Extremality of stabilizer states

• URL: http://arxiv.org/abs/2403.13632v1
• Date: Wed, 20 Mar 2024 14:30:59 GMT
• Title: Extremality of stabilizer states
• Authors: Kaifeng Bu,
• Abstract summary: We investigate the extremality of stabilizer states to reveal their exceptional role in the space of all $n$-qubit/qudit states. Our results highlight the remarkable information-theoretic properties of stabilizer states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the extremality of stabilizer states to reveal their exceptional role in the space of all $n$-qubit/qudit states. We establish uncertainty principles for the characteristic function and the Wigner function of states, respectively. We find that only stabilizer states achieve saturation in these principles. Furthermore, we prove a general theorem that stabilizer states are extremal for convex information measures invariant under local unitaries. We explore this extremality in the context of various quantum information and correlation measures, including entanglement entropy, conditional entropy and other entanglement measures. Additionally, leveraging the recent discovery that stabilizer states are the limit states under quantum convolution, we establish the monotonicity of the entanglement entropy and conditional entropy under quantum convolution. These results highlight the remarkable information-theoretic properties of stabilizer states. Their extremality provides valuable insights into their ability to capture information content and correlations, paving the way for further exploration of their potential in quantum information processing.

Related papers

• Quantum information scrambling in adiabatically-driven critical systems [49.1574468325115]
  Quantum information scrambling refers to the spread of the initially stored information over many degrees of freedom of a quantum many-body system. We extend the notion of quantum information scrambling to critical quantum many-body systems undergoing an adiabatic evolution.
  arXiv  Detail & Related papers  (2024-08-05T18:00:05Z)
• Critical behaviors of non-stabilizerness in quantum spin chains [0.0]
  Non-stabilizerness measures the extent to which a quantum state deviates from stabilizer states. In this work, we investigate the behavior of non-stabilizerness around criticality in quantum spin chains.
  arXiv  Detail & Related papers  (2023-09-01T18:00:04Z)
• 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)
• Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain [62.997667081978825]
  We show that local projective measurements induce a modification of the out-of-equilibrium probability distribution function of the local magnetization. In particular we describe how the probability distribution of the former shows different behaviour in the area-law and volume-law regimes.
  arXiv  Detail & Related papers  (2022-12-19T12:34:37Z)
• Unconventional mechanism of virtual-state population through dissipation [125.99533416395765]
  We report a phenomenon occurring in open quantum systems by which virtual states can acquire a sizable population in the long time limit. This means that the situation where the virtual state remains unpopulated can be metastable. We show how these results can be relevant for practical questions such as the generation of stable and metastable entangled states in dissipative systems of interacting qubits.
  arXiv  Detail & Related papers  (2022-02-24T17:09:43Z)
• Stabilizer R\'enyi entropy [0.0]
  We introduce a novel measure for the quantum property of nonstabilizerness - commonly known as "magic" We show that this is a good measure of nonstabilizerness from the point of view of resource theory and show bounds with other known measures. We show that the nonstabilizerness is intimately connected to out-of-time-order correlation functions and that maximal levels of nonstabilizerness are necessary for quantum chaos.
  arXiv  Detail & Related papers  (2021-06-23T18:00:02Z)
• Catalytic Transformations of Pure Entangled States [62.997667081978825]
  Entanglement entropy is the von Neumann entropy of quantum entanglement of pure states. The relation between entanglement entropy and entanglement distillation has been known only for the setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open. Our results imply that entanglement entropy quantifies the amount of entanglement available in a bipartite pure state to be used for quantum information processing, giving results an operational meaning also in entangled single-copy setup.
  arXiv  Detail & Related papers  (2021-02-22T16:05:01Z)
• Stability of quantum eigenstates and kinetics of wave function collapse in a fluctuating environment [0.0]
  The work analyzes the stability of the quantum eigenstates when they are submitted to fluctuations. In the limit of sufficiently slow kinetics, the quantum eigenstates show to remain stationary configurations. The work shows that the final stationary eigenstate depends by the initial configuration of the superposition of states.
  arXiv  Detail & Related papers  (2020-11-25T10:41:53Z)
• Exact many-body scars and their stability in constrained quantum chains [55.41644538483948]
  Quantum scars are non-thermal eigenstates characterized by low entanglement entropy. We study the response of these exact quantum scars to perturbations by analysing the scaling of the fidelity susceptibility with system size.
  arXiv  Detail & Related papers  (2020-11-16T19:05:50Z)
• Robust feedback stabilization of N-level quantum spin systems [0.0]
  We consider N-level quantum angular momentum systems interacting with electromagnetic fields undergoing continuous-time measurements. We study the behavior of such a system in presence of a feedback controller.
  arXiv  Detail & Related papers  (2020-07-08T15:52:49Z)
• Quantum Zeno effect appears in stages [64.41511459132334]
  In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates. We show that the onset of the Zeno regime is marked by a $textitcascade of transitions$ in the system dynamics as the measurement strength is increased.
  arXiv  Detail & Related papers  (2020-03-23T18:17:36Z)

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.