The Church of the Symmetric Subspace
By Aram Wettroth Harrow. 2013
225 citations recorded by the source corpus.
The symmetric subpace has many applications in quantum information theory. This review article begins by explaining key background facts about the symmetric subspace from a quantum information perspective. Then we review, and in some places extend, work of Werner and Chiribella that connects the symmetric subspace to state estimation, optimal cloning, the de Finetti theorem and other topics. In the third and final section, we discuss how the symmetric subspace can yield concentration-of-measure results via the calculation of higher moments of random quantum states. There are no new results in this article, but only some new proofs of existing results, such as a variant of the exponential de Finetti theorem. The purpose of the article is (a) pedagogical, and (b) to collect in one place many, if not all, of the quantum information applications of the symmetric subspace.
Subfields: Clinical Psychology, Philosophy
View Paper: https://www.semanticscholar.org/paper/528f6a1e8b0cfd7db8ab22113714d13349818bdd
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In Clinical Psychology
In Philosophy
Citations in the corpus
- Emergent Quantum State Designs from Individual Many-Body Wave Functions (2021, background): “For a Hilbert space H with dimension d, it has the form [35]”
- Emergent statistical mechanics of entanglement in random unitary circuits (2018, background): “The first one can be worked out by subtracting all the other 1 d2 terms from the sum [98] ∑”
- Local random quantum circuits are approximate polynomial-designs: numerical results (2012, background): “⊓ ⊔ The facts used here about Psym,t,dn are proved and discussed in a quantum-information setting in [43].”
- Random Quantum Circuits (2022, unknown): “The Haar average of u⊗ u∗ ⊗ u⊗ u∗ is a projection operator onto the subspace of the q(4)-dimensional Hilbert space that is invariant under u⊗ u∗ ⊗ u⊗ u∗ for every u (160).”