Quantifying the intrinsic randomness of quantum measurements

• URL: http://arxiv.org/abs/2211.03581v1
• Date: Mon, 7 Nov 2022 14:17:11 GMT
• Title: Quantifying the intrinsic randomness of quantum measurements
• Authors: Gabriel Senno, Thomas Strohm, Antonio Ac\'in
• Abstract summary: Intrinsic quantum randomness is produced when a projective measurement on a given basis is implemented on a pure state that is not an element of the basis. We show that, unlike the case of projective measurements, in the setting of generalized measurements and mixed states, Eve's guessing probability differs depending on whether she can prepare classically or quantumly correlated strategies.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Intrinsic quantum randomness is produced when a projective measurement on a given basis is implemented on a pure state that is not an element of the basis. The prepared state and implemented measurement are perfectly known, yet the measured result cannot be deterministically predicted. In realistic situations, however, measurements and state preparation are always noisy, which introduces a component of stochasticity in the outputs that is not a consequence of the intrinsic randomness of quantum theory. Operationally, this stochasticity is modelled through classical or quantum correlations with an eavesdropper, Eve, whose goal is to make the best guess about the outcomes produced in the experiment. In this work, we study Eve's maximum guessing probability when she is allowed to have correlations with, both, the state and the measurement. We show that, unlike the case of projective measurements (as it was already known) or pure states (as we prove), in the setting of generalized measurements and mixed states, Eve's guessing probability differs depending on whether she can prepare classically or quantumly correlated strategies.

Related papers

• To Believe or Not to Believe Your LLM [51.2579827761899]
  We explore uncertainty quantification in large language models (LLMs) We derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large. We conduct a series of experiments which demonstrate the advantage of our formulation.
  arXiv  Detail & Related papers  (2024-06-04T17:58:18Z)
• Testing trajectory-based determinism via time probability distributions [44.99833362998488]
  Bohmian mechanics (BM) has inherited more predictive power than quantum mechanics (QM) We introduce a prescription for constructing a flight-time probability distribution within generic trajectory-equipped theories. We derive probability distributions that are unreachable by QM.
  arXiv  Detail & Related papers  (2024-04-15T11:36:38Z)
• Classical Invasive Description of Informationally-Complete Quantum Processes [0.0]
  In classical theory, the joint probability distributions of a process obey by definition the Kolmogorov consistency conditions. Here, we derive conditions that characterize uniquely classical processes that are probed by a reasonable class of invasive measurements. We then analyse under what circumstances such classical processes can simulate the statistics arising from quantum processes associated with informationally-complete measurements.
  arXiv  Detail & Related papers  (2023-12-11T17:31:32Z)
• 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)
• Causal State Estimation and the Heisenberg Uncertainty Principle [12.465699707229648]
  We show that any causal estimate of linear observables of a linear, but not necessarily Markovian, system will satisfy the uncertainty principle. Results clarify the role of causal estimators to a large class of quantum systems.
  arXiv  Detail & Related papers  (2023-04-27T19:30:12Z)
• Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning [47.991114317813555]
  Quantum models implement implicit probabilistic predictors that produce multiple random decisions for each input through measurement shots. This paper proposes to leverage such randomness to define prediction sets for both classification and regression that provably capture the uncertainty of the model.
  arXiv  Detail & Related papers  (2023-04-06T22:05:21Z)
• Upper Bounds on the Distillable Randomness of Bipartite Quantum States [15.208790082352351]
  distillable randomness of a bipartite quantum state is an information-theoretic quantity. We prove measures of classical correlations and prove a number of their properties. We then further bound these measures from above by some that are efficiently computable by means of semi-definite programming.
  arXiv  Detail & Related papers  (2022-12-18T12:06:25Z)
• Certifying randomness in quantum state collapse [4.5070885135627226]
  In this paper, we explore the quantitive connection between the randomness generation and the state collapse. We provide a randomness verification protocol under the assumptions: (I) independence between the source and the measurement devices and (II) the L"uders' rule for collapsing state.
  arXiv  Detail & Related papers  (2022-10-29T15:31:16Z)
• Intrinsic randomness under general quantum measurements [2.8101673772585736]
  When measuring a state with von Neumann measurements, the intrinsic randomness can be quantified by the quantum coherence of the state on the measurement basis. We propose an adversary scenario for general measurements with arbitrary input states, based on which, we characterize the intrinsic randomness. Our results show that intrinsic randomness can quantify coherence under general measurements, which generalizes the result in the standard resource theory of state coherence.
  arXiv  Detail & Related papers  (2022-03-16T13:53:20Z)
• How well can we guess the outcome of measurements of non-commuting observables? [0.0]
  Heisenberg's uncertainty relation says there is an ultimate limit to how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this limit may be violated by an arbitrarily large factor if one aims, instead, to guess the unknown value of a past measurement.
  arXiv  Detail & Related papers  (2021-03-30T13:31:36Z)
• Experimental Test of Sequential Weak Measurements for Certified Quantum Randomness Extraction [0.0]
  We study the feasibility of weak measurements to extract randomness from a single state. We show that the weak measurements are real, but can improve the performance of randomness generation only in close-to-ideal conditions.
  arXiv  Detail & Related papers  (2021-01-28T15:46:58Z)

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.