We consider the classical correlations that two observers can extract by measurements on a bipartite quantum state, and we discuss how they are related to the quantum mutual information of the state. We show with several examples how complementarity gives rise to a gap between the quantum and the classical correlations, and we relate our quantitative finding to the so-called classical correlation locked in a quantum state. We derive upper bounds for the sum of classical correlation obtained by measurements in different mutually unbiased bases and we show that the complementarity gap is also present in the deterministic quantum computation with one quantum bit.
We argue that the essence of nonclassicality of a bipartite correlation is a positive signal deficit-- the communication cost excess over the available signaling. By this criterion, while violations of Bell-type and contextuality inequalities are necessarily non-classical, some violations of the Leggett-Garg inequality are classical. Further, signaling tends to diminish nonclassical properties, such as intrinsic randomness, no-cloning, complementarity, etc. Signal deficit is shown to have its ultimate origin in intrinsic randomness. A possible analogy of nonclassicality to the metamathematical…
Instituto de Fisica Gleb Wataghin, Universidade Estadual de Campinas（坎皮纳斯州立大学格莱布·瓦塔金物理研究所）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；Department of Physics and Astronomy, University of Waterloo（滑铁卢大学物理与天文学系）；Department of Physics, University of Toronto（多伦多大学物理系）
The ongoing exploration of the ambiguous boundary between the quantum and the classical worlds has spurred substantial developments in quantum science and technology. Recently, the nonclassicality of dynamical processes has been proposed from a quantum-information-theoretic perspective, in terms of witnessing nonclassical correlations with Hamiltonian ensemble simulations. To acquire insights into the quantum-dynamical mechanism of the process nonclassicality, here we propose to investigate the nonclassicality of the electron spin free-induction-decay process associated with an NV$^-$ center. …
Two notions of nonclassicality that have been investigated intensively are: (i) negativity, that is, the need to posit negative values when representing quantum states by quasiprobability distributions such as the Wigner representation, and (ii) contextuality, that is, the impossibility of a noncontextual hidden variable model of quantum theory (also known as the Bell-Kochen-Specker theorem). Although both of these notions were meant to characterize the conditions under which a classical explanation cannot be provided, we demonstrate that they prove inadequate to the task and we argue for a pa…
Complementarity or wave-particle duality has been the basis of quantum mechanics over the last century. Since the Hanbury Brown and Twiss experiments in 1956, the particle nature of single photons has been intensively studied for various quantum phenomena such as anticorrelation and Bell inequality violation. Regarding the fundamental question on quantumness or nonclassicality, however, no clear answer exists for what quantum entanglement should be and how to generate it. Here, we experimentally demonstrate the secrete of quantumness using the wave nature of single photons.
In quantum physics we are confronted with new entities which consist indivisible of an energy packet and a coupled wave. The complementarity principle for certain properties of these quantum objects may be their main mystery. Photons are especially useful to investigate these complementary properties. A series of new experiments using spontaneous parametric down conversion (SPDC) as a tool allowed the detailed analysis of the physical background of this complementarity and offers a new conceptual perspective. Based on these results a straightforward explanation of these sometimes counter-intui…
Bohr's interpretation of quantum mechanics has been criticized as incoherent and opportunistic, and based on doubtful philosophical premises. If so Bohr's influence, in the pre-war period of 1927-1939, is the harder to explain, and the acceptance of his approach to quantum mechanics over de Broglie's had no reasonable foundation. But Bohr's interpretation changed little from the time of its first appearance, and stood independent of any philosophical presuppositions. The principle of complementarity is itself best read as a conjecture of unusually wide scope, on the nature and future course of…
Optical experiments designed to explore quantum complementarity are reanalyzed. It is argued that, for each, a classical explanation is not only possible, but more coherent and less contrived. The final conclusion is that these experiments actually constitute support for criticism of the photon paradigm of electric charged particle interaction. They offer little or nothing to say about quantum complementarity once the photon concept is not imposed by mandate.
It is well known that Wheeler proposed several delayed choice experiments in order to show the impossibility to speak of the way a quantum system behaves before being detected. In a double-slit experiment, when do photons decide to travel by one way or by two ways? Delayed choice experiments seem to indicate that, strangely, it is possible to change the decision of the photons until the very last moment before they are detected. This led Wheeler to his famous sentence: No elementary quantum phenomenon is a phenomenon until it is a registered phenomenon, brought to a close by an irreversible ac…
Wheeler's delayed choice experiment, a well known manifestation of the complementarity principle, has proved somewhat difficult to physically interpret. We show that, restated in quantum field theoretic language, the experiment submits to a simple explanation: that wave- or particle-nature is imposed not at the slit plane but at the detector system. The intepretational difficulty conventionally encountered is due to the assumption of enforcement of complementarity at the former.
The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual behavior, Bell-inequality violation, and contextuality. However, no intuitive criterion is available for determining the compatibility of even two (generalized) observables, despite the overarching importance of this problem and intensive efforts of many researchers. Here we introduce an information theoretic paradigm together with an intuitive geometric pic…
Coherence as a resource for $N$-box and quantum pigeonhole paradoxes
INL – International Iberian Nanotechnology Laboratory（国际伊比利亚纳米技术实验室）；Institute of Theoretical Physics, Ulm University（乌尔姆大学理论物理研究所）；Center for Integrated Quantum Science and Technology (IQST)（集成量子科学与技术中心）；Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）
In the history of quantum mechanics, much has been written about the double-slit experiment, and much debate as to its interpretation has ensued. Indeed, to explain the interference patterns for sub-atomic particles, explanations have been given not only in terms of the principle of complementarity and wave-particle duality but also in terms of quantum consciousness and parallel universes. In this paper, the topic will be discussed from the perspective of spin-coupling in the hope of further clarification. We will also suggest that this explanation allows for a realist interpretation of the Af…
We summarise a recent reconstruction of the quantum theory of qubits from rules constraining an observer's acquisition of information about physical systems. This review of [arXiv:1412.8323, arXiv:1511.01130] is accessible and fairly self-contained, focussing on the main ideas and results and not the technical details. The reconstruction offers an informational explanation for the architecture of the theory and specifically for its correlation structure. In particular, it explains entanglement, monogamy and non-locality compellingly from limited accessible information and complementarity. As a…
We look at certain thought experiments based upon the 'delayed choice' and 'quantum eraser' interference experiments, which present a complementarity between information gathered from a quantum measurement and interference effects. It has been argued that these experiments show the Bohm interpretation of quantum theory is untenable. We demonstrate that these experiments depend critically upon the assumption that a quantum optics device can operate as a measuring device, and show that, in the context of these experiments, it cannot be consistently understood in this way. By contrast, we then sh…
In this paper we attempt to analyze the physical and philosophical meaning of quantum contextuality. We will argue that there exists a general confusion within the foundational literature arising from the improper "scrambling" of two different meanings of quantum contextuality. While the first one, introduced by Bohr, is related to an epistemic interpretation of contextuality which stresses the incompatibility (or complementarity) of certain measurement situations described in classical terms; the second meaning of contextuality is related to a purely formal understanding of contextuality as e…
