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arXiv:2502.15625 · Physical review. D/Physical review. D.

Critical unstable qubits: An application to the B 0 B ¯ 0 meson system

Dimitrios Karamitros, Thomas McKelvey, Apostolos Pilaftsis A

Published May 16, 2025• 1 citation
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Abstract

We extend our previous work on a novel class of unstable qubits which we have identified recently and called them critical unstable qubits (CUQs). The characteristic property of CUQs is that the energy-level and decay-width vectors, E and Γ , are orthogonal to one another, and the key parameter r = | Γ | / | 2 E | is less than 1. Most remarkably, CUQs exhibit two atypical behaviors: (i) they display coherence-decoherence oscillations in a co-decaying frame of the system described by a unit Bloch vector b , and (ii) the unit Bloch vector b describing a pure CUQ sweeps out unequal areas during equal intervals of time, while rotating about the vector E . The latter phenomenon emerges beyond the usual oscillatory pattern due to the energy-level difference of the two-level quantum system, which governs an ordinary qubit. By making use of a Fourier series decomposition, we define anharmonicity observables that quantify the degree of oscillation of a CUQ. We apply the results of our formalism to the B 0 B ¯ 0 -meson system and derive, for the first time, generic upper limits on these new observables.

DOI
10.1103/physrevd.111.096020

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We extend our previous work on a novel class of unstable qubits which we have identified recently and called them critical unstable qubits (CUQs). The characteristic property of CUQs is that the energy-level and decay-width vectors, E and Γ , are orthogonal to one another, and the key parameter r = | Γ | / | 2 E | is less than 1. Most remarkably, CUQs exhibit two atypical behaviors: (i) they display coherence-decoherence oscillations in a co-decaying frame of the system described by a unit Bloch vector b , and (ii) the unit Bloch vector b describing a pure CUQ sweeps out unequal areas during equal intervals of time, while rotating about the vector E . The latter phenomenon emerges beyond the usual oscillatory pattern due to the energy-level difference of the two-level quantum system, which governs an ordinary qubit. By making use of a Fourier series decomposition, we define anharmonicity observables that quantify the degree of oscillation of a CUQ. We apply the results of our formalism to the B 0 B ¯ 0 -meson system and derive, for the first time, generic upper limits on these new observables.
We study in detail the dynamics of unstable two-level quantum systems by adopting the Bloch-vector representation. We identify a novel class of critical scenarios in which the so-called energy-level and decay-width vectors, E{\bf E}E and Γ{\bf\Gamma}Γ, are orthogonal to one another, and the parameter r=∣Γ∣/(2∣E∣)r = |{\bf \Gamma}|/(2|{\bf E}|)r=∣Γ∣/(2∣E∣) is less than 1. Most remarkably, we find that critical unstable qubit systems exhibit atypical behaviours like coherence--decoherence oscillations when analysed in an appropriately defined co-decaying frame of the system. By making use of a Fourier series decomposition, we define anharmonicity observables that quantify the degree of non-sinusoidal oscillation of a CUQ. We apply the results of our formalism to the neutral-meson systems and derive generic upper limits on these new observables. In particular, we provide a compilation table of all well-explored meson--antimeson two-level systems in terms of Bloch-sphere parameters.
We study in detail the dynamics of unstable two-level quantum systems by adopting the Bloch-vector representation. We identify a novel class of critical scenarios in which the so-called energy-level and decay-width vectors, E{\bf E}E and Γ{\bfΓ}Γ, are orthogonal to one another, and the parameter r=∣Γ∣/(2∣E∣)r = |{\bf Γ}|/(2|{\bf E}|)r=∣Γ∣/(2∣E∣) is less than~1. Most remarkably, we find that critical unstable qubit systems exhibit atypical behaviours like coherence--decoherence oscillations when analysed in an appropriately defined co-decaying frame of the system. By making use of a Fourier series decomposition, we define anharmonicity observables that quantify the degree of non-sinusoidal oscillation of a CUQ. We apply the results of our formalism to the neutral-meson systems and derive generic upper limits on these new observables. In particular, we provide a compilation table of all well-explored meson--antimeson two-level systems in terms of Bloch-sphere parameters.
We extend previous studies on a novel class of unstable two-level systems which were called Critical Unstable Qubits (CUQs). In an appropriately defined co-decaying frame, the CUQs exhibit striking phenomena of indefinite anharmonic oscillations between two states and coherence-decoherence oscillations of mixed states. These features are distinct from the usual Rabi oscillations observed in the Hermitian counterpart of two-level systems, which are harmonic and preserve the coherence of the quantum state. We employ the density matrix formalism to study these phenomena for mixed states and delve into the nature of the trajectory traversed by these states in the Bloch sphere by studying the time evolution of the Bloch vector that describes the quantum state of the unstable qubit. In particular, we provide for the first time explicit geometric constructions to obtain trajectories of both pure and mixed CUQs in and on the Bloch sphere. This enables us to identify the stationary points of CUQs, at which the states do not evolve in time in the co-decaying frame. The potential implications of our findings for particle cosmology and quantum simulations of non-Hermitian Hamiltonians are discussed.
