Replica topological order in quantum mixed states and quantum error
correction
- URL: http://arxiv.org/abs/2402.09516v1
- Date: Wed, 14 Feb 2024 19:00:03 GMT
- Title: Replica topological order in quantum mixed states and quantum error
correction
- Authors: Zhuan Li, Roger S. K. Mong
- Abstract summary: Topological phases of matter offer a promising platform for quantum computation and quantum error correction.
We give two definitions for replica topological order in mixed states, which involve $n$ copies of density matrices of the mixed state.
We show that in the quantum-topological phase, there exists a postselection-based error correction protocol that recovers the quantum information, while in the classical-topological phase, the quantum information has decohere and cannot be fully recovered.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Topological phases of matter offer a promising platform for quantum
computation and quantum error correction. Nevertheless, unlike its counterpart
in pure states, descriptions of topological order in mixed states remain
relatively under-explored. Our work give two definitions for replica
topological order in mixed states, which involve $n$ copies of density matrices
of the mixed state. Our framework categorizes topological orders in mixed
states as either quantum, classical, or trivial, depending on the type of
information that can be encoded. For the case of the toric code model in the
presence of decoherence, we associate for each phase a quantum channel and
describes the structure of the code space. We show that in the
quantum-topological phase, there exists a postselection-based error correction
protocol that recovers the quantum information, while in the
classical-topological phase, the quantum information has decohere and cannot be
fully recovered. We accomplish this by describing the mixed state as a
projected entangled pairs state (PEPS) and identifying the symmetry-protected
topological order of its boundary state to the bulk topology. We discuss the
extent that our findings can be extrapolated to $n \to 1$ limit.
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