv  Detail & Related papers  (2022-05-20T12:37:09Z)
• Minimal Port-based Teleportation [0.0]
  We introduce the minimal set of requirements that define a feasible port-based teleportation (PBT) protocol. We construct a simple PBT protocol that satisfies these requirements. We define the corresponding efficient superdense coding protocols which transmit more classical bits with fewer maximally entangled states.
  arXiv  Detail & Related papers  (2021-11-10T02:39:56Z)
• Square-root measurements and degradation of the resource state in port-based teleportation scheme [0.0]
  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.
  arXiv  Detail & Related papers  (2021-05-31T11:20:34Z)
• Discrimination of quantum states under locality constraints in the many-copy setting [18.79968161594709]
  We prove that the optimal average error probability always decays exponentially in the number of copies. We show an infinite separation between the separable (SEP) and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB) On the technical side, we prove this result by providing a quantitative version of the well-known statement that the tensor product of UPBs is a UPB.
  arXiv  Detail & Related papers  (2020-11-25T23:26:33Z)
• On Projection Robust Optimal Transport: Sample Complexity and Model Misspecification [101.0377583883137]
  Projection robust (PR) OT seeks to maximize the OT cost between two measures by choosing a $k$-dimensional subspace onto which they can be projected. Our first contribution is to establish several fundamental statistical properties of PR Wasserstein distances. Next, we propose the integral PR Wasserstein (IPRW) distance as an alternative to the PRW distance, by averaging rather than optimizing on subspaces.
  arXiv  Detail & Related papers  (2020-06-22T14:35:33Z)
• Projection Robust Wasserstein Distance and Riemannian Optimization [107.93250306339694]
  We show that projection robustly solidstein (PRW) is a robust variant of Wasserstein projection (WPP) This paper provides a first step into the computation of the PRW distance and provides the links between their theory and experiments on and real data.
  arXiv  Detail & Related papers  (2020-06-12T20:40:22Z)
• Optimal exploitation of the resource in remote state preparation [0.0]
  The encoding and decoding strategies of the protocol are restricted to the physically relevant classes of projective and unitary operators. The TE of the protocol in terms of both linear and quadratic fidelities is evaluated in a fully optimized scenario. The results show that in this scenario, the TE scales with the sum of the two largest eigenvalues of the squared correlation matrix of the resource state that is zero only for product states.
  arXiv  Detail & Related papers  (2020-03-21T21:31:13Z)
• Gaussian Process States: A data-driven representation of quantum many-body physics [59.7232780552418]
  We present a novel, non-parametric form for compactly representing entangled many-body quantum states. The state is found to be highly compact, systematically improvable and efficient to sample. It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
  arXiv  Detail & Related papers  (2020-02-27T15:54:44Z)

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.