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Erasure Tolerant Quantum Memory and the Quantum Null Energy Condition in Holographic Systems
Avik Banerjee1, Tanay Kibe1, Nehal Mittal1
1Center for Quantum Information Theory of Matter and Spacetime, and Center for Strings, Gravitation and Cosmology, Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India.
Physical Review Letters
|November 18, 2022
Summary
We explored quantum information storage at finite temperatures using holographic conformal field theories. The quantum null energy condition determines the minimum temperature for qubit erasure, consistent with Landauer's principle.
Area of Science:
- Quantum Information Theory
- Holographic Duality
- Quantum Thermodynamics
Background:
- Storing quantum information at finite temperatures without extensive error correction is a key challenge.
- Quantum thermodynamics imposes constraints on many-body quantum systems.
Purpose of the Study:
- Investigate principles for robust quantum information storage at finite temperatures.
- Analyze qubit erasure processes in 2D holographic conformal field theories (CFTs).
Main Methods:
- Utilized the quantum null energy condition (QNEC) in 2D holographic CFTs.
- Modeled qubit encoding into chirally propagating excitations with finite entropy.
- Simulated erasure via energy-momentum inflow from a memoryless bath, transitioning the system to a thermal state.
- Employed generalized Anti-de Sitter (AdS)-Vaidya geometries to describe holographic erasure processes.
Main Results:
- QNEC provides analytic results for the minimum temperature required for qubit erasure.
- The minimum erasure temperature exceeds the initial background temperature, aligning with Landauer's principle.
- Derived a simple expression for the minimum final temperature for erasing multiple qubits.
- Identified a critical localization length; erasure is impossible if qubits are encoded within this length.
- Determined that this localization length is maximized for an optimal number of encoding qubits, dependent on the central charge.
Conclusions:
- The QNEC offers a powerful tool for understanding thermodynamic constraints on quantum information processing.
- Established conditions and limitations for fast qubit erasure at finite temperatures.
- Estimated optimal encoding strategies for protecting qubits against fast erasure.
- Discussed potential applications for fault-tolerant quantum gates at finite temperatures.
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