Frozen condition of quantum coherence

Abstract

Quantum coherence as an important physical resource plays the key role in implementing various quantum tasks, whereas quantum coherence is often deteriorated due to the noise. In this paper, we analyse under which dynamical conditions the $l_1$-norm or the relative entropy of coherence can remain unchanged during the whole evolution (freezing coherence). For single qubit systems, a nice formula is given to realize freezing coherence. Conversely, for a $d(d>2)$ dimensional system, we identify universal geometric conditions of freezing coherence. This offers an affirmative answer to the open question: how can one determine whether a unital quantum operation can be decomposed as a convex combination of unitary operations [M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, (Cambridge University Press, Cambridge, 2000)]. Based on this analysis, we also give a complete classification of coherent states from operational coherence theory. This builds the counterpart of entanglement classification under LOCC.

arXiv comment9 pages, 73 references

References in corpus (61)

• Decoherence, einselection, and the quantum origins of the classical
• Advances in Quantum Metrology
• Gaussian Quantum Information
• Quantum-enhanced measurements: beating the standard quantum limit
• Quantifying Coherence
• Quantum Coherence as a Resource
• Operational Resource Theory of Coherence
• Entanglement monotones
• Robustness of coherence: An operational and observable measure of quantum coherence
• Information-theoretic aspects of quantum inseparability of mixed states
• Observable measure of quantum coherence in finite dimensional systems
• Characterizing Nonclassical Correlations via Local Quantum Uncertainty
• Exact and Asymptotic Measures of Multipartite Pure State Entanglement
• Converting Coherence to Quantum Correlations
• Using entanglement against noise in quantum metrology
• Frozen Quantum Coherence
• Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation
• The Entanglement of Formation for Isotropic States
• Quantum coherence and uncertainty in the anisotropic XY chain
• I-concurrence and tangle for isotropic states
• Alternative framework for quantifying coherence
• Non-Local Advantage of Quantum Coherence
• Quantum Correlations and Coherence in Spin-1 Heisenberg Chains
• Operational Advantage of Quantum Resources in Subchannel Discrimination
• Measure-Independent Freezing of Quantum Coherence
• Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem
• Coherence susceptibility as a probe of quantum phase transitions
• Observation of time-invariant coherence in a room temperature quantum simulator
• Structure of the resource theory of quantum coherence
• Evolution equation for quantum coherence
• On the Role of Coherence in Shor's Algorithm
• Quantum coherence of steered states
• Factorization and Criticality in the Anisotropic XY Chain via Correlations
• A Unified Treatment of Convexity of Relative Entropy and Related Trace Functions, with Conditions for Equality
• Extracting quantum coherence via steering
• Quantum advantages for Pauli channel estimation
• Demonstrating quantum coherence and metrology that is resilient to transversal noise
• Indistinguishability-enabled coherence for quantum metrology
• Axiomatic and operational connections between the $l_1$-norm of coherence and negativity
• Generic bound coherence under strictly incoherent operations
• Coherence orders, decoherence and quantum metrology
• Logarithmic coherence: Operational interpretation of ${\ell }_1$-norm coherence
• Dynamics of Quantum Coherence and Quantum Fisher Information After Sudden Quench
• Experimental investigation of nonlocal advantage of quantum coherence
• Witnessing multipartite entanglement by detecting asymmetry
• Markovian evolution of quantum coherence under symmetric dynamics
• Discriminating Strength: a bona fide measure of non-classical correlations
• Ordering states with coherence measures
• Quantum circuit design for accurate simulation of qudit channels
• Frozen condition of quantum coherence for atoms on a stationary trajectory
• Not-so-normal mode decomposition
• Witnessing quantum resource conversion within deterministic quantum computation using one pure superconducting qubit
• Quantum metrology enhanced by coherence-induced-driving in a cavity QED setup
• Quantum advantage for noisy channel discrimination
• Experimental demonstration of one-shot coherence distillation: High-dimensional state conversions
• Tsallis relative $\alpha$ entropy of coherence dynamics in Grover's search algorithm
• The Power of One Clean Qubit in Supervised Machine Learning
• Quantum metrology and coherence
• Non-Markovian coherence dynamics of driven spin boson model: damped quantum beat or large amplitude coherence oscillation
• Incoherent Gaussian equivalence of $m-$mode Gaussian states
• Reversibility of dynamics and multiple-quantum coherences