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Physical Review A

Equivalence between macroscopic quantum superpositions and maximally entangled states: Application to phase-shift detection

Alfredo Luis

Published Oct 5, 2001• 43 citations
Publisher

Abstract

We demonstrate that the superpositions of macroscopically distinct coherent states are maximally entangled states. Among other possible applications of this result, in this paper we show that the experimental arrangements generating superpositions of macroscopically distinct coherent states may be adapted for precision phase-shift detection reaching the maximum sensitivity allowed by quantum physics (Heisenberg limit).

DOI
10.1103/physreva.64.054102

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We demonstrate that the superpositions of macroscopically distinct coherent states are maximally entangled states. Among other possible applications of this result, in this paper we show that the experimental arrangements generating superpositions of macroscopically distinct coherent states may be adapted for precision phase-shift detection reaching the maximum sensitivity allowed by quantum physics (Heisenberg limit).
Although the principle of superposition lies at the heart of quantum mechanics and is the root of almost all quantum phenomena such as coherence and entanglement, its quantification, except for that related to the resource theory of coherence and interference, remains relatively less studied. In this work, we address quantification of superposition from an information-theoretic perspective. We introduce a family of quantifiers of superposition, the phase-sensitive superposition, by taking into account the phases of amplitudes in the superposition of a fixed basis states (e.g., computational basis states). We establish a conservation relation for the phase-sensitive superposition, which is a kind of complementary relation and is reminiscent of wave-particle duality. We evaluate explicitly the second moment of phase-sensitive superposition and show that it is intrinsically related to the l2l^2l2-norm coherence. We characterize the dephasing channel induced by the maximally superposed states. We investigate the minimum and maximum superpositions, reveal their basic properties, and illustrate them through various examples. We further explore the dynamics of superposition in the Grover search algorithm, and demonstrate a complementary relation between superposition and success probability of the search algorithm. These results and quantifiers offer tools for analyzing structural features and implications of quantum superposition.