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Operational Interpretations of the l1 Norm Coherence in Pure Quantum Systems

Feng Liu, Dong-Mei Gao, Xiao‐Qiu Cai

International Journal of Theoretical PhysicsAug 6, 20191 citation

Modification of the expression of l1-norm of coherence

Manis Hazra, Debabrata Goswami

Though a well-verified approach of quantifying quantum coherence is l1-norm, this is not normalized for a multi-qubit (multi-level) system. We propose a modification to show that the altered expression normalizes a multi-qubit (multi-level) system coherence with numerical studies.

Quantum 2.0 Conference and ExhibitionJan 1, 20221 citation

Modeling of qubit coherence variability due to two-level systems

J. Tersoff, James Michael Hannon

Bulletin of the American Physical SocietyMar 16, 20213 citations

Time–Energy Uncertainty Relation in Nonrelativistic Quantum Mechanics

Danko Dimchev Georgiev

The time–energy uncertainty relation in nonrelativistic quantum mechanics has been intensely debated with regard to its formal derivation, validity, and physical meaning. Here, we analyze two formal relations proposed by Mandelstam and Tamm and by Margolus and Levitin and evaluate their validity using a minimal quantum toy model composed of a single qubit inside an external magnetic field. We show that the ℓ1 norm of energy coherence C is invariant with respect to the unitary evolution of the quantum state. Thus, the ℓ1 norm of energy coherence C of an initial quantum state is useful for the classification of the ability of quantum observables to change in time or the ability of the quantum state to evolve into an orthogonal state. In the single-qubit toy model, for quantum states with the submaximal ℓ1 norm of energy coherence, C<1, the Mandelstam–Tamm and Margolus–Levitin relations generate instances of infinite “time uncertainty” that is devoid of physical meaning. Only for quantum states with the maximal ℓ1 norm of energy coherence, C=1, the Mandelstam–Tamm and Margolus–Levitin relations avoid infinite “time uncertainty”, but they both reduce to a strict equality that expresses the Einstein–Planck relation between energy and frequency. The presented results elucidate the fact that the time in the Schrödinger equation is a scalar variable that commutes with the quantum Hamiltonian and is not subject to statistical variance.The time–energy uncertainty relation in nonrelativistic quantum mechanics has been intensely debated with regard to its formal derivation, validity, and physical meaning. Here, we analyze two formal relations proposed by Mandelstam and Tamm and by Margolus and Levitin and evaluate their validity using a minimal quantum toy model composed of a single qubit inside an external magnetic field. We show that the ℓ1 norm of energy coherence C is invariant with respect to the unitary evolution of the quantum state. Thus, the ℓ1 norm of energy coherence C of an initial quantum state is useful for the classification of the ability of quantum observables to change in time or the ability of the quantum state to evolve into an orthogonal state. In the single-qubit toy model, for quantum states with the submaximal ℓ1 norm of energy coherence, C<1, the Mandelstam–Tamm and Margolus–Levitin relations generate instances of infinite “time uncertainty” that is devoid of physical meaning. Only for quantum states with the maximal ℓ1 norm of energy coherence, C=1, the Mandelstam–Tamm and Margolus–Levitin relations avoid infinite “time uncertainty”, but they both reduce to a strict equality that expresses the Einstein–Planck relation between energy and frequency. The presented results elucidate the fact that the time in the Schrödinger equation is a scalar variable that commutes with the quantum Hamiltonian and is not subject to statistical variance.

arXiv:2401.07634SymmetryJan 14, 20243 citations

Coherence, correlation and non-Markovianity in qubit systems

Ning Tang, Wen Cheng, Hao‐Sheng Zeng

The European Physical Journal DSep 30, 20147 citations

From Trace Distance to Coherence in a Dephasing Qubit: A Single-Qubit View of

Humberto Arrabal

We consider a single qubit undergoing pure dephasing with fixed populations and show that, fora natural pair of phase-opposite states, the trace distance coincides exactly with the ℓ1-norm ofcoherence. This allows the Breuer–Laine–Piilo (BLP) non-Markovianity indicator to be expresseddirectly in terms of single-qubit coherence dynamics within this setting, avoiding the usual optimizationover initial states. We also derive a simple relation between the entropy rate and coherence,showing that coherence revivals necessarily correspond to intervals of decreasing von Neumann entropy.Together, these results provide a transparent way to connect coherence, distinguishability,and information flow in dephasing qubits.We consider a single qubit undergoing pure dephasing with fixed populations and show that, fora natural pair of phase-opposite states, the trace distance coincides exactly with the ℓ1-norm ofcoherence. This allows the Breuer–Laine–Piilo (BLP) non-Markovianity indicator to be expresseddirectly in terms of single-qubit coherence dynamics within this setting, avoiding the usual optimizationover initial states. We also derive a simple relation between the entropy rate and coherence,showing that coherence revivals necessarily correspond to intervals of decreasing von Neumann entropy.Together, these results provide a transparent way to connect coherence, distinguishability,and information flow in dephasing qubits.

Apr 25, 20260 citations

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