Stabilizers may be poor bounds for fidelities

• URL: http://arxiv.org/abs/2512.14811v1
• Date: Tue, 16 Dec 2025 19:00:00 GMT
• Title: Stabilizers may be poor bounds for fidelities
• Abstract summary: Ideal Gottesman-Kitaev-Preskill (GKP) states are unchanged by stabilizers.<n>Can one use the amount to which a state is unchanged by the stabilizers as a proxy for the quality of a GKP state?<n>This is shown to hold in the opposite manner to which it is routinely assumed, because in fact the fidelity a state has to an ideal GKP state is only upper bounded by the stabilizer expectation values.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The defining feature of ideal Gottesman-Kitaev-Preskill (GKP) states is that they are unchanged by stabilizers, which allow them to detect and correct for common errors without destroying the quantum information encoded in the states. Given this property, can one use the amount to which a state is unchanged by the stabilizers as a proxy for the quality of a GKP state? This is shown to hold in the opposite manner to which it is routinely assumed, because in fact the fidelity a state has to an ideal GKP state is only upper bounded by the stabilizer expectation values. This means that, for qubits encoded in harmonic oscillators via the GKP code, a good stabilizer expectation value does not guarantee proximity to an ideal GKP state in terms of any distance based on fidelity.

Related papers

• Quantum Decision Theory for Displacement Detection with Finite-Energy GKP States [46.2474896050764]
  We develop a framework for detecting phase-space displacements with finite-energy, $d$-level Gottesman-Kitaev-Preskill (GKP) probes.<n>For single-mode and entanglement-assisted architectures, we derive the Bayesian minimum-error probability.<n>We benchmark the resulting protocols against coherent-state, direction-matched squeezed-vacuum, and twin-beam schemes.
  arXiv  Detail & Related papers  (2026-08-08T10:32:05Z)
• Reachability Guarantees for Cart-Pole Swing-Up and Stabilization [0.7310043452300737]
  We present a reachability analysis of a switched energy-based/LQR controller that certifies convergence to the upright equilibrium.<n>We also propose an augmented Lyapunov function to regulate the steady-state cart velocity to zero, for which we establish almost-global convergence.<n>For the controller handoff, a switching region is designed to lie strictly within the LQR region of attraction, formally certifying the swing-up-to-stabilization transition.
  arXiv  Detail & Related papers  (2026-06-26T22:03:21Z)
• The stabilizer ground state and applications to quantum simulation [13.248696881014924]
  The optimal stabilizer ground state is defined as the stabilizer ground state which has the highest fidelity with the true ground state.<n>We show applications of this state in the context of measurement-based deterministic imaginary time evolution.
  arXiv  Detail & Related papers  (2026-03-06T13:46:37Z)
• Trading athermality for nonstabiliserness [0.13048920509133805]
  Nonstabiliserness is a resource for quantum advantage, capturing how much a quantum state breaks the symmetries that would make it classically simulable.<n>Can nonstabiliserness be generated from stabiliser states simply by coupling them to a heat bath?<n>We explore the thermodynamic limits of nonstabiliserness under minimal assumptions and derive a necessary and sufficient condition for when such a process can create it from an initial stabiliser state.
  arXiv  Detail & Related papers  (2025-11-17T19:01:00Z)
• Realistic GKP stabilizer states enable universal quantum computation [0.0]
  Physical Gottesman-Kitaev-Preskill (GKP) states are inherently noisy as ideal ones would require infinite energy.<n>This work demonstrates that imperfect GKP stabilizer states can be leveraged in order to apply non-Clifford gates using only linear optical elements.
  arXiv  Detail & Related papers  (2025-11-05T21:42:54Z)
• Quantum sensing of displacements with stabilized GKP states [41.94295877935867]
  We show how protocols for the stabilization of Gottesman-Kitaev-Preskill states can be used for the estimation of two-quadrature displacement sensing.<n>Thanks to the stabilization, this sensor is backaction evading and can function continuously without reset, making it well suited for the detection of itinerant signals.
  arXiv  Detail & Related papers  (2025-06-25T17:18:50Z)
• Prepare-and-Magic: Semi-Device Independent Magic Certification in the Prepare-and-Measure Scenario [0.12314765641075437]
  We develop a semi-device-independent framework for certifying non-stabilizer states in prepare-and-measure scenarios.<n>We provide analytical proofs that threshold violations of prepare-and-measure witnesses certify non-stabilizerness.
  arXiv  Detail & Related papers  (2025-06-02T20:11:10Z)
• General detectability measure [45.85698554568285]
  Distinguishing resource states from resource-free states is a fundamental task in quantum information.<n>We derived the optimal exponential decay rate of the failure probability for detecting a given $n$-tensor product state.
  arXiv  Detail & Related papers  (2025-01-16T05:39:22Z)
• Spectral stabilizability [0.0]
  We develop conditions for stabilizability based on the target state's eigendecomposition. We use the spectral approach to derive upper bounds on stabilizability for a number of exemplary open system scenarios.
  arXiv  Detail & Related papers  (2022-12-23T10:38:31Z)
• Coherent phase states in the coordinate and Wigner representations [0.0]
  We study numerically the coordinate wave functions and the Wigner functions of the coherent phase states (CPS) Some measures of (non)Gaussianity of CPS are considered.
  arXiv  Detail & Related papers  (2022-11-11T14:59:30Z)
• A Quantum Optimal Control Problem with State Constrained Preserving Coherence [68.8204255655161]
  We consider a three-level $Lambda$-type atom subjected to Markovian decoherence characterized by non-unital decoherence channels. We formulate the quantum optimal control problem with state constraints where the decoherence level remains within a pre-defined bound.
  arXiv  Detail & Related papers  (2022-03-24T21:31:34Z)
• Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty [77.18483084440182]
  Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are popular tools for enforcing safety and stability of a controlled system, respectively. We present a Gaussian Process (GP)-based approach to tackle the problem of model uncertainty in safety-critical controllers that use CBFs and CLFs.
  arXiv  Detail & Related papers  (2021-06-13T23:08:49Z)
• Shannon theory for quantum systems and beyond: information compression for fermions [68.8204255655161]
  We show that entanglement fidelity in the fermionic case is capable of evaluating the preservation of correlations. We introduce a fermionic version of the source coding theorem showing that, as in the quantum case, the von Neumann entropy is the minimal rate for which a fermionic compression scheme exists.
  arXiv  Detail & Related papers  (2021-06-09T10:19:18Z)
• Gaussian conversion protocols for cubic phase state generation [104.23865519192793]
  Universal quantum computing with continuous variables requires non-Gaussian resources. The cubic phase state is a non-Gaussian state whose experimental implementation has so far remained elusive. We introduce two protocols that allow for the conversion of a non-Gaussian state to a cubic phase state.
  arXiv  Detail & Related papers  (2020-07-07T09:19:49Z)
• Fine-Grained Analysis of Stability and Generalization for Stochastic Gradient Descent [55.85456985750134]
  We introduce a new stability measure called on-average model stability, for which we develop novel bounds controlled by the risks of SGD iterates. This yields generalization bounds depending on the behavior of the best model, and leads to the first-ever-known fast bounds in the low-noise setting. To our best knowledge, this gives the firstever-known stability and generalization for SGD with even non-differentiable loss functions.
  arXiv  Detail & Related papers  (2020-06-15T06:30:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.