Quantum copying: Fundamental inequalities

Abstract

How well one can copy an arbitrary qubit? To answer this question we consider two arbitrary vectors in a two-dimensional state space and an abstract copying transformation which will copy these two vectors. If the vectors are orthogonal, then perfect copies can be made. If they are not, then errors will be introduced. The size of the error depends on the inner product of the two original vectors. We derive a lower bound for the amount of noise induced by quantum copying. We examine both copying transformations which produce one copy and transformations which produce many, and show that the quality of each copy decreases as the number of copies increases.

5 pages + 1 figure, LaTeX with revtex, epsfig submitted to Phys. Rev. A

References in corpus (1)

• Broadcasting of entanglement via local copying

Cited by in corpus (32)

• Optimal Quantum Cloning Machines
• Optimal Cloning of Pure States
• Probabilistic cloning and identification of linearly independent quantum states
• Optimal Cloning of Pure States, Judging Single Clones
• Quantum copying: A network
• The optimal cloning of quantum coherent states is non-Gaussian
• Quantum Cloning Machines and the Applications
• Remote information concentration using a bound entangled state
• Quantum State Separation, Unambiguous Discrimination and Exact Cloning
• Broadcasting of entanglement via local copying
• Quantum information distribution via entanglement
• "Assisted cloning'' and "orthogonal-complementing" of an unknown state
• Reexamination of optimal quantum state estimation of pure states
• Optimal minimal measurements of mixed states
• Strategies and Networks for State-Dependent Quantum Cloning
• Probabilistic quantum cloning via Greenberger-Horne-Zeilinger states
• Lower bound on the relative error of mixed-state cloning and related operations
• The nonequilibrium cost of accurate information processing
• Optimal Probabilistic Simulation of Quantum Channels from the Future to the Past
• Realizing probabilistic identification and cloning of quantum states via universal quantum logic gates
• Probabilistic cloning with supplementary information
• Quantum Network Coding for General Graphs
• Bounds for state-dependent quantum cloning
• Global-fidelity limits of state-dependent cloning of mixed states
• Geometrical Conditions for CPTP Maps and their Application to a Quantum Repeater and a State-dependent Quantum Cloning Machine
• Quantum Clone and States Estimation for n-state System
• Improving the Fidelity of Quantum Cloning by Fast Cycling away the Unwanted Transition
• Universal Asymmetric Quantum Cloning Revisited
• Some bounds for quantum copying
• A simple eavesdropping strategy of BB84 protocol
• No-cloning theorem for a single POVM
• Some bounds for quantum copying with multiple copies