Distinguishing Phases via Non-Markovian Dynamics of Entanglement in
Topological Quantum Codes under Parallel Magnetic Field
- URL: http://arxiv.org/abs/2108.11198v2
- Date: Mon, 30 May 2022 21:28:15 GMT
- Title: Distinguishing Phases via Non-Markovian Dynamics of Entanglement in
Topological Quantum Codes under Parallel Magnetic Field
- Authors: Harikrishnan K. J. and Amit Kumar Pal
- Abstract summary: Localizable entanglement is studied on nontrivial loops of topological quantum codes with parallel magnetic field.
We study the behavior of these lower bounds in the vicinity of the topological to nontopological quantum phase transition of the system.
We find that in the case of the non-Markovian dephasing noise, at large time, the canonical measurement-based lower bound oscillates with a larger amplitude.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We investigate the static and the dynamical behavior of localizable
entanglement and its lower bounds on nontrivial loops of topological quantum
codes with parallel magnetic field. Exploiting the connection between the
stabilizer states and graph states in the absence of the parallel field and
external noise, we identify a specific measurement basis, referred to as the
canonical measurement basis, that optimizes localizable entanglement when
measurement is restricted to single-qubit Pauli measurements only, thereby
providing a lower bound. We also propose an approximation of the lower bound
that can be computed for larger systems according to the computational resource
in hand. Additionally, we compute a lower bound of the localizable entanglement
that can be computed by determining the expectation value of an appropriately
designed witness operator. We study the behavior of these lower bounds in the
vicinity of the topological to nontopological quantum phase transition of the
system, and perform a finite-size scaling analysis. We also investigate the
dynamical features of these lower bounds when the system is subjected to
Markovian or non-Markovian single-qubit dephasing noise. We find that in the
case of the non-Markovian dephasing noise, at large time, the canonical
measurement-based lower bound oscillates with a larger amplitude when the
initial state of the system undergoing dephasing dynamics is chosen from the
nontopological phase, compared to the same for an initial state from the
topological phase. These features can be utilized to distinguish the
topological phase of the system from the nontopological phase in the presence
of dephasing noise.
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