Mana in Haar-random states
read the original abstract
Mana is a measure of the amount of non-Clifford resources required to create a state; the mana of a mixed state on $\ell$ qudits bounded by $\le \frac 1 2 (\ell \ln d - S_2)$; $S_2$ the state's second Renyi entropy. We compute the mana of Haar-random pure and mixed states and find that the mana is nearly logarithmic in Hilbert space dimension: that is, extensive in number of qudits and logarithmic in qudit dimension. In particular, the average mana of states with less-than-maximal entropy falls short of that maximum by $\ln \pi/2$. We then connect this result to recent work on near-Clifford approximate $t$-designs; in doing so we point out that mana is a useful measure of non-Clifford resources precisely because it is not differentiable.
This paper has not been read by Pith yet.
Forward citations
Cited by 5 Pith papers
-
Fortuity and Complexity in a Simple Quark Model
In a toy qubit model of quarks, BRST cohomology designates baryons as fortuitous and mesons as monotone, with the former displaying super-exponential complexity and the latter power-law complexity in the Veneziano limit.
-
Computing quantum magic of state vectors
Efficient algorithms compute stabilizer Rényi entropy and mana for quantum states from vectors at O(N d^{2N}) cost using fast Hadamard transform, with open-source implementation.
-
Wigner negativity in Krylov space and emergent semiclassicality
Wigner negativity in Krylov space stays O(1) or grows as t^{1/2} (without Hilbert-space scaling) in 2d CFTs, one-cut matrix models, and double-scaled SYK, indicating emergent semiclassicality.
-
Resource generation and dynamical complexities in open random quantum circuits
Memoryful open random quantum circuits sustain entanglement and magic growth like unitary circuits while memoryless ones show decaying entanglement but persistent magic, with memoryful dynamics approaching k-designs m...
-
Fortuity and Complexity in a Simple Quark Model
In a toy qubit model of quarks, baryons are fortuitous with exponential counting and super-exponential complexity while mesons are monotone with polynomial counting and power-law complexity.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.