We examine the complementarity among coherence (visibility), predictability, and entanglement for qubit and qutrit systems subjected to noisy quantum channels. Using the system-path entanglement framework, analytical expressions for all three quantities are derived for two- and three-slit interferometric setups. The study first establishes the validity of the triality relation in ideal conditions and then investigates its behavior under amplitude and phase damping. We find that amplitude damping redistributes coherence and population imbalance without violating complementarity, while phase damping reduces coherence but leaves predictability unchanged. These results demonstrate that the complementarity relation remains preserved even in open quantum systems, highlighting its robustness against decoherence and providing a unified analytical understanding of noisy quantum interferometry in low-dimensional systems.
We examine the complementarity among coherence (visibility), predictability, and entanglement for qubit and qutrit systems subjected to noisy quantum channels. Using the system-path entanglement framework, analytical expressions for all three quantities are derived for two- and three-slit interferometric setups. The study first establishes the validity of the triality relation in ideal conditions and then investigates its behavior under amplitude and phase damping. We find that amplitude damping redistributes coherence and population imbalance without violating complementarity, while phase damping reduces coherence but leaves predictability unchanged. These results demonstrate that the complementarity relation remains preserved even in open quantum systems, highlighting its robustness against decoherence and providing a unified analytical understanding of noisy quantum interferometry in low-dimensional systems.
Besides Heisenberg uncertainty, entanglement is another mechanism that can enforce complementarity in multipartite quantum systems. Analysing its effects in a bipartite system of two qubits, M. Jakob and J. Bergou had shown that the usual wave-particle duality relation, in interferometric systems, regarding which-way information and interference visibility, should be extended to a ¿triality¿ relation containing, in addition, a quantitative entanglement measure. Employing a model for the neutral K-meson propagation in free space in which its weak decay products are included as a second party, we study its effect in the neutral kaon interferometry. We show that a new quantitative triality relation can also be established in this case. The state of the total system remains pure in the course of dynamics, so, we can use the von Neumann entropy of a reduced party as a quantitative measure of entanglement. The other two quantities in the triality relation are the distinguishability between the decay products states corresponding to the two distinct kaon propagation modes KS and KL, and the wave-like path interference between these states. These two distinct modes are the analogues to the two separated paths in usual interferometric devices. The inequality obtained here can account for the complementarity between strangeness oscillations and lifetime information previously considered in the literature. Moreover, it allows us to visualise through the K0 ¿ K0 oscillations the fundamental role of entanglement in quantum complementarity.
We introduce a complete set of complementary quantities in bipartite, two-dimensional systems. Complementarity then relates the quantitative entanglement measure concurrence which is a bipartite property to the single-particle quantum properties predictability and visibility, for the most general quantum state of two qubits. Consequently, from an interferometric point of view, the usual wave-particle duality relation must be extended to a ``triality'' relation containing, in addition, the quantitative entanglement measure concurrence, which has no classical counterpart and manifests a genuine quantum aspect of bipartite systems. A generalized duality relation, that also governs possible violations of the Bell's inequality, arises between single- and bipartite properties.
Quantum dots are nanometer-scale semiconductor particles that exhibit size-dependent quantum mechanical properties. In this work, we investigate the dynamics of quantum correlations, quantified by the concurrence and the quantum coherence, in a bipartite system of coupled double quantum dots. The analysis is carried out within both Markovian and non-Markovian regimes, and further extended to different noisy quantum channels, including amplitude damping, phase flip, and phase damping. Our results show that environmental memory plays a crucial role in the preservation of quantum correlations, leading to oscillatory behavior and partial revivals in the non-Markovian regime, in contrast to the monotonic decay observed under Markovian dynamics. Moreover, distinct decoherence mechanisms induce qualitatively different effects: dissipative channels rapidly suppress correlations, while phase-based channels lead to either redistribution or gradual degradation. A key finding is that quantum coherence exhibits a higher robustness compared to entanglement under all considered conditions, highlighting its relevance as a reliable quantum resource in noisy environments. These results provide valuable insights into the control and protection of quantum correlations in realistic solid-state systems.
We systematically characterize quantum entanglement in all sixteen combinations of two-qubit Bell states across three operational regimes: pure superposition, noiseless mixing, and asymmetric mixing of one noisy and one pure Bell state. For pure superpositions, we calculate the von Neumann entropy and show that entanglement depends critically on the relative phase phi between superposed states. For mixed states, we use concurrence C under three physically motivated decoherence channels. The Depolarizing (DP) and Phase Damping (PD) channels are modeled as global, collective operations on the two-qubit Hilbert space, while Amplitude Damping (AD) is treated as independent local decay on each qubit, reflecting the asymmetric, energy-dissipating nature of spontaneous emission. A central and counterintuitive result is that increasing noise can raise concurrence in specific parameter regimes across all three channels. We further map the boundary between mathematical entanglement (C > 0) and operational quantum non-locality using the Horodecki criterion, finding this boundary to be strongly channel-dependent. Under Phase Damping, the Bell-local entanglement regime vanishes entirely for identical and same-bases mixtures, meaning any surviving entanglement guarantees a CHSH violation. Under Depolarizing noise, a large Bell-local region requires mixing probability r > 1/sqrt(2) to recover non-locality at maximum noise. For Amplitude Damping, certain mixtures exhibit a non-monotonic Horodecki parameter M(T): concurrence decreases monotonically with noise, yet the capacity for CHSH violation is lost at intermediate noise levels and restored at high noise, as maximal damping repurifies the noisy branch. These results provide a unified analytical reference for entanglement and non-locality management across Bell-state combinations and decoherence channels relevant to NISQ architectures.
Abstract This paper systematically investigates the coherence dynamics of a two-qubit system under correlated channels. Through density matrix transformation and operator algebra derivation, we analyze the regulatory effects of memory properties of correlated amplitude damping, phase damping, and depolarization channels on three kinds of coherence, namely l 2 -norm coherence, Tsallis 2-relative entropy coherence, and Rényi 2-relative entropy coherence. The results show that phase damping and depolarization channels induce coherence freezing under perfect memory conditions, where coherence values remain invariant with channel damping rate variations. In partial memory environments, l 2 -norm coherence exhibits superior stability and retains coherence more efficiently than the other two coherence measures. In addition, we quantitatively evaluate the cohering and decohering power of these coherences under the correlated amplitude damping channel. This work provides theoretical support for anti-noise design of quantum technologies in open quantum systems.
Abstract We study the distribution and monogamous relations of quantum coherence for three-qubit systems under the influence of local amplitude-damping, phase-damping and random unitary channels, respectively. We find that under the influence of the considered channels, the W state has both global and bipartite coherence, and its monogamy is always equal to zero. For the Greenberger–Horne–Zeilinger) state, however, there is only global coherence in the time evolution and the monogamy is always positive. We also present a partially entangled state, | Ψ ⟩ , which has global, bipartite, and monomeric coherences and negative monogamy during the whole time evolution.