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arXiv:quant-ph/9901072 · Physical Review Letters

Spin Flips and Quantum Information for Antiparallel Spins

Nicolas Gisin, Sandu Popescu

Published Jul 12, 1999• 249 citations
arXivHTMLPDF

Abstract

We consider two different ways to encode quantum information, by parallel or antiparallel pairs of spins. We find that there is more information in the antiparallel ones. This purely quantum mechanical effect is due to entanglement, not of the states but occurring in the course of the measuring process. We also introduce a range of quantum information processing machines, such as spin flip and anticloning.

DOI
10.1103/physrevlett.83.432

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We consider two different ways to encode quantum information, by parallel or antiparallel pairs of spins. We find that there is more information in the antiparallel ones. This purely quantum mechanical effect is due to entanglement, not of the states but occurring in the course of the measuring process. We also introduce a range of quantum information processing machines, such as spin flip and anticloning.
We investigate the properties of two particular sets of separable two-qubit states with maximally mixed marginals, named parallel states and antiparallel states respectively. Although these two sets of states are prepared by the same type of quantum operations acting on classically correlated states with equal classical correlations, they share different properties. By comparing two fundamental figures of merit based on quantum correlations and quantum Fisher information for accessing information quality, the superiority of parallel states over antiparallel ones is investigated. This is different from the previous results that antiparallel state turns out to be more effective in the tasks such as sending unknown direction information. The amount of the information that can be extracted from the local measurements is also presented, which turns out to be the same for these two states. This work reveals new aspects of information encoding and extraction problem.
We revisit the issue of extracting information from parallel and antiparallel spins, as initiated by Gisin and Popescu [Phys. Rev. Lett. 83, 432 (1999)], from the viewpoint of parameter estimation. By comparing two fundamental figures of merit based on fidelity and quantum Fisher information for assessing information quality, we demonstrate that these criteria yield different strategies for optimally extracting spin information. A surprising observation is that while for a single spin, as well as for parallel spins, quantum Fisher information cannot be fully extracted by any uniform measurement, this is not the case for antiparallel spins. A simple uniform measurement fully extracting quantum Fisher information in antiparallel spins is identified. This reveals a significant feature of antiparallel spins from the perspective of Fisher information and provides an alternative illustration of the idea that antiparallel spins carry more information than parallel spins.
Computation and quantum information [1] are an extension of the information process concept, and they are used for the effects of quantum mechanic [2]. This new scheme provides a work scene that is not restricted to only two operations; on the contrary, this can gain multiple intermediate states as a result of these two ways of superposition. By performing this operation, the system can evaluate all possibilities in only one step by making a parallel computation; meanwhile, in the classic way, this evaluation is carried out independently of each other, and in different steps. The quantum parallelism can be defined as a reduction in time and an increase in the fast of information process. In this chapter, the fundamental elements that make possible to use the mechanical-quantum phenomena as a tool in the process information are presented.
We consider a pair of antiparallel spins polarized in a random direction to encode quantum information. We wish to extract as much information as possible on the polarization direction attainable by an unentangled measurement, i.e., by a measurement whose outcomes are associated with product states. We develop analytically the upper bound 0.7935bits0.7935\phantom{\rule{0.3em}{0ex}}\text{bits}0.7935bits to the Shannon mutual information obtainable by an unentangled measurement, which is definitely less than the value 0.8664bits0.8664\phantom{\rule{0.3em}{0ex}}\text{bits}0.8664bits attained by an entangled measurement. This proves our main result, that not every ensemble of product states can be optimally distinguished by an unentangled measurement, if the measure of distinguishability is defined in the sense of Shannon. We also present results from numerical calculations and discuss briefly the case of parallel spins.
"Quantum information" refers to the information-theoretic properties of quantum systems. There is still a general prejudice among physicists against the idea that these systems express information due to the nonlocal behavior of entangled quantum systems. The present paper calculates the information content of simple two-state entangled systems (anti-aligned spin-1/2 electron-positron pair, anti-polarized spin-1 photon pair). This calculation involves a modified application of the entropy formalism of quantum statistical mechanics. In addition, the classical and quantum analogues of mutual information are calculated for the entangled particles and experimental devices used to measure them. It is shown that the amount of information expressed by the spin measurement devices depends upon their parameter settings; the spin information of an entangled system prior to measurement is a constant. These results indicate a distinction between information available to a system's sub-components versus that available to measurement devices outside the system. This "inaccessible" information is likely carried by other physical properties of the system.