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Journal of Modern Optics

Observations and quantum information

Stig Stenholm

Published Feb 1, 2000• 5 citations
Publisher

Abstract

The concept of quantum information in a state is analysed. For a component of an entangled state, the potential measurements are claimed to define a context, against which the information is to be interpreted. Projective measurements are shown to allow the processing of information contained in the incoming quantum states. Finally the process of a quantum measurement is considered as a mapping between different parts of the system, a quantum information transfer.

DOI
10.1080/09500340008244044

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The concept of quantum information in a state is analysed. For a component of an entangled state, the potential measurements are claimed to define a context, against which the information is to be interpreted. Projective measurements are shown to allow the processing of information contained in the incoming quantum states. Finally the process of a quantum measurement is considered as a mapping between different parts of the system, a quantum information transfer.
The concept of generalised quantum measurement is introduced as a transformation establishing the correspondence between the initial state of an object and the final state of the object—instrument system with the help of a classical information index one-to-one related to a classically compatible set of the states of the object—instrument system. It is shown that this measurement includes all the types of measurements: standard projective, entangling, soft, and generalised measurements with a partial or complete dest-ruction of the initial information contained in the object. A special class of partially destructing measurements is considered which establish the correspondence between a continual set of states of finite-dimensional quantum systems and systems with an infinite-dimensional space of states. The information sense of these measurements is discussed and some information characteristics are calculated.
Information-theoretical restrictions on the information transfer in quantum measurements are studied. They are derived for the measurement of system S by detector D, registrated and processed by information system O. The formalism of inference maps in Hilbert space is used for it; it permit to calculate O restricted state which contains all finally available information on S parameters. It's shown that the principal information losses, inevitable in this formalism, stipulate the stochasticity of measurement outcomes registrated by O in the individual events.
A framework for a quantum information theory is introduced that is based on the measure of quantum information associated with probability distribution predicted by quantum measuring of state. The entanglement between states of measured system and "pointer" states of measuring apparatus, which is generated by dynamical process of quantum measurement, plays a dominant role in expressing quantum characteristics of information theory. The quantum mutual information of transmission and reception of quantum states along a noisy quantum channel is given by the change of quantum measured information. In our approach, it is not necessary to purify the transmitted state by means of the reference system. It is also clarified that there exist relations between the approach given in this letter and those given by other authors.
The possibility of performing simultaneous measurements in quantum mechanics is investigated in the context of the Curie-Weiss model for a projective measurement. Concretely, we consider a spin--12\frac{1}{2}21​ system simultaneously interacting with two magnets, which act as measuring apparatuses of two different spin components. We work out the dynamics of this process and determine the final state of the measuring apparatuses, from which we can find the probabilities of the four possible outcomes of the measurements. The measurement is found to be nonideal, as (i) the joint statistics do not coincide with the one obtained by separately measuring each spin component, and (ii) the density matrix of the spin does not collapse in either of the measured observables. However, we give an operational interpretation of the process as a generalized quantum measurement, and show that it is fully informative: The expected value of the measured spin components can be found with arbitrary precision for sufficiently many runs of the experiment.
The concept of generalized quantum measurement is introduced as a transformation that sets a one-to-one correspondence between the initial states of the measured object system and final states of the object-meter system with the help of a classical informational index, unambiguously linked to a classically compatible set of quantum states. It is shown that the generalized quantum measurement concept covers all key types of quantum measurement---standard projective, entangling, fuzzy, and generalized measurements with a partial or complete destruction of initial information associated with the object. A special class of soft quantum measurements as a basic model for the fuzzy measurements widespread in physics is introduced and its information properties are studied in detail. Also, a special class of partially destructive measurements mapping all states of the Hilbert space of a finite-dimensional quantum system onto the basis states of an infinite-dimensional quantum system is considered.