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arXiv:1112.5830 · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

Classical to quantum in large-number limit

Kavan Kishore Modi, Rosario Fazio, Saverio Pascazio, Vlatko Vedral, Kazuya Yuasa

Published Sep 3, 2012• 9 citations
arXivHTMLPDF

Abstract

We construct a quantumness witness following the work of Alicki & van Ryn (AvR). We reformulate the AvR test by defining it for quantum states rather than for observables. This allows us to identify the necessary quantities and resources to detect quantumness for any given system. The first quantity turns out to be the purity of the system. When applying the witness to a system with even moderate mixedness, the protocol is unable to reveal any quantumness. We then show that having many copies of the system leads the witness to reveal quantumness. This seems contrary to the Bohr correspondence, which asserts that, in the large-number limit, quantum systems become classical, whereas the witness shows quantumness when several non-quantum systems, as determined by the witness, are considered together. However, the resources required to detect the quantumness increase dramatically with the number of systems. We apply the quantumness witness for systems that are highly mixed but in the large-number limit that resembles nuclear magnetic resonance (NMR) systems. We make several conclusions about detecting quantumness in NMR-like systems.

DOI
10.1098/rsta.2011.0353

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We construct a quantumness witness following the work of Alicki & van Ryn (AvR). We reformulate the AvR test by defining it for quantum states rather than for observables. This allows us to identify the necessary quantities and resources to detect quantumness for any given system. The first quantity turns out to be the purity of the system. When applying the witness to a system with even moderate mixedness, the protocol is unable to reveal any quantumness. We then show that having many copies of the system leads the witness to reveal quantumness. This seems contrary to the Bohr correspondence, which asserts that, in the large-number limit, quantum systems become classical, whereas the witness shows quantumness when several non-quantum systems, as determined by the witness, are considered together. However, the resources required to detect the quantumness increase dramatically with the number of systems. We apply the quantumness witness for systems that are highly mixed but in the large-number limit that resembles nuclear magnetic resonance (NMR) systems. We make several conclusions about detecting quantumness in NMR-like systems.
We construct a quantumness witness following the work of Alicki and van Ryn (AvR) in “A simple test of quantumness for a single system ” [J. Phys. A: Math. Theor., 41, 062001 (2008)]. The AvR test is designed to detect quantumness. We reformulate the AvR test by defining it for quantum states rather than for observ-ables. This allows us to identify the necessary quantities and resources to detect quantumness for any given system. The first quantity turns out to be the purity of the system. When applying the witness to a system with even moderate mixedness the protocol is unable to reveal any quantumness. We then show that having many copies of the system leads the witness to reveal quantumness. This seems contrary to the Bohr correspondence, which asserts that in the large number limit quan-tum systems become classical, while the witness shows quantumness when several non-quantum systems, as determined by the witness, are considered together. How-ever, the resources required to detect the quantumness increase dramatically with the number of systems. We apply the quantumness witness for systems that are highly mixed but in the large number limit, which resembles nuclear magnetic res-onance (NMR) systems. We make several conclusion about detecting quantumness in NMR-like systems.
A recently proposed test of quantumness Alicki and Van Ryn ( 2008 J. Phys. A: Math. Theor. 41 062001 ) is put into a broader mathematical and physical perspective. The notion of quantumness witnesses is introduced, in analogy to entanglement witnesses, and is illustrated by examples of single qubit and many-body systems with additive observables. We also compare our proposal with the quantumness test based on quantum correlations (entanglement) and Bell inequalities, and go on to discuss a class of quantumness witnesses associated with the phase-space representation of quantum mechanics.
Abstract The task of testing whether quantum theory applies to all physical systems and all scales requires considering situations where a quantum probe interacts with another system that need not obey quantum theory in full. Important examples include the cases where a quantum mass probes the gravitational field, for which a unique quantum theory of gravity does not yet exist, or a quantum field, such as light, interacts with a macroscopic system, such as a biological molecule, which may or may not obey unitary quantum theory. In this context a class of experiments has recently been proposed, where the non-classicality of a physical system that need not obey quantum theory (the gravitational field) can be tested indirectly by detecting whether or not the system is capable of entangling two quantum probes. Here we illustrate some of the subtleties of the argument, to do with the role of locality of interactions and of non-classicality, and perform proof-of-principle experiments illustrating the logic of the proposals, using a Nuclear Magnetic Resonance quantum computational platform with four qubits.
The universality of quantum theory has been questioned ever since it was proposed. Key to this long-unsolved question is to test whether a given physical system has non-classical features. Here we connect recently proposed witnesses of non-classicality, based on information-theoretic ideas, with the theory of temporal entanglement. We provide a protocol to witness the non-classicality of a system by probing it with a qubit: we show that, assuming a general conservation law, violating temporal Bell inequalities on the qubit probe implies the non-classicality of the system under investigation. We also perform proof-of-principle experimental emulations of the proposed witness of non-classicality, using a three qubit Nuclear Magnetic Resonance quantum computer. Our result is robust, as it relies on minimal assumptions, and remarkably it can be applied in a broad range of contexts, from quantum biology to quantum gravity.
Nonclassicality Analysis and Entanglement Witnessing in Spin-1/21/21/2 NMR Systems
We investigate quantum features and non-classical nature of two-spin-1/21/21/2 NMR systems at thermal equilibrium under external magnetic fields. More specifically, using suitable quantifiers, we analyze quantum coherence, mixedness, and entanglement in NMR systems and examine their features within the system. We derive closed-form analytical expressions for the quantum elements and show how they depend on temperature and magnetic field strength. We demonstrate that at zero temperature, the system exhibits a quantum critical point, characterized by non-analytic behavior in the measures of coherence, and a sharp peak in mixedness. Moreover, we analyze the entanglement of the system using a suitable entanglement witness. This provides an experimentally friendly setting for testing entanglement in NMR systems. In other words, the witness links the entanglement in the system to quantum observables, making it directly provable in NMR experiments. We establish a connection between quantum information quantifiers and experimentally accessible NMR spectra of the system, enabling the quantification of entanglement, coherence, and mixedness through NMR signal processing.
In view of the tomographic-probability representation of quantum states, we reconsider the approach to quantumness tests of a single system developed by Alicki and Van Ryn (2008 J. Phys. A: Math. Theor. 41 062001). For qubits we introduce a general family of quantumness witnesses, which are operators depending on an extra parameter. Spin tomogram and dual-spin tomographic symbols are used to study qubit examples and the test inequalities which are shown to satisfy simple relations within the framework of the standard probability theory.