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原子与分子物理学报

Unknowability of Quantum State forbids perfectly quantum operations

CAIQing-yu, LIBai-wen

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

We analyze the oonnection between quantum operations and accessible information. And we find that the accessible information decreases under quantum operations. We show that it is impossible to perfectly manipulate an unknown state in an open quantum system. That the accessible information decreases under quantum operations gives a fundamental limitation in the microscopic world.

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We analyze the oonnection between quantum operations and accessible information. And we find that the accessible information decreases under quantum operations. We show that it is impossible to perfectly manipulate an unknown state in an open quantum system. That the accessible information decreases under quantum operations gives a fundamental limitation in the microscopic world.
In this work, we reveal a type of impossibility discovered in our recent research which forbids comparing the closeness of multiple unknown quantum states with any nontrivial threshold in a perfect or unambiguous way. This impossibility is distinct from the existing impossibilities in that it is a ``collective'' impossibility on multiple quantum states; most other ``no-go'' theorems are concerned with only one single state each time, i.e., it is an impossibility on a nonlocal quantum operation. This impossibility may provide new insight into the nature of quantum mechanics, and it implies more limitations on quantum information tasks than the existing no-go theorems.
In this work, we reveal a new type of impossibility discovered in our recent research which forbids comparing the closeness of multiple unknown quantum states with any non-trivial threshold in a perfect or an unambiguous way. This impossibility is distinct from the existing impossibilities in that it is a collective impossibility on multiple quantum states while most other no-go theorems concern with only one single state each time, i.e., it is an impossibility on a non-local quantum operation. This novel impossibility may provide a new insight into the nature of quantum mechanics and it implies more limitations on quantum information tasks than the existing no-go theorems.
One of the fundamental insights of quantummechanics is that complete knowledge of the state of a quantum system is not possible. Such incomplete knowledge of a physical system is the norm rather than the exception. This is becoming increas-ingly apparent as we apply scientific methods to increasingly complex situations. Empirically intensive disciplines in the biological, human, and geosciences all operate in situations where valid conclusions must be drawn, but deductive com-pleteness is impossible. This paper argues that such situations are emerging exam-ples of Open World Science. In this paradigm, scientific models are known to be acting with incomplete information. Open World models acknowledge their incompleteness, and respond positively when new information becomes available. Many methods for creating Open World models have been explored analytically in quantitative disciplines such as statis-tics, and the increasingly mature area of machine learning. This paper examines the role of quantum theory and quan-tum logic in the underpinnings of Open World models, ex-amining the importance of structural features of such as non-commutativity, degrees of similarity, induction, and the im-pact of observation. Quantum mechanics is not a problem around the edges of classical theory, but is rather a secure bridgehead in the world of science to come.
Preface List of Illustrations Open Fundamental Questions of Limits to Information in the Quantum Measurement of a Single System Impossibility of Determining the Unknown Quantum Wavefunction of a Single System Quantum Nondemolition (QND) Measurements of a Single System Measurements without Entanglement of a Single Quantum System Adiabatic Measurements of a Single Quantum System Quantum Zeno Effect of a Single System Fundamental Quantum Limit to External Force Detection via Monitoring a Single Harmonic Oscillator (or Free Mass) Established Limits to Information in the Quantum Measurement of a Single System Bibliography Index.