Energy-constrained discrimination of unitaries, quantum speed limits and a Gaussian Solovay-Kitaev theorem
arXiv:2006.06659 · doi:10.1103/PhysRevLett.126.190504
Abstract
We investigate the energy-constrained (EC) diamond norm distance between unitary channels acting on possibly infinite-dimensional quantum systems, and establish a number of results. Firstly, we prove that optimal EC discrimination between two unitary channels does not require the use of any entanglement. Extending a result by Acín, we also show that a finite number of parallel queries suffices to achieve zero error discrimination even in this EC setting. Secondly, we employ EC diamond norms to study a novel type of quantum speed limits, which apply to pairs of quantum dynamical semigroups. We expect these results to be relevant for benchmarking internal dynamics of quantum devices. Thirdly, we establish a version of the Solovay--Kitaev theorem that applies to the group of Gaussian unitaries over a finite number of modes, with the approximation error being measured with respect to the EC diamond norm relative to the photon number Hamiltonian.
arXiv comment24 pages, no figures. In v2 we added the estimates in Eq. (3) and (4), and improved Thm 6. In v3, which is close to the published version, we improved the overall presentation (e.g. of the proof of Thm 3 in the SM)
References in corpus (49)
- Quantum information with continuous variables
- Gaussian Quantum Information
- Encoding a qubit in an oscillator
- General Benchmarks for Quantum Repeaters
- Fundamental Limits of Repeaterless Quantum Communications
- The maximum speed of dynamical evolution
- Dynamics of Loschmidt echoes and fidelity decay
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- The Quantum Chernoff Bound
- Quantum speed limits in open system dynamics
- The Real Symplectic Groups in Quantum Mechanics and Optics
- Quantum limits to dynamical evolution
- Quantum Data Hiding
- The fundamental limit on the rate of quantum dynamics: the unified bound is tight
- Statistical distinguishability between unitary operations
- Using entanglement improves precision of quantum measurements
- Asymptotic Error Rates in Quantum Hypothesis Testing
- Hiding bits in Bell states
- Generalized Geometric Quantum Speed Limits
- The Chernoff lower bound for symmetric quantum hypothesis testing
- Distinguishability of quantum states under restricted families of measurements with an application to quantum data hiding
- Quantum Speed Limit is Not Quantum
- Tightening Quantum Speed Limits for Almost All States
- Quantum linear Boltzmann equation
- The Perfect Distinguishability of Quantum Operations
- Entanglement Is Not Necessary for Perfect Discrimination between Unitary Operations
- Efficient Discrete Approximations of Quantum Gates
- A Generalization of Quantum Stein's Lemma
- Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
- Geometric Speed Limit of Accessible Many-Body State Preparation
- Discrimination of two channels by adaptive methods and its application to quantum system
- A search for a border between classical and quantum worlds
- How hard is it to approximate the Jones polynomial?
- A chain rule for the quantum relative entropy
- Trading inverses for an irrep in the Solovay-Kitaev theorem
- Energy-constrained diamond norms and their use in quantum information theory
- Local Distinguishability of Multipartite Unitary Operations
- Ultimate data hiding in quantum mechanics and beyond
- How energy conservation limits our measurements
- Monitoring derivation of the quantum linear Boltzmann equation
- Energy-constrained diamond norm with applications to the uniform continuity of continuous variable channel capacities
- Measures of quantum correlations in infinite-dimensional systems
- Entanglement in channel discrimination with restricted measurements
- Quantum optical versus quantum Brownian motion master-equation in terms of covariance and equilibrium properties
- Convergence rates for quantum evolution & entropic continuity bounds in infinite dimensions
- Quantum dynamical semigroups for diffusion models with Hartree interaction
- On the Chernoff distance for asymptotic LOCC discrimination of bipartite quantum states
- Assisted concentration of Gaussian resources
- Characterizing the performance of continuous-variable Gaussian quantum gates
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- Quantum speed limit for states and observables of perturbed open systems
- Continuous-variable quantum state designs: theory and applications
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- Maximal gap between local and global distinguishability of bipartite quantum states
- Infinite-Dimensional Programmable Quantum Processors
- Error bounds for Lie Group representations in quantum mechanics
- Quantum Speed Limit for Change of Basis
- Optimal single-shot discrimination of optical modes
- Energy-limited quantum dynamics
- Convergence Rates for the Trotter Splitting for Unbounded Operators
- Learning and simulating bosonic systems via finite-energy locality
- Tight bounds of quantum speed limit for noisy dynamics via maximum rotation angles