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Quantum Non-Local Nonstabilizerness
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Quantum Non-Local Nonstabilizerness
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Quantum entanglement and quantum nonstabilizerness are fundamental resources that characterize distinct aspects of a quantum state: entanglement reflects non-local correlations, while nonstabilizerness quantifies the deviation from stabilizer states. A quantum state becomes a valuable resource for applications like universal quantum computation only when both quantities are present. Here, we propose that quantum non-local nonstabilizerness (NN) serves as an effective measure of this combined resource, incorporating both entanglement and nonstabilizerness. We demonstrate that NN can be precisely computed for two-qubit pure states, where it is directly related to the entanglement spectrum. We then extend the definition of NN to mixed states and explore its presence in many-body quantum systems, revealing that the two-point NN decays according to a power law in critical states. Furthermore, we explore measurement-induced NN and uncover an intriguing phenomenon termed "nonstabilizerness swapping", analogous to entanglement swapping, wherein post-measurement NN decays more slowly than any pre-measurement correlations. Our results thus represent a pivotal step towards accurately quantifying the "quantumness" of a state and reveal the potential for manipulating this resource through measurements.
Forward citations
Cited by 10 Pith papers
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In h→τ^-τ^+ Z decays, the spin state is genuinely qubit-qubit-qutrit entangled almost everywhere, violates Bell inequalities throughout, and carries up to 1.95 bits of non-local magic.
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Magic without a phase: phase-independent stabilizer R\'enyi entropy in gluon scattering
A phase-averaged stabilizer Rényi entropy is introduced for tree-level gluon scattering, with color-independent phase-independent magic that is larger in 3→2 than 2→2 and has a soft-limit lower bound in 2→3.
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Analytical Landscape of Maximal Magic for Two-Qutrit States and Beyond
Maximal stabilizer Rényi entropy for two-qutrit states is ln(81/17), achieved at 18 degenerate maxima; a general prime-d formula ln[d⁴/(2d²−1)] is conjectured and verified for d=2,3,5.
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Nonlocal nonstabilizerness in free fermion models
Nonlocal magic in fermionic Gaussian states is bounded by the entanglement spectrum of the covariance matrix, is extensive in the Haar ensemble, peaks at criticality in the Kitaev chain, and grows diffusively under ra...
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Local Thermalization of SU(2) Lattice Gauge Fields on Quantum Computers
Quantum hardware simulation of SU(2) lattice gauge thermalization matches classical extrapolations up to 101 plaquettes after error mitigation, establishing feasibility for chaotic quantum field systems.
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Connecting Magic Dynamics in Thermofield Double States to Spectral Form Factors
For chaotic all-to-all systems, the stabilizer Rényi entropy of thermofield double states is set by the spectral form factor and saturates through a first-order dynamical transition.
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Magic-protected entanglement and Clifford-irreducible structure in magic state space
Quantum states are classified by how much bipartite entanglement survives optimal simplification by classically easy Clifford operations, yielding a split into weakly protected T-magic and strongly protected W-magic regimes.
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Local Thermalization of SU(2) Lattice Gauge Fields on Quantum Computers
Error-mitigated IBM quantum hardware reproduces extrapolated classical simulations of entanglement growth and local thermalization for a truncated SU(2) gauge theory on chains up to 101 plaquettes.
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The Quantum Complexity of String Breaking in the Schwinger Model
Quantum complexity measures applied to the Schwinger model reveal nonlocal correlations along the string and show that entanglement and magic give complementary views of string formation and breaking.
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Quantum Resources and Wigner Symmetry in Nucleon-Nucleon Scattering from Effective Field Theory
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