Unified quantum no-go theorems and transforming of quantum states in a restricted set

Abstract

The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. It remains an open problem of finding general forbidden principles to unify these results. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed state in Hilbert space of finite dimension. Two general forms include the no-cloning theorem, the no-deleting theorem, and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may yield to fruitful results that are completely characterized with the linear independence of the input pure states. The generalized upper bounds for the success probability will be proved. Third, we generalize a recent superposing of unknown states with fixed overlaps when multiple copies of the input states are available.

References in corpus (41)

• Quantum Cryptography
• Advances in Quantum Metrology
• The Security of Practical Quantum Key Distribution
• Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
• Unconditional Security Of Quantum Key Distribution Over Arbitrarily Long Distances
• Security of quantum key distribution using d-level systems
• Multiple Particle Interference and Quantum Error Correction
• Quantum Copying: Beyond the No-Cloning Theorem
• Optimal Quantum Cloning Machines
• Noncommuting mixed states cannot be broadcast
• Quantum cloning
• Optimal Universal and State-Dependent Quantum Cloning
• Optimal Cloning of Pure States
• Probabilistic cloning and identification of linearly independent quantum states
• Unambiguous Discrimination Between Linearly-Independent Quantum States
• Optimal universal quantum cloning and state estimation
• Experimental Quantum Cloning of Single Photons
• A high-fidelity noiseless amplifier for quantum light states
• Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence
• Quantum cloning and the capacity of the Pauli channel
• Impossibility of deleting an unknown quantum state
• Distinguishability of quantum states under restricted families of measurements with an application to quantum data hiding
• Quantum Cloning Machines and the Applications
• Experimental Quantum Cloning with Prior Partial Information
• Experimental realization of optimal asymmetric cloning and telecloning via partial teleportation
• Quantum State Separation, Unambiguous Discrimination and Exact Cloning
• Optimal Copying of One Quantum Bit
• Quantum superposition of multiple clones and the novel cloning machine
• On the existence of physical transformations between sets of quantum states
• Multipartite Asymmetric Quantum Cloning
• Creation of superposition of unknown quantum states
• Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states
• Superbroadcasting of mixed states
• General impossible operations in quantum information
• The Forbidden Quantum Adder
• Unified Universal Quantum Cloning Machine and Fidelities
• Region of fidelities for a 1 -> N universal qubit quantum cloner
• Mixed Qubit Cannot Be Universally Broadcast
• Optimal Broadcasting of Mixed States
• Generalised Asymmetric Quantum Cloning
• Controlling the flow of information in quantum cloners: Asymmetric cloning

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• Quantum cloning of steering
• Impossibility of creating a superposition of unknown quantum states
• Characterizing the superposition of arbitrary random quantum states and a known quantum state