How difficult is it to prepare a quantum state?

Abstract

Consider a quantum system prepared in an input state. One wants to drive it into a target state. Assuming classical states and operations as free resources, I identify a geometric cost function which quantifies the difficulty of the protocol in terms of how different it is from a classical process. The quantity determines a lower bound to the number of commuting unitary transformations required to complete the task. I then discuss the link between the quantum character of a state preparation and the amount of coherence and quantum correlations that are created in the target state.

arXiv commentPublished version

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Cited by in corpus (23)

• When Entanglement meets Classical Communications: Quantum Teleportation for the Quantum Internet (Invited Paper)
• Unifying Quantum and Classical Speed Limits on Observables
• Circuit Complexity across a Topological Phase Transition
• Operational definition of a quantum speed limit
• Resource theory of quantum uncomplexity
• Measuring coherence of quantum measurements
• Quantum speed limit for complex dynamics
• Information geometry approach to quantum stochastic thermodynamics
• Complexity of Pure and Mixed Qubit Geodesic Paths on Curved Manifolds
• Tight and attainable quantum speed limit for open systems
• Bhatia-Davis formula in the quantum speed limit
• Quantifying the difference between many-body quantum states
• Resource theoretic efficacy of the single copy of a two-qubit entangled state in a sequential network
• Quantum Speed Limit in Terms of Coherence Variations
• Information flow and error scaling for fully-quantum control
• A geometrical description of non-Hermitian dynamics: speed limits in finite rank density operators
• Information geometry of transitions between quantum nonequilibrium steady states
• First Law of Quantum Thermodynamics in a Driven Open Two-Level System
• Experimental realization of optimal time-reversal on an atom chip for quantum undo operations
• One-step direct measurement of the entangled W states with cross-Kerr nonlinearity
• Tight bounds of quantum speed limit for noisy dynamics via maximum rotation angles
• Evaluating Pauli errors on cluster states by weighted distances
• Typicality of Contextuality