[Paper Review] Disentanglement in qubit-qutrit systems

Mazhar Ali, A. Rau+1 more|ArXiv.org|Oct 11, 2007

Quantum Computing Algorithms and Architecture1 references3 citations

TL;DR

This paper investigates entanglement sudden death (ESD) in qubit-qutrit systems, demonstrating that both pure and mixed entangled states can lose entanglement abruptly in finite time due to decoherence. Using negativity as a measure and modeling decay via quantum optical reservoirs, the study reveals that interference between decay channels of the qutrit's upper levels can delay or suppress ESD, highlighting a key control mechanism in higher-dimensional systems beyond qubits.

ABSTRACT

We examine the phenomenon of {\it entanglement sudden death} (ESD) for $(2 imes 3)$-dimensional systems. As for $2 imes 2$ systems, the negativity vanishes in finite time for some entangled pure as well as mixed states. While locally equivalent pure states do so asymptotically. Interference between the decay of the two upper levels to the lowest one in the qutrit adds further richness to ESD in this systems.

Motivation & Objective

• To investigate whether entanglement sudden death (ESD) occurs in qubit-qutrit systems, which have unequal Hilbert space dimensions.
• To determine if ESD is a generic feature in higher-dimensional systems beyond two-qubit systems.
• To analyze the role of quantum interference between decay channels of the qutrit in modulating ESD dynamics.
• To quantify entanglement using negativity for both pure and mixed states in $2\times3$ systems.
• To explore the robustness of mixed entangled states under decoherence and identify conditions for finite-time entanglement loss.

Proposed method

• Modeling the qubit-qutrit system using two- and three-level atoms coupled to independent reservoirs, representing decoherence via amplitude damping.
• Using the negativity measure, defined as twice the absolute sum of negative eigenvalues of the partially transposed density matrix, to quantify entanglement.
• Deriving the time evolution of the density matrix under independent decay channels with rates $\gamma_1$, $\gamma_2$, and $\gamma$, accounting for interference effects.
• Applying local unitary transformations to pure states to generate families of entangled states and analyzing their ESD behavior.
• Constructing a specific class of mixed states with parameters $a$, $b$, and $c$, and analyzing their time evolution under decoherence.
• Using numerical evaluation and contour plots to visualize negativity dynamics and identify regions of ESD for varying parameters and interference levels.

Experimental results

Research questions

• RQ1 Does entanglement sudden death (ESD) occur in $2\times3$-dimensional systems, which are not symmetric in Hilbert space dimension?
• RQ2 How does quantum interference between decay channels of the qutrit affect the onset and timing of ESD in entangled states?
• RQ3 Can ESD be observed in mixed entangled states of qubit-qutrit systems, and how do the parameters of the state influence this?
• RQ4 Is ESD a generic phenomenon across all dimensions of Hilbert space, or is it restricted to specific system types?
• RQ5 How does the asymptotic behavior of entanglement differ between locally equivalent pure states and non-equivalent ones in $2\times3$ systems?

Key findings

• Entanglement sudden death (ESD) occurs in both pure and mixed entangled states of qubit-qutrit systems, with negativity vanishing in finite time for certain states.
• For pure states, ESD occurs in finite time for a specific class of entangled states, while locally equivalent states lose entanglement asymptotically.
• Interference between decay channels of the qutrit delays the onset of ESD, reducing the range of parameters for which ESD occurs—e.g., for $b=0.02$, ESD range shrinks from $c\lesssim0.302$ (no interference) to $c\lesssim0.2775$ (maximum interference).
• For mixed states with $b=0.06$, ESD occurs for $c\lesssim0.5493$ without interference, but only up to $c\lesssim0.46295$ under maximum interference, confirming the delaying effect.
• The system evolves asymptotically to a pure state $\rho_\infty = |12\rangle\langle12|$, indicating complete loss of entanglement at infinite time for all states.
• The study confirms that ESD is not exclusive to qubit systems but is a generic feature in higher-dimensional Hilbert spaces, including $2\times3$ systems.