Optimal cloning of unitary transformations

Abstract

After proving a general no-cloning theorem for black boxes, we derive the optimal universal cloning of unitary transformations, from one to two copies. The optimal cloner is realized by quantum channels with memory, and greately outperforms the optimal measure-and-reprepare cloning strategy. Applications are outlined, including two-way quantum cryptographic protocols.

4 pages, 1 figure, published version

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Cited by in corpus (52)

• Advances in Quantum Cryptography
• Quantum computations without definite causal structure
• Theoretical framework for quantum networks
• Probabilistic theories with purification
• Quantum Cloning Machines and the Applications
• Quantum Physical Unclonable Functions: Possibilities and Impossibilities
• Optimal quantum networks and one-shot entropies
• Optimal probabilistic storage and retrieval of unitary channels
• Probabilistic exact universal quantum circuits for transforming unitary operations
• Generalized channels: channels for convex subsets of the state space
• Optimal networks for Quantum Metrology: semidefinite programs and product rules
• Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality
• Universal super-replication of unitary gates
• Complex conjugation supermap of unitary quantum maps and its universal implementation protocol
• Symmetries of quantum evolutions
• Deterministic superreplication of one-parameter unitary transformations
• Success-or-Draw: A Strategy Allowing Repeat-Until-Success in Quantum Computation
• Information - Disturbance Tradeoff in the Estimation of a Unitary Transformation
• Extremal quantum protocols
• Quantum Strategies and Local Operations
• Minimal computational-space implementation of multi-round quantum protocols
• Decoy States and Two Way Quantum Key Distribution Schemes
• Translating Uncontrolled Systems in Time
• Units of rotational information
• Identification of a reversible quantum gate: assessing the resources
• Communication Cost of Quantum Processes
• Quantum-enhanced learning of rotations about an unknown direction
• Optimal universal quantum circuits for unitary complex conjugation
• Universal construction of decoders from encoding black boxes
• Cloning of a quantum measurement
• Normal completely positive maps on the space of quantum operations
• No-iteration of unknown quantum gates
• No-signalling constrains quantum computation with indefinite causal structure
• Quantum superreplication of states and gates
• No-signaling bounds for quantum cloning and metrology
• Parallelizable adiabatic gate teleportation
• Memory cost of quantum protocols
• Fundamental limits on quantum cloning from the no-signalling principle
• Experimental replication of single-qubit quantum phase gates
• Entropic Bounds For Unitary Testers and Mutually Unbiased Unitary Bases
• Extremal generalized quantum measurements
• Universal adjointation of isometry operations using conversion of quantum supermaps
• Independent Attacks in Imperfect Settings; A Case for A Two Way Quantum Key Distribution Scheme
• Representation matching for delegated quantum computing
• Constructions of mutually unbiased entangled bases
• Quantum Advantage in Storage and Retrieval of Isometry Channels
• Dilation, Discrimination and Uhlmann's Theorem of Link Products of Quantum Channels
• Information Disturbance Tradeoff in Bidirectional QKD
• Optimal cloning with respect to the relative error
• Analytical Lower Bound on Query Complexity for Transformations of Unknown Unitary Operations
• Virtual Cloning of Quantum States
• No-cloning theorem for a single POVM