Quantum coherence functions

R. A. Brewster, J. D. Franson

José Tito Mendonça, Hugo Terças

Lin Yin, Ming‐Da Huang, Yu Ya-Fei +1 more

Quantum coherence is an essential ingredient in quantum information processing and plays an important role in quantum computation. Therefore, it is a hot issue about how to quantify the coherence of quantum states in theoretical framework. The coherence effect of a state is usually described by the off-diagonal elements of its density matrix with respect to a particular reference basis. Recently, based on the established notions from quantitative theory of entanglement, a resource theory of coherence quantification has been proposed[1,2]. In the theory framework, a proper measure of coherence should satisfy three criteria: the coherence should be zero for all incoherent state; the coherence should not increase under mixing quantum states; the coherence should not increase under incoherent operations. Then, a number of coherence measures have been suggested, such as l1 norm of coherence and the relative entropy of coherence[2]. Wigner function is known as an important tool to study the non-classical property of quantum states for continuous-variable quantum systems. It has been generalized to finite-dimensional Hilbert spaces, and named as discrete Wigner function[9-16]. The magic property of quantum states, which promotes stabilizer computation to universal quantum computation, can be generally measured by the absolute sum of the negative items (negativity sum) in the discrete Wigner function of the observed quantum states. In this paper we investigate quantum coherence from the view of discrete Wigner function. From the definition of the discrete Wigner function of the quantum systems with odd prime dimensions, for a given density matrix we analyze in phase space the performance of its diagonal and off-diagonal items. We find that, the discrete Wigner function of a quantum state contains two aspects: the true quantum coherence and the classical mixture, where the part of classical mixture can be excluded by only considering the discrete Wigner function of the diagonal items of the density matrix. Thus, we propose a possible measure method for quantum coherence from the discrete Wigner function of the off-diagonal items of the density matrix. We show that the proposed measure method satisfies the criteria (C1) and (C2) of coherence measure perfectly. For the criteria (C3), we give a numerical proof in three-dimensional quantum system. Meanwhile, we compare the proposed coherence measure with l1 norm coherence, and get an inequality relationship between them. Finally, an inequality is obtained to discuss the relation between quantum coherence and the negativity sum of discrete Wigner function, which shows that the quantum coherence is only necessary but not sufficient for quantum computation speed-up.

Borros Arneth

Quantum coherence lies at the heart of quantum mechanics and underlies interference, entanglement, and quantum information. Within conventional quantum theory, coherence is mathematically represented by the wavefunction or, more generally, by the off-diagonal elements of the density matrix. Although this formalism predicts experimental observations with extraordinary precision, the physical origin of coherence and its apparent disappearance during measurement continue to motivate diverse interpretations, including the Copenhagen interpretation, decoherence theory, many-worlds, relational quantum mechanics, and QBism. In the present work we propose a complementary structural interpretation based on Green-Function Architecture Theory (GFAT). Rather than considering quantum coherence to be a primitive property of the wavefunction, we propose that coherence is fundamentally a property of connected Green-function architectures represented by diagram spaces. The wavefunction is interpreted as an effective Hilbert-space representation of an underlying Green-function architecture. Within this framework, quantum interference arises from architecture coherence associated with a common holonomy, whereas measurement corresponds to an architecture transformation that redistributes coherence without destroying it. Consequently, wavefunction collapse is interpreted as an emergent description of a deeper structural process occurring within the underlying Green-function architecture. The proposed framework leaves the mathematical predictions of quantum mechanics completely unchanged while suggesting a deeper structural origin for quantum coherence, interference, and measurement. The double-slit experiment is discussed as the first physical application of this architecture-based interpretation.

Karen Southwell

Jianming Cai, Martin Bodo Plenio

It is known that more than 50 species use the Earth's magnetic field for orientation and navigation. Intensive studies, particularly behavior experiments with birds, provide support for a chemical compass based on magnetically sensitive free radical reactions as a source of this sense. However, the fundamental question of how quantum coherence plays an essential role in such a chemical compass model of avian magnetoreception yet remains controversial. Here, we show that the essence of the chemical compass model can be understood in analogy to a quantum interferometer exploiting global quantum coherence rather than any subsystem coherence. Within the framework of quantum metrology, we quantify global quantum coherence and correlate it with the function of chemical magnetoreception. Our results allow us to understand and predict how various factors can affect the performance of a chemical compass from the unique perspective of quantum coherence assisted metrology. This represents a crucial step to affirm a direct connection between quantum coherence and the function of a chemical compass.