Pure State Inspired Lossless Post-selected Quantum Metrology of Mixed States

• URL: http://arxiv.org/abs/2405.00405v1
• Date: Wed, 1 May 2024 09:21:06 GMT
• Title: Pure State Inspired Lossless Post-selected Quantum Metrology of Mixed States
• Authors: Jing Yang,
• Abstract summary: We show that quantum Fisher information can be losslessly compressed into a subensemble with a much smaller number of samples. We find that if the parametric derivative of the density operator of a mixed state, vanishes on the support of the density matrix, lossless post-selection can be achieved. Our results are useful for realistic post-selected quantum metrology in the presence of decoherence.
• Score: 3.4840877804354236
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Given an ensemble of identical pure quantum states that depend on an unknown parameter, recently it was shown that the quantum Fisher information can be losslessly compressed into a subensemble with a much smaller number of samples. However, generalization to mixed states leads to a technical challenge that is formidable to overcome directly. In this work, we avoid such technicality by unveiling the physics of a featured lossless post-selection measurement: while the post-selected quantum state is unchanged, the parametric derivative of the density operator is amplified by a large factor equal to the square root of the inverse of the post-selection success probability. This observation not only clarifies the intuition and essence of post-selected quantum metrology but also allows us to develop a mathematically compact theory for the lossless post-selection of mixed states. We find that if the parametric derivative of the density operator of a mixed state, or alternatively the symmetric logarithmic derivative, vanishes on the support of the density matrix, lossless post-selection can be achieved with an arbitrarily large amplification factor. We exemplify with the examples of superresolution imaging and unitary encoding of mixed initial states. Our results are useful for realistic post-selected quantum metrology in the presence of decoherence and of foundational interests to several problems in quantum information theory.

Related papers

• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the extreme multimode bosonic Gaussian channels [53.253900735220796]
  Inequality determines the minimum conditional von Neumann entropy of the output of the most general linear mixing of bosonic quantum modes. Bosonic quantum systems constitute the mathematical model for the electromagnetic radiation in the quantum regime.
  arXiv  Detail & Related papers  (2024-10-18T13:59:50Z)
• Quantum circuit design for mixture and preparation of arbitrary pure and mixed quantum states [25.01488143369413]
  This paper addresses the challenge of preparing arbitrary mixed quantum states. Two circuit design methods are presented: one via a mixture of pure states and the other via purification.
  arXiv  Detail & Related papers  (2024-03-28T06:37:00Z)
• Tight concentration inequalities for quantum adversarial setups exploiting permutation symmetry [0.5242869847419834]
  We show that our one-sided concentration inequalities for a quantum state require the $N$-qudit system to be permutation invariant. We numerically demonstrate the tightness of our bounds in simple quantum information processing tasks.
  arXiv  Detail & Related papers  (2024-03-18T12:20:46Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [46.99825956909532]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system. This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• On the optimal error exponents for classical and quantum antidistinguishability [3.481985817302898]
  Antidistinguishability has been used to investigate the reality of quantum states. We show that the optimal error exponent vanishes to zero for classical and quantum antidistinguishability. It remains an open problem to obtain an explicit expression for the optimal error exponent for quantum antidistinguishability.
  arXiv  Detail & Related papers  (2023-09-07T14:03:58Z)
• Quantum circuits for measuring weak values, Kirkwood--Dirac quasiprobability distributions, and state spectra [0.0]
  We propose simple quantum circuits to measure weak values, KD distributions, and spectra of density matrices without the need for post-selection. An upshot is a unified view of nonclassicality in all those tasks.
  arXiv  Detail & Related papers  (2023-02-01T19:01:25Z)
• Suppressing Amplitude Damping in Trapped Ions: Discrete Weak Measurements for a Non-unitary Probabilistic Noise Filter [62.997667081978825]
  We introduce a low-overhead protocol to reverse this degradation. We present two trapped-ion schemes for the implementation of a non-unitary probabilistic filter against amplitude damping noise. This filter can be understood as a protocol for single-copy quasi-distillation.
  arXiv  Detail & Related papers  (2022-09-06T18:18:41Z)
• Experimental demonstration of optimal unambiguous two-out-of-four quantum state elimination [52.77024349608834]
  A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements. Here we implement a quantum state elimination measurement which unambiguously rules out two of four pure, non-orthogonal quantum states.
  arXiv  Detail & Related papers  (2022-06-30T18:00:01Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Scattering as a quantum metrology problem: a quantum walk approach [0.0]
  We address the scattering of a quantum particle by a one-dimensional barrier potential over a set of discrete positions. We formalize the problem as a continuous-time quantum walk on a lattice with an impurity, and use the quantum Fisher information as a mean to quantify the maximal possible accuracy in the estimation of the height of the barrier.
  arXiv  Detail & Related papers  (2020-10-23T14:42:25Z)
• The role of boundary conditions in quantum computations of scattering observables [58.720142291102135]
  Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. As with present-day calculations, quantum computation strategies still require the restriction to a finite system size. We quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty.
  arXiv  Detail & Related papers  (2020-07-01T17:43:11Z)

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.