There is No New Problem for Quantum Mechanics
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There is No New Problem for Quantum Mechanics Lev Vaidman1 Received: 2 June 2020 / Accepted: 13 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract A recent claim by Meehan that quantum mechanics has a new “control problem” that puts limits on our ability to prepare quantum states and revises our understanding of the no-cloning theorem is examined. We identify flaws in Meehan’s analysis and argue that such a problem does not exist. Keywords Measurement problem · Interpretations of quantum mechanics · No-cloning theorem
1 Introduction Recently, Alexander Meehan [1] argued for a new problem for quantum mechanics, distinct from the standard problems associated with measurement in quantum theory. His thesis is that a new problem, which he labels the control problem, forces any interpretation of quantum mechanics to take into account the preparation of states, distinct from considerations of measurement. Meehan’s “new problem” is an alleged inconsistency of three statements related to the preparation of quantum states. In this comment, we identify the following flaws in his argument: • There is no compelling reason to accept one of the statements, so the inconsist-
ency, if it exists, does not represent a problem for quantum mechanics.
• There exists a particular set-up in which all Meehan’s claims are found to be
true, so we prove by construction that his inconsistency proof fails.
• Demonstrating his “new problem” Meehan presents a set-up involving meas-
urement (which is known to be a problem in quantum mechanics) together with preparation. He tries to derive the inconsistency from the preparation of states, but makes an error (dividing by zero) in his proof.
* Lev Vaidman [email protected] 1
Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, 69978 Tel‑Aviv, Israel
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Vol.:(0123456789)
Foundations of Physics
• Finally, in his critical comment regarding the no-cloning theorem of quantum
mechanics, he confuses approximate cloning with precise cloning.
In Section 1 of his paper, Meehan defines the “control problem”: “The following claims are jointly incompatible: (B1) We can successfully prepare quantum states: at least some of our preparation devices are such that, if determinately fed many inputs, they output a non-trivial fraction of those inputs in some specified range of quantum states. [Preparation] (here the ‘inputs’ are subsystems, and we define ‘the quantum state of a subsystem’ in the standard way, as its reduced state). (B2) The quantum state of an isolated system always evolves in accord with a deterministic dynamical equation that preserves the inner product, such as the Schrödinger equation [Unitarity]. (B3) It is always determinate whether or not a subsystem has been input into a given (measuring or preparation) device [Determinate Input].” By presenting (below) a counterexample we will show that Meehan’s claim is incorrect: (B1), (B2), and (B3) are compatible. There is no control problem as stated in Meehan’s
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