Sequential Implementation of Global Quantum Operations

Abstract

We study the possibility for a global unitary applied on an arbitrary number of qubits to be decomposed in a sequential unitary procedure, where an ancillary system is allowed to interact only once with each qubit. We prove that sequential unitary decompositions are in general impossible for genuine entangling operations, even with an infinite-dimensional ancilla, being the controlled-NOT gate a paradigmatic example. Nevertheless, we find particular nontrivial operations in quantum information that can be performed in a sequential unitary manner, as is the case of quantum error correction and quantum cloning.

4 pages, accepted in Physical Review Letters

References in corpus (5)

• Quantum cloning
• DMRG and periodic boundary conditions: a quantum information perspective
• Sequential generation of entangled multi-qubit states
• Sequential Generation of Matrix-Product States in Cavity QED
• Sequential Quantum Cloning

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• Sequential generation of projected entangled-pair states
• NMR Experimental Demonstration of Probabilistic Quantum Cloning
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• Categorical Tensor Network States
• Biomimetic Cloning of Quantum Observables
• Entanglement classification with matrix product states
• Universal quantum computation by the unitary control of ancilla qubits and using a fixed ancilla-register interaction
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• Ancilla-driven quantum computation for qudits and continuous variables
• Sequential quantum cloning under real-life conditions
• Multipartite maximally entangled states in symmetric scenarios
• Sequential Adiabatic Generation of Chiral Topological States
• Nonexistence of a universal quantum machine to examine the precision of unknown quantum states
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• Minimal ancilla mediated quantum computation
• A Unified Quantum NOT Gate
• Genuine fidelity gaps associated with a sequential decomposition of genuinely entangling isometry and unitary operations