Extreme expected values and their applications in quantum information processing

• URL: http://arxiv.org/abs/2111.00466v1
• Date: Sun, 31 Oct 2021 11:10:39 GMT
• Title: Extreme expected values and their applications in quantum information processing
• Authors: Wangjun Lu, Lei Shao, Xingyu Zhang, Zhucheng Zhang, Jie Chen, Hong Tao, and Xiaoguang Wang
• Abstract summary: We consider the probability distribution when the monotonic function $F(X)$ of the independent variable $X$ takes the maximum or minimum expected value. We apply the proved theory to solve three problems in quantum information processing.
• Score: 7.4733340808812505
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the probability distribution when the monotonic function $F(X)$ of the independent variable $X$ takes the maximum or minimum expected value under the two constraints of a certain probability and a certain expected value of the independent variable $X$. We proposed an equal probability and equal expected value splitting method. With this method, we proved four inequalities, and two of them can be reduced to Jensen's inequalities. Subsequently, we find that after dividing the non-monotone function $H(X)$ into multiple monotone intervals, the problem of solving the maximum and minimum expected values of $H(X)$ can be transformed into the problem of solving the extreme value of a multiple-variable function. Finally, we apply the proved theory to solve three problems in quantum information processing. When studying the quantum parameter estimation in Mach-Zehnder interferometer, for an equal total input photon number, we find an optimal path-symmetric input state that makes the quantum Fisher information take the maximum value, and we prove that the NOON state is the path-symmetric state that makes the quantum Fisher information takes the minimum value. When studying the quantum parameter estimation in Landau-Zener-Jaynes-Cummings model, we find the optimal initial state of the cavity field that makes the system obtain the maximum quantum Fisher information. Finally, for an equal initial average photon number, we find the optimal initial state of the cavity field that makes the Tavis-Cummings quantum battery have the maximum stored energy and the maximum average charging power.

Related papers

• Fundamental limits of metrology at thermal equilibrium [0.0]
  We consider the estimation of an unknown parameter $theta$ through a quantum probe at thermal equilibrium. We find the maximal Quantum Fisher Information attainable via arbitrary $HC$, which provides a fundamental bound on the measurement precision.
  arXiv  Detail & Related papers  (2024-02-09T18:01:45Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Heisenberg Limit beyond Quantum Fisher Information [0.0]
  Using entangled quantum states, it is possible to scale the precision with $N$ better than when resources would be used independently. I derive bounds on the precision of the estimation for the case of noiseless unitary evolution. I analyze the problem of the Heisenberg limit when multiple parameters are measured simultaneously on the same physical system.
  arXiv  Detail & Related papers  (2023-04-27T17:43:45Z)
• Sparse random Hamiltonians are quantumly easy [105.6788971265845]
  A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state. Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
  arXiv  Detail & Related papers  (2023-02-07T10:57:36Z)
• Estimation precision of the acceleration for a two-level atom coupled to fluctuating vacuum electromagnetic fields [1.6881346757176978]
  We study the quantum Fisher information of acceleration for a uniformly accelerated two-level atom coupled to fluctuating electromagnetic fields in the Minkowski vacuum. Although the atom response to the vacuum fluctuation electromagnetic fields is different from the case of massless scalar fields, the quantum Fisher information eventually reaches a stable value.
  arXiv  Detail & Related papers  (2022-09-26T13:38:09Z)
• Distributed quantum sensing with optical lattices [0.0]
  In distributed quantum sensing the correlations between multiple modes, typically of a photonic system, are utilized to enhance the measurement precision of an unknown parameter. We show that it can allow for parameter estimation at the Heisenberg limit of $(N(M-1)T)2$, where $N$ is the number of particles, $M$ is the number of modes, and $T$ is the measurement time.
  arXiv  Detail & Related papers  (2022-08-10T03:47:44Z)
• Optimal Second-Order Rates for Quantum Soft Covering and Privacy Amplification [19.624719072006936]
  We study quantum soft covering and privacy amplification against quantum side information. For both tasks, we use trace distance to measure the closeness between the processed state and the ideal target state. Our results extend to the moderate deviation regime, which are the optimal rates when the trace distances vanish at sub-exponential speed.
  arXiv  Detail & Related papers  (2022-02-23T16:02:31Z)
• Average-case Speedup for Product Formulas [69.68937033275746]
  Product formulas, or Trotterization, are the oldest and still remain an appealing method to simulate quantum systems. We prove that the Trotter error exhibits a qualitatively better scaling for the vast majority of input states. Our results open doors to the study of quantum algorithms in the average case.
  arXiv  Detail & Related papers  (2021-11-09T18:49:48Z)
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification [56.61325554836984]
  The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. We derive the exact exponent for the decay of the small modification of the quantum state in smoothing the max-relative entropy based on purified distance.
  arXiv  Detail & Related papers  (2021-11-01T16:35:41Z)
• Bosonic field digitization for quantum computers [62.997667081978825]
  We address the representation of lattice bosonic fields in a discretized field amplitude basis. We develop methods to predict error scaling and present efficient qubit implementation strategies.
  arXiv  Detail & Related papers  (2021-08-24T15:30:04Z)
• On the properties of the asymptotic incompatibility measure in multiparameter quantum estimation [62.997667081978825]
  Incompatibility (AI) is a measure which quantifies the difference between the Holevo and the SLD scalar bounds. We show that the maximum amount of AI is attainable only for quantum statistical models characterized by a purity larger than $mu_sf min = 1/(d-1)$.
  arXiv  Detail & Related papers  (2021-07-28T15:16:37Z)

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.