We study the non-Markovian effects on the dynamics of entanglement in an exactly solvable model that involves two independent oscillators, each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional integral methods to find an exact solution to the single-oscillator problem which includes an analytic expression for the density matrix and the complete statistics, i.e., the probability distribution functions for observables. For long bath time correlations, we see nonmonotonic evolution of the uncertainties in observables. Further, we extend this exact solution to the two-particle problem and find the dynamics of entanglement in a subspace. We find the phenomena of ``sudden death'' and ``rebirth'' of entanglement. Interestingly, all memory effects enter via the functional form of the energy and hence the time of death and rebirth is controlled by the amount of noisy energy added into each oscillator. If this energy increases above (decreases below) a threshold, we obtain sudden death (rebirth) of entanglement.We study the non-Markovian effects on the dynamics of entanglement in an exactly solvable model that involves two independent oscillators, each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional integral methods to find an exact solution to the single-oscillator problem which includes an analytic expression for the density matrix and the complete statistics, i.e., the probability distribution functions for observables. For long bath time correlations, we see nonmonotonic evolution of the uncertainties in observables. Further, we extend this exact solution to the two-particle problem and find the dynamics of entanglement in a subspace. We find the phenomena of ``sudden death'' and ``rebirth'' of entanglement. Interestingly, all memory effects enter via the functional form of the energy and hence the time of death and rebirth is controlled by the amount of noisy energy added into each oscillator. If this energy increases above (decreases below) a threshold, we obtain sudden death (rebirth) of entanglement.

arXiv:1202.1614Physical Review BMay 22, 201219 citations

Manipulating the Sudden Death of Entanglement in Two-qubit Atomic Systems

Mahmood Irtiza Hussain, Rabia Tahira, Manzoor Ikram

Journal of the Korean Physical SocietyOct 14, 201111 citations

Observation of entanglement sudden death and rebirth by controlling a solid-state spin bath

Fei Wang, Pan‐Yu Hou, Yidong Huang +8 more

Quantum entanglement, the essential resource for quantum information processing, has rich dynamics under different environments. Probing different entanglement dynamics typically requires exquisite control of complicated system-environment coupling in real experimental systems. Here, by a simple control of the effective solid-state spin bath in a diamond sample, we observe rich entanglement dynamics, including the conventional asymptotic decay as well as the entanglement sudden death, a term coined for the phenomenon of complete disappearance of entanglement after a short finite time interval. Furthermore, we observe counterintuitive entanglement rebirth after its sudden death in the same diamond sample by tuning an experimental parameter, demonstrating that we can conveniently control the non-Markovianity of the system-environment coupling through a natural experimental knob. Further tuning of this experimental knob can make the entanglement dynamics completely coherent under the same environmental coupling. Probing of entanglement dynamics, apart from its fundamental interest, may find applications in quantum information processing through control of the environmental coupling.Quantum entanglement, the essential resource for quantum information processing, has rich dynamics under different environments. Probing different entanglement dynamics typically requires exquisite control of complicated system-environment coupling in real experimental systems. Here, by a simple control of the effective solid-state spin bath in a diamond sample, we observe rich entanglement dynamics, including the conventional asymptotic decay as well as the entanglement sudden death, a term coined for the phenomenon of complete disappearance of entanglement after a short finite time interval. Furthermore, we observe counterintuitive entanglement rebirth after its sudden death in the same diamond sample by tuning an experimental parameter, demonstrating that we can conveniently control the non-Markovianity of the system-environment coupling through a natural experimental knob. Further tuning of this experimental knob can make the entanglement dynamics completely coherent under the same environmental coupling. Probing of entanglement dynamics, apart from its fundamental interest, may find applications in quantum information processing through control of the environmental coupling.