We study in detail the dynamics of unstable two-level quantum systems by adopting the Bloch-sphere formalism of qubits. By employing the Bloch-vector representation for such unstable qubit systems, we identify a novel class of critical scenarios in which the so-called energy-level and decay-width vectors, E\mathbf{E}E and $\mathbf{\ensuremath{\Gamma}}$, are orthogonal to one another, and the parameter $r=|\mathbf{\ensuremath{\Gamma}}|/(2|\mathbf{E}|)$ is less than 1. Most remarkably, we find that critical unstable qubit systems exhibit atypical behaviors like coherence-decoherence oscillations when analyzed in an appropriately defined codecaying frame of the system. In the same frame, a unit Bloch vector b\mathbf{b}b describing a pure critical qubit will sweep out unequal areas during equal intervals of time, while rotating about the vector E\mathbf{E}E. These phenomena emerge beyond the usual oscillatory pattern due to the energy-level difference of the two-level quantum system. Interestingly enough, we observe that these new features will persist even for quasicritical scenarios, in which the vectors E\mathbf{E}E and $\mathbf{\ensuremath{\Gamma}}$ are not perfectly orthogonal to each other. Applications of our results to quantum information and to unstable meson-antimeson and other systems are discussed.
Progress in fabrication of semiconductor and superconductor qubits has greatly diminished the number of decohering defects, thus decreasing the devastating low-frequency 1 / f noise and extending the qubits' coherence times (dephasing time T 2 * and the echo decay time T 2 ). However, large qubit-to-qubit variation of the coherence properties remains a problem, making it difficult to produce a large-scale register where all qubits have a uniformly high quality. In this work, we show that large variability is a characteristic feature of a qubit dephased by a sparse bath made of many ( n ≫ 1 ) decohering defects, coupled to the qubit with similar strength. We model the defects as two-level fluctuators (TLFs) whose transition rates γ are sampled from a log-uniform distribution over an interval [ γ m , γ M ] , which is a standard model for 1 / f noise. We investigate decoherence by such a bath in the limit of high-quality qubit, i.e., when the TLF density d is small (the limit of sparse bath, with d = n / w ≪ 1 , where n is the number of TLFs and w = ln [ γ M / γ m ] is the log-width of the distribution). We show that different realizations of the bath produce very similar noise power spectra S ( f ) ∼ 1 / f , but lead to drastically different coherence times T 2 * and T 2 . Thus the spectral density S ( f ) does not determine coherence of a qubit coupled to a sparse TLF bath, as opposed to a dense bath; instead, decoherence is controlled by only a few exceptional fluctuators, determined by their value of γ . We show that removing only two of these TLFs greatly increases T 2 and T 2 * times. Our findings help theoretical understanding and further improvements in the coherence properties of semiconductor and superconductor qubits, battling the 1 / f noise in these platforms. Published by the American Physical Society 2024
A bstract With the advent of Belle II and the LHCb upgrade, the precision measurements of various B-Physics observables are on cards. This holds significant potential for delving into physics beyond the standard model of electroweak interactions. These measurements can also serve as means to establish limits on phenomena occurring at much finer length scales, such as quantum decoherence, which may arise due to potential discreteness in space-time or non-trivial topological effects. In this work, we set up the formalism to investigate the impact of quantum decoherence on several potential observables in B meson systems. The approach employs the trace-preserving Kraus operator formalism, extending unitary evolution to non-unitary dynamics while maintaining complete positivity. In this formalism, the decoherence effects are parametrized in terms of a single parameter. Through the analysis of purely leptonic, semileptonic, and non-leptonic decays of B mesons, we identify observables that could, in principle, be influenced by decoherence. The theoretical expressions are provided without neglecting the impact of decay width difference (∆Γ) and CP violation in mixing. Considering that many of these observables can be measured with high precision using the abundant data collected by LHCb and Belle II, our formalism can be applied to establish constraints on the decoherence parameter through multiple decay channels. This offers an alternative set-up for such studies, which, at present, are predominantly conducted in the neutrino sector.