Optimal Copying of One Quantum Bit

Abstract

A quantum copying machine producing two (in general non-identical) copies of an arbitrary input state of a two-dimensional Hilbert space (qubit) is studied using a quality measure based on distinguishability of states, rather than fidelity. The problem of producing optimal copies is investigated with the help of a Bloch sphere representation, and shown to have a well-defined solution, including cases in which the two copies have unequal quality, or the quality depends upon the input state (is ``anisotropic'' in Bloch sphere language), or both. A simple quantum circuit yields the optimal copying machine. With a suitable choice of parameters it becomes an optimal eavesdropping machine for some versions of quantum cryptography, or reproduces the Buzek and Hillery result for isotropic copies.

RevTex, 26 pages, 2 Postscript figures

References in corpus (4)

• Optimal Quantum Cloning Machines
• Optimal Universal and State-Dependent Quantum Cloning
• Optimal universal quantum cloning and state estimation
• Quantum copying: A network

Cited by in corpus (52)

• Quantum cloning
• Quantum cloning and the capacity of the Pauli channel
• Optimal Cloning of Pure States, Judging Single Clones
• On Quantum Fidelities and Channel Capacities
• Asymmetric quantum cloning machines in any dimension
• Optimal cloning of coherent states with a linear amplifier and beam splitters
• Quantum Network Coding
• Coherent pulse implementations of quantum cryptography protocols resistant to photon number splitting attacks
• Two qubit copying machine for economical quantum eavesdropping
• Quantum Cloning Machines and the Applications
• The structure of degradable quantum channels
• Quantum information distributors: Quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit
• Experimental realization of optimal asymmetric cloning and telecloning via partial teleportation
• Optimal N-to-M Cloning of Quantum Coherent States
• Asymptotic quantum cloning is state estimation
• Scheme for the implementation of a universal quantum cloning machine via cavity-assisted atomic collisions in cavity QED
• Multipartite Asymmetric Quantum Cloning
• Experimental Realization of $1\to 2$ Asymmetric Phase-Covariant Quantum Cloning
• Quantum information becomes classical when distributed to many users
• Extremal equation for optimal completely-positive maps
• Symmetric Extension of Two-Qubit States
• Quantum partial teleportation as optimal cloning at a distance
• Practical quantum key distribution: On the security evaluation with inefficient single-photon detectors
• Separability in Asymmetric Phase-Covariant Cloning
• Optimal cloning of qubits given by arbitrary axisymmetric distribution on Bloch sphere
• Conditional implementation of asymmetrical universal quantum cloning machine
• Simulating a single qubit channel using a mixed state environment
• Distribution of quantum Fisher information in asymmetric cloning machines
• Optimal multicopy asymmetric Gaussian cloning of coherent states
• Unified quantum no-go theorems and transforming of quantum states in a restricted set
• Mixed Qubit Cannot Be Universally Broadcast
• Detecting Consistency of Overlapping Quantum Marginals by Separability
• Optimal partial estimation of quantum states from several copies
• Optimal copying of entangled two-qubit states
• Reversibility of continuous-variable quantum cloning
• Extremal asymmetric universal cloning machines
• Asymmetric quantum multicast network coding: asymmetric optimal cloning over quantum networks
• Quantum key distribution with authentication
• Probing Quantum Telecloning on Superconducting Quantum Processors
• Experimental demonstration of optimal universal asymmetric quantum cloning of polarization states of single photons by partial symmetrization
• Quantum Telecloning on NISQ Computers
• Allowing leakage can increase quantum transmission
• Cloning of arbitrary mirror-symmetric distributions on Bloch sphere: Optimality proof and proposal for practical photonic realization
• Controlling the flow of information in quantum cloners: Asymmetric cloning
• The pitfalls of deciding whether a quantum channel is (conjugate) degradable and how to avoid them
• Optimal one-shot entanglement sharing
• A Graphic Representation of States for Quantum Copying Machines
• Universal Asymmetric Quantum Cloning Revisited
• On optimal cloning and incompatibility
• Irreducibly $SU(2)$-covariant quantum channels of low rank
• Virtual Cloning of Quantum States
• Test of Common Sense in Quantum Copying Process