Finite-dimensional quantum channel

Depends on

• Real and complex inner-product spaces and their induced length
• Finite-dimensional vector space, and its dimension $\dim_F V$; infinite-dimensional means having no finite basis
• Linear map between vector spaces over the same field
• Completely positive maps
• The basis-independent trace of an endomorphism of a finite-dimensional vector space

Used by

• Distance corrects unlocated errors and known erasures Corollary
• Broadcasting Family Definition
• Complementary channels and coherent information Definition
• Degradable and antidegradable channels Definition
• End-to-end channel and output error contract Definition
• Exact correction of a protected subsystem Definition
• Exact recovery of an encoded quantum code Definition
• Finite authenticated key-distribution protocol Definition
• Finite IID quantum source and compression code Definition
• Finite ordered channel-location schedules Definition
• Finite-dimensional quantum erasure channel Definition
• Local-Stochastic Correlated Quantum Noise Definition
• Operational quantum, private, and entanglement-assisted capacities Definition
• Parameterized variational quantum objective Definition
• A degenerate code with a non-diagonal Knill–Laflamme matrix Example
• Orthogonal error spaces and a recovery branch Example
• Qubit dephasing decreases quantum relative entropy Example
• A finite POVM defines a classical-output quantum channel Lemma
• Complement and degradation maps of the erasure channel Lemma
• Every finite extension is obtained from a purification by a channel Lemma
• Finite channel information maxima are attained Lemma
• Finite cq wiretap achievability with strong Holevo secrecy Lemma
• Kraus operators in an identity-channel representation are scalar Lemma
• Optimal Cloner Attains Bound Lemma
• Optimal Cloning Worst Case Upper Bound Lemma
• Preserving the logical marginal forces a gauge-only channel Lemma
• Replacing Bob's key by a copy of Alice's costs the correctness error Lemma
• The finite classical key-copy map is a quantum channel Lemma
• The Local Noise Model Composes With Circuit Semantics Lemma
• Unitary conjugation is a channel Proposition
• An explicit syndrome recovery corrects a Knill–Laflamme error family Theorem
• An isometry followed by partial trace is a channel Theorem
• Channel Composition Hybrid Bound Theorem
• Channel data processing for finite quantum relative entropy Theorem
• Channel Diamond Norm One Theorem
• Channel Tensor Error Bound Theorem
• Every finite-dimensional channel has a finite isometric dilation Theorem
• Exact Mixed State Cloning Fidelity Criterion Theorem
• Exact recovery implies the Knill–Laflamme condition Theorem
• Fidelity Data Processing Theorem

…and 9 more results.

Dependency tree · two levels

30 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• John Watrous, The Theory of Quantum Information (2018), §2.2.1 (standard reference, not scraped)
• John Preskill, Quantum Computation, Chapter 3, §§3.2.1 and 3.2.6 (standard reference, not scraped)