Quantum Advantage in Storage and Retrieval of Isometry Channels

Abstract

Storage and retrieval refer to the task of encoding an unknown quantum channel $\Lambda$ into a quantum state, known as the program state, such that the channel can later be retrieved. There are two strategies for this task: classical and quantum strategies. The classical strategy uses multiple queries to $\Lambda$ to estimate $\Lambda$ and retrieves the channel based on the estimate represented in classical bits. The classical strategy turns out to offer the optimal performance for the storage and retrieval of unitary channels. In this work, we analyze the asymptotic performance of the classical and quantum strategies for the storage and retrieval of isometry channels. We show that the optimal fidelity for isometry estimation is given by $F=1-\frac{d(D-d)}{n}+O(n^{-2})$, where $d$ and $D$ denote the input and output dimensions of the isometry, and $n$ is the number of queries. This result indicates that, unlike in the case of unitary channels, the classical strategy is suboptimal for the storage and retrieval of isometry channels, which requires $n=\Theta ({\epsilon }^{-1})$ to achieve the diamond-norm error $\epsilon$. We propose a more efficient quantum strategy based on port-based teleportation, which stores the isometry channel in a program state using only $n=\Theta (1/\sqrt{\epsilon })$ queries, achieving a quadratic improvement over the classical strategy. As an application, we extend our approach to general quantum channels, achieving improved program cost compared to prior results by Gschwendtner, Bluhm, and Winter [Quantum \textbf{5}, 488 (2021)].

33 pages, 2 figures

References in corpus (71)

• Quantum algorithm for solving linear systems of equations
• Quantum correlations with no causal order
• Quantum advantage in learning from experiments
• Quantum computations without definite causal structure
• Quantum Circuits Architecture
• Programmable quantum gate arrays
• Information-theoretic bounds on quantum advantage in machine learning
• Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
• Truncations of random unitary matrices
• Memory effects in quantum channel discrimination
• Asymptotic teleportation scheme as a universal programmable quantum processor
• Optimal quantum learning of a unitary transformation
• Optimal state estimation for d-dimensional quantum systems
• Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial
• Simplified instantaneous non-local quantum computation with applications to position-based cryptography
• Quantum teleportation scheme by selecting one of multiple output ports
• Optimal estimation of group transformations using entanglement
• Optimal estimation of quantum dynamics
• Storing quantum dynamics in quantum states: stochastic programmable gate for U(1) operations
• Quantum multimeters: A programmable state discriminator
• A fidelity measure for quantum channels
• Probabilistic implementation of universal quantum processors
• Optimal cloning of unitary transformations
• Asymptotic theory of quantum channel estimation
• Quantum circuits with classical versus quantum control of causal order
• Universal measurement apparatus controlled by quantum software
• Optimal probabilistic storage and retrieval of unitary channels
• Generating random quantum channels
• Fast rate estimation of an unitary operation in SU(d)
• Port-based teleportation in arbitrary dimension
• Programmable quantum state discriminators with simple programs
• A quantum gate array can be programmed to evaluate the expectation value of any operator
• Efficient universal programmable quantum measurements
• Implementation of quantum maps by programmable quantum processors
• Optimal universal programming of unitary gates
• Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies
• Convex optimization of programmable quantum computers
• Optimization and learning of quantum programs
• Entanglement assisted alignment of reference frames using a dense covariant coding
• Approximate programmable quantum processors
• Quantum learning algorithms for quantum measurements
• Multi-copy programmable discrimination of general qubit states
• Probabilistic quantum multimeters
• Optimal quantum-programmable projective measurement with linear optics
• Efficient multi port-based teleportation schemes
• Resource Quantification for the No-Programming Theorem
• Generalized teleportation and entanglement recycling
• Programmable unknown quantum-state discriminators with multiple copies of program and data: A Jordan basis approach
• Optimal universal programmable detectors for unambiguous discrimination
• Scalable programmable quantum gates and a new aspect of the additivity problem for the classical capacity of quantum channels
• Multi-output programmable quantum processor
• Improving performance of probabilistic programmable quantum processors
• Multiport based teleportation -- transmission of a large amount of quantum information
• Probabilistic programmable quantum processors with multiple copies of program state
• Programmability of covariant quantum channels
• Optimal processing of reversible quantum channels
• Optimality of programmable quantum measurements
• Optimal Multi-port-based Teleportation Schemes
• Storing unitary operators in quantum states
• Success probabilities for universal unambiguous discriminators between unknown pure states
• Generalized measurements via programmable quantum processor
• Probabilistic storage and retrieval of qubit phase gates
• Universal construction of decoders from encoding black boxes
• Optimal covariant quantum networks
• Infinite-Dimensional Programmable Quantum Processors
• Storage and retrieval of von Neumann measurements
• Universal adjointation of isometry operations using conversion of quantum supermaps
• Representation matching for delegated quantum computing
• One-to-One Correspondence between Deterministic Port-Based Teleportation and Unitary Estimation
• Programming of channels in generalized probabilistic theories
• Robustness of optimal probabilistic storage and retrieval of unitary channels to noise