arXiv:1801.02729Physical review. B./Physical review. BAug 27, 201848 citations

Sudden death of entanglement, rebirth of magic

Chenfeng Cao

Local Markovian noise cannot bring entanglement back, but it can bring magic back. Unlike separability, stabilizer membership is not preserved by local channels, allowing dissipation to push states out of the stabilizer polytope as well as in. Under local amplitude damping, the $n$ -qubit GHZ family $α|0^n\rangle+β|1^n\rangle$ ( $0<α<β$ ) loses its magic at a lower damping strength $γ_-$ and regains it at a higher one $γ_+$ , while entanglement is irreversibly lost at $γ_e$ . This magic--entanglement complementarity, $γ_e+γ_+=1$ for every $n$ , reflects a system--environment duality of amplitude damping. Within real phase-covariant Markovian semigroups the phenomenon is mapped out in full: zero-temperature rebirth occurs if and only if $T_2>T_1$ , unital dynamics produce no rebirth, and sufficiently weak thermal excitation confines rebirth to a finite magic island ending in a second sudden death. For small $α$ , the reborn magic resides in a fully separable state with all proper marginals stabilizer, yet parity-syndrome extraction concentrates it onto a single qubit for magic-state distillation, without loss of expected robustness and with optimal per-register yield $α^2/2$ . Local dissipation further divides pure stabilizer states into magic-generators and magic-insulators: at two qubits, the Bell state $|Φ^+\rangle$ generates magic immediately, while its Bell-state partner $|Ψ^+\rangle$ remains stabilizer. Together, magic and entanglement reveal a symmetry invisible to either alone.Local Markovian noise cannot bring entanglement back, but it can bring magic back. Unlike separability, stabilizer membership is not preserved by local channels, allowing dissipation to push states out of the stabilizer polytope as well as in. Under local amplitude damping, the $n$-qubit GHZ family $α|0^n\rangle+β|1^n\rangle$ ($0<α<β$) loses its magic at a lower damping strength $γ_-$ and regains it at a higher one $γ_+$, while entanglement is irreversibly lost at $γ_e$. This magic--entanglement complementarity, $γ_e+γ_+=1$ for every $n$, reflects a system--environment duality of amplitude damping. Within real phase-covariant Markovian semigroups the phenomenon is mapped out in full: zero-temperature rebirth occurs if and only if $T_2>T_1$, unital dynamics produce no rebirth, and sufficiently weak thermal excitation confines rebirth to a finite magic island ending in a second sudden death. For small $α$, the reborn magic resides in a fully separable state with all proper marginals stabilizer, yet parity-syndrome extraction concentrates it onto a single qubit for magic-state distillation, without loss of expected robustness and with optimal per-register yield $α^2/2$. Local dissipation further divides pure stabilizer states into magic-generators and magic-insulators: at two qubits, the Bell state $|Φ^+\rangle$ generates magic immediately, while its Bell-state partner $|Ψ^+\rangle$ remains stabilizer. Together, magic and entanglement reveal a symmetry invisible to either alone.

quant-pharXiv:2605.22603May 22, 20260 citations

Quantifying Quantumness with Sudden Birth or Death of Entanglement for Two-Qubits System

A.‐B. A. Mohamed

International Journal of Theoretical PhysicsApr 18, 201210 citations

n

-qubit GHZ family

α|0^n\rangle+β|1^n\rangle

(

0<α<β

) loses its magic at a lower damping strength

γ_-

and regains it at a higher one

γ_+

, while entanglement is irreversibly lost at

γ_e

. This magic--entanglement complementarity,

γ_e+γ_+=1

for every

n

, reflects a system--environment duality of amplitude damping. Within real phase-covariant Markovian semigroups the phenomenon is mapped out in full: zero-temperature rebirth occurs if and only if

T_2>T_1

, unital dynamics produce no rebirth, and sufficiently weak thermal excitation confines rebirth to a finite magic island ending in a second sudden death. For small

α

, the reborn magic resides in a fully separable state with all proper marginals stabilizer, yet parity-syndrome extraction concentrates it onto a single qubit for magic-state distillation, without loss of expected robustness and with optimal per-register yield

α^2/2

. Local dissipation further divides pure stabilizer states into magic-generators and magic-insulators: at two qubits, the Bell state

|Φ^+\rangle

generates magic immediately, while its Bell-state partner

|Ψ^+\rangle

remains stabilizer. Together, magic and entanglement reveal a symmetry invisible to either alone.