Storage and retrieval of two unknown unitary channels

• URL: http://arxiv.org/abs/2410.23376v1
• Date: Wed, 30 Oct 2024 18:27:46 GMT
• Title: Storage and retrieval of two unknown unitary channels
• Authors: Michal Sedlák, Robert Stárek, Nikola Horová, Michal Mičuda, Jaromir Fiurášek, Alessandro Bisio,
• Abstract summary: We consider the case where the unknown unitary is selected with equal prior probability from two options. First, we prove that the optimal storage strategy involves the sequential application of the $n$ uses of the unknown unitary. Next, we show that incoherent "measure-and-prepare" retrieval achieves the maximum fidelity between the retrieved operation and the original (qubit) unitary.
• Score: 37.928612512813494
• License:
• Abstract: We address the fundamental task of converting $n$ uses of an unknown unitary transformation into a quantum state (i.e., storage) and later retrieval of the transformation. Specifically, we consider the case where the unknown unitary is selected with equal prior probability from two options. First, we prove that the optimal storage strategy involves the sequential application of the $n$ uses of the unknown unitary, and it produces the optimal state for discrimination between the two possible unitaries. Next, we show that incoherent "measure-and-prepare" retrieval achieves the maximum fidelity between the retrieved operation and the original (qubit) unitary. We then identify the retrieval strategy that maximizes the probability of successfully and perfectly retrieving the unknown transformation. In the regime in which the fidelity between the two possible unitaries is large the probability of success scales as $ P_{succ} = 1 - \mathcal{O}(n^{-2} ) $, which is a quadratic improvement with respect to the case in which the unitaries are drawn from the entire unitary group $U(d)$ with uniform prior probability. Finally, we present an optical experiment for this approach and assess the storage and retrieval quality using quantum tomography of states and processes. The results are discussed in relation to non-optimal measure-and-prepare strategy, highlighting the advantages of our protocol.

Related papers

• Generalized Hybrid Search and Applications to Blockchain and Hash Function Security [50.16790546184646]
  We first examine the hardness of solving various search problems by hybrid quantum-classical strategies. We then construct a hybrid quantum-classical search algorithm and analyze its success probability.
  arXiv  Detail & Related papers  (2023-11-07T04:59:02Z)
• Optimal high-dimensional entanglement concentration in the bipartite scenario [0.0]
  entanglement concentration is the procedure where from $N$ copies of a partially entangled state, a single state with higher entanglement can be obtained. Getting a maximally entangled state is possible for $N=1$, but associated success probability can be extremely low. We study two methods to achieve a probabilistic entanglement concentration for bipartite quantum systems with a large dimensionality for $N=1$.
  arXiv  Detail & Related papers  (2023-04-10T22:36:49Z)
• Optimal Horizon-Free Reward-Free Exploration for Linear Mixture MDPs [60.40452803295326]
  We propose a new reward-free algorithm for learning linear Markov decision processes (MDPs) At the core of our algorithm is uncertainty-weighted value-targeted regression with exploration-driven pseudo-reward. We show that our algorithm only needs to explore $tilde O( d2varepsilon-2)$ episodes to find an $varepsilon$-optimal policy.
  arXiv  Detail & Related papers  (2023-03-17T17:53:28Z)
• Probabilistic pure state conversion on the majorization lattice [0.0]
  Entanglement is among the most fundamental-and at the same time puzzling-properties of quantum physics. We show that the majorization lattice provides an efficient framework in order to characterize the allowed transformations of pure entangled states.
  arXiv  Detail & Related papers  (2023-03-17T16:10:50Z)
• Reversing Unknown Qubit-Unitary Operation, Deterministically and Exactly [0.9208007322096532]
  We consider the most general class of protocols transforming unknown unitary operations within the quantum circuit model. In the proposed protocol, the input qubit-unitary operation is called 4 times to achieve the inverse operation. We show a method to reduce the large search space representing all possible protocols.
  arXiv  Detail & Related papers  (2022-09-07T03:33:09Z)
• Navigating to the Best Policy in Markov Decision Processes [68.8204255655161]
  We investigate the active pure exploration problem in Markov Decision Processes. Agent sequentially selects actions and, from the resulting system trajectory, aims at the best as fast as possible.
  arXiv  Detail & Related papers  (2021-06-05T09:16:28Z)
• Byzantine-Resilient Non-Convex Stochastic Gradient Descent [61.6382287971982]
  adversary-resilient distributed optimization, in which. machines can independently compute gradients, and cooperate. Our algorithm is based on a new concentration technique, and its sample complexity. It is very practical: it improves upon the performance of all prior methods when no. setting machines are present.
  arXiv  Detail & Related papers  (2020-12-28T17:19:32Z)
• 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)
• Revisiting Shor's quantum algorithm for computing general discrete logarithms [0.0]
  We show that Shor's algorithm for computing general discrete logarithms achieves an expected success probability of approximately 60% to 82% in a single run. By slightly increasing the number of group operations that are evaluated quantumly, we show how the algorithm can be further modified to achieve a success probability thatally exceeds 99% in a single run.
  arXiv  Detail & Related papers  (2019-05-22T11:47:38Z)

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.