REVIEW 7 cited by
Diagnostics of mixed-state topological order and breakdown of quantum memory
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Diagnostics of mixed-state topological order and breakdown of quantum memory
read the original abstract
Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed states describing corrupted memories. Here we provide an intrinsic characterization of the breakdown of topological quantum memory, which both gives a bound on the performance of decoding algorithms and provides examples of topologically distinct mixed states. We employ three information-theoretical quantities that can be regarded as generalizations of the diagnostics of ground-state topological order, and serve as a definition for topological order in error-corrupted mixed states. We consider the topological contribution to entanglement negativity and two other metrics based on quantum relative entropy and coherent information. In the concrete example of the 2D Toric code with local bit-flip and phase errors, we map three quantities to observables in 2D classical spin models and analytically show they all undergo a transition at the same error threshold. This threshold is an upper bound on that achieved in any decoding algorithm and is indeed saturated by that in the optimal decoding algorithm for the Toric code.
Forward citations
Cited by 7 Pith papers
-
Decoding coherent errors in toric codes on honeycomb and square lattices: duality to Majorana monitored dynamics and symmetry classes
Toric code decodability under coherent X/Z errors is dual to Majorana monitored dynamics whose symmetry class (D or DIII) dictates whether the generic transition is a measurement-induced entanglement transition or a t...
-
Charge Scrambling in Strong-to-Weak Spontaneous Symmetry Breaking
Long-range Rényi-1 SWSSB order implies extensive block-charge variance for continuous symmetries with rapid asymptotic approach, with conditional counterexamples and a new twist overlap correlator separating symmetry ...
-
Steady-state topological order
Steady-state topological order is defined via degeneracy and entropy in open-system Liouvillians, with models showing exponential splitting but algebraically closing gaps.
-
Topologically Ordered Steady States in Open Quantum Systems
Engineered dissipation produces topologically degenerate steady states that form a stable many-body phase in three dimensions but not two.
-
Phases of decodability in the surface code with unitary errors
Numerical simulations of the surface-code ML decoder under single- and two-qubit unitary rotations reveal a ferromagnetic volume-law phase in which classical information is retained yet hard to recover.
-
Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model
Decohered non-Abelian Kitaev quantum double states exhibit strong-to-weak spontaneous symmetry breaking of non-invertible higher-form symmetries and form an information convex set whose dimension equals the pure-state...
-
Handbook of Error-Correcting Codes
The paper compiles a curated handbook reference of error-correcting codes, their symbol-based classifications, and interrelations with mathematical objects and physical phases.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.