Fundamental limits on quantum cloning from the no-signalling principle
arXiv:2305.02002 · doi:10.1103/PhysRevA.109.022221
Abstract
The no-cloning theorem is a cornerstone of quantum cryptography. Here we generalize and rederive in a unified framework various upper bounds on the maximum achievable fidelity of probabilistic and deterministic cloning machines. Building on ideas by Gisin [Phys.~Lett.~A, 1998], our result starts from the fact that remote state preparation is possible and the no-signalling principle holds. We apply our general theorem to several subsets of states that are of interest in quantum cryptography.
References in corpus (41)
- Quantum cryptography: Public key distribution and coin tossing
- Quantum secret sharing
- How to share a quantum secret
- Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
- Optimal Quantum Cloning Machines
- A simple formula for the average gate fidelity of a quantum dynamical operation
- Quantum Information and Relativity Theory
- Exact and Approximate Unitary 2-Designs: Constructions and Applications
- On the Theory of Quantum Secret Sharing
- Optimal Cloning of Pure States
- Probabilistic cloning and identification of linearly independent quantum states
- General properties of Nonsignaling Theories
- Hudson's Theorem for finite-dimensional quantum systems
- Multiqubit Clifford groups are unitary 3-designs
- Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms
- Quantum cloning without signaling
- Mutually unbiased binary observable sets on N qubits
- Optimal purification of single qubits
- The no-signaling condition and quantum dynamics
- Quantum cloning machines for equatorial qubits
- Unitary designs and codes
- Economical Phase-Covariant Cloning of Qudits
- Random quantum circuits are approximate unitary -designs in depth
- Reexamination of optimal quantum state estimation of pure states
- Quantum homomorphic encryption from quantum codes
- Unconditionally Secure Key Distribution In Higher Dimensions By Depolarization
- Optimal cloning of unitary transformations
- Optimal probabilistic cloning and purification of quantum states
- Quantum replication at the Heisenberg limit
- Quantum circuits for exact unitary -designs and applications to higher-order randomized benchmarking
- No Signalling and Probabilistic Quantum Cloning
- Universal super-replication of unitary gates
- Certifying quantumness: Benchmarks for the optimal processing of generalized coherent and squeezed states
- Deterministic superreplication of one-parameter unitary transformations
- 6-qubit Optimal Clifford Circuits
- Cloning of spin-coherent states
- Approximate reconstructability of quantum states and noisy quantum secret sharing schemes
- Probabilistic exact cloning and probabilistic no-signalling
- Experimental limit on non-linear state-dependent terms in quantum theory
- Privacy and correctness trade-offs for information-theoretically secure quantum homomorphic encryption
- No-signaling bounds for quantum cloning and metrology