A nonstabilizerness monotone from stabilizerness asymmetry

Abstract

We introduce a nonstabilizerness monotone which we name basis-minimised stabilizerness asymmetry (BMSA). It is based on the notion of $G$-asymmetry, a measure of how much a certain state deviates from being symmetric with respect to a symmetry group $G$. For pure states, we show that the BMSA is a strong monotone for magic-state resource theory, while it can be extended to mixed states via the convex roof construction. We discuss its relation with other magic monotones, first showing that the BMSA coincides with the recently introduced basis-minimized measurement entropy, thereby establishing the strong monotonicity of the latter. Next, we provide inequalities between the BMSA and other nonstabilizerness measures known in the literature. Finally, we present numerical methods to compute the BMSA, highlighting its advantages and drawbacks compared to other nonstabilizerness measures in the context of pure many-body quantum states. We also discuss the importance of additivity and strong monotonicity for measures of nonstabilizerness in many-body physics, motivating the search for additional computable nonstabilizerness monotones.

19 pages, 3 figures

References in corpus (64)

• Quantum entanglement
• Quantifying Coherence
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Improved Simulation of Stabilizer Circuits
• Quantum Resource Theories
• Logical quantum processor based on reconfigurable atom arrays
• The Resource Theory of Stabilizer Computation
• Restrictions on Transversal Encoded Quantum Gate Sets
• Entropy scaling and simulability by Matrix Product States
• Application of a resource theory for magic states to fault-tolerant quantum computing
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Trading classical and quantum computational resources
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Stabilizer Rényi entropy
• Simulation of quantum circuits by low-rank stabilizer decompositions
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Magic State Distillation: Not as Costly as You Think
• Entanglement asymmetry as a probe of symmetry breaking
• Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules
• Quantifying nonstabilizerness of matrix product states
• Quantifying quantum speedups: improved classical simulation from tighter magic monotones
• Stabilizer entropies and nonstabilizerness monotones
• Scalable measures of magic resource for quantum computers
• Measuring magic on a quantum processor
• Schur-Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations
• Conformal field theories are magical
• Quantum Chaos is Quantum
• Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
• Experimental Estimation of Quantum State Properties from Classical Shadows
• Stabilizer entropies are monotones for magic-state resource theory
• Magic-state resource theory for the ground state of the transverse-field Ising model
• Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance
• Random quantum circuits are approximate unitary $t$-designs in depth $O\left(n{t}^{5+o(1)}\right)$
• Nonstabilizerness via matrix product states in the Pauli basis
• Measuring nonstabilizerness via multifractal flatness
• Phase transition in magic with random quantum circuits
• Nonstabilizerness determining the hardness of direct fidelity estimation
• Magic spreading in random quantum circuits
• Efficient quantum algorithms for stabilizer entropies
• Efficient optimization of the quantum relative entropy
• Dynamical Magic Transitions in Monitored Clifford+T Circuits
• Resource theory of quantum scrambling
• Non-stabilizerness versus entanglement in matrix product states
• Complexity of frustration: a new source of non-local non-stabilizerness
• Symmetry-protected sign problem and magic in quantum phases of matter
• Entanglement-magic separation in hybrid quantum circuits
• Critical behaviors of non-stabilizerness in quantum spin chains
• Augmenting Density Matrix Renormalization Group with Clifford Circuits
• Pseudomagic Quantum States
• Magic in generalized Rokhsar-Kivelson wavefunctions
• Stabilizer Tensor Networks: universal quantum simulator on a basis of stabilizer states
• Characterization of an operational quantum resource in a critical many-body system
• Nonstabilizerness in U(1) lattice gauge theory
• Phase transition in Stabilizer Entropy and efficient purity estimation
• Exact solution of long-range stabilizer Rényi entropy in the dual-unitary XXZ model
• Quantifying dynamical magic with completely stabilizer preserving operations as free
• Real-time operator evolution in two and three dimensions via sparse Pauli dynamics
• Mana and thermalization: probing the feasibility of near-Clifford Hamiltonian simulation
• Handbook for Quantifying Robustness of Magic
• Doped stabilizer states in many-body physics and where to find them
• Pseudorandom density matrices
• The axiomatic and the operational approaches to resource theories of magic do not coincide
• Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond
• Faster computation of nonstabilizerness

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