Scavenging quantum information: Multiple observations of quantum systems

Abstract

Given an unknown state of a qudit that has already been measured optimally, can one still extract any information about the original unknown state? Clearly, after a maximally informative measurement, the state of the system `collapses' into a post-measurement state from which the {\em{same}} observer cannot obtain further information about the original state of the system. However, the system still encodes a significant amount of information about the original preparation for a second observer who is unaware of the actions of the first one. We study how a series of independent observers can obtain, or scavenge, information about the unknown state of a system (quantified by the fidelity) when they sequentially measure it. We give closed-form expressions for the estimation fidelity, when one or several qudits are available to carry information about the single-qudit state, and study the `classical' limit when an arbitrarily large number of observers can obtain (nearly) complete information on the system. In addition to the case where all observers perform most informative measurements we study the scenario where a finite number of observers estimate the state with equal fidelity,regardless of their position in the measurement sequence; and the scenario where all observers use identical measurement apparata (up to a mutually unknown orientation) chosen so that a particular observer's estimation fidelity is maximized.

17 pages, 1 figure

References in corpus (8)

• Reference frames, superselection rules, and quantum information
• Quantum jumps of light recording the birth and death of a photon in a cavity
• Degradation of a quantum reference frame
• Dynamics of a Quantum Reference Frame
• Non-unity gain minimal disturbance measurement
• Quantum Reference Frames and the Classification of Rotationally-Invariant Maps
• Optimal partial estimation of quantum states from several copies
• Recycling of quantum information: Multiple observations of quantum systems

Cited by in corpus (7)

• Extracting information from a qubit by multiple observers: Toward a theory of sequential state discrimination
• Sequential State Discrimination and Requirement of Quantum Dissonance
• Testing sequential quantum measurements: how can maximal knowledge be extracted?
• Sequential discrimination of qudits by multiple observers
• Near optimal discrimination of binary coherent signals via atom-light interaction
• The Helstrom measurement: A nondestructive implementation
• Retrodiction of a sequence of measurement results in qubit interferometers