Abstract We propose a new family of coherence monotones, named the generalized coherence concurrence (or coherence k -concurrence), which is an analogous concept to the generalized entanglement concurrence. The coherence k -concurrence of a state is nonzero if and only if the coherence number (a recently introduced discrete coherence monotone) of the state is not smaller than k , and a state can be converted to a state with nonzero entanglement k -concurrence via incoherent operations if and only if the state has nonzero coherence k -concurrence. We apply the coherence concurrence family to the problem of wave-particle duality in multi-path interference phenomena. We obtain a sharper equation for path distinguishability (which witnesses the duality) than the known one and show that the amount of each concurrence for the quanton state determines the number of slits which are identified unambiguously.
Abstract We propose a new family of coherence monotones, named the generalized coherence concurrence (or coherence k -concurrence), which is an analogous concept to the generalized entanglement concurrence. The coherence k -concurrence of a state is nonzero if and only if the coherence number (a recently introduced discrete coherence monotone) of the state is not smaller than k , and a state can be converted to a state with nonzero entanglement k -concurrence via incoherent operations if and only if the state has nonzero coherence k -concurrence. We apply the coherence concurrence family to the problem of wave-particle duality in multi-path interference phenomena. We obtain a sharper equation for path distinguishability (which witnesses the duality) than the known one and show that the amount of each concurrence for the quanton state determines the number of slits which are identified unambiguously.
We propose a family of coherence monotones, named the \emph{generalized coherence concurrence} (or coherence k-concurrence), which has a close relation with the generalized entanglement concurrence. The coherence k-concurrence of a state is nonzero if and only if the coherence number (a recently introduced discrete coherence monotone) of the state is not smaller than k, and a state can be converted to a state with nonzero entanglement k-concurrence via incoherent operations if and only if the state has nonzero coherence k-concurrence. The generalized coherence concurrence can be considered as the entanglement-based coherence monotone.
We derive a generalized wave-particle duality relation for arbitrary multipath quantum interference phenomena. Beyond the conventional notion of the wave nature of a quantum system, i.e., the interference fringe visibility, we introduce a quantifier as the normalized quantum coherence, recently defined in the framework of quantum information theory. To witness the particle nature, we quantify the path distinguishability or the which-path information based on unambiguous quantum state discrimination. Then, the Bohr complementarity principle for multipath quantum interference can be stated as a duality relation between the quantum coherence and the path distinguishability. For two-path interference, the quantum coherence is identical to the interference fringe visibility, and the relation reduces to the well-known complementarity relation. The duality relation continues to hold in the case where mixedness is introduced due to possible decoherence effects.
Abstract In an asymmetric multislit interference experiment, a quanton is more likely to pass through certain slits than some others. In such a situation one may be able to predict which slit a quanton is more likely to go through, even without using any path-detecting device. This allows one to talk of path predictability . It has been shown earlier that for a two-slit interference, the predictability and fringe visibility are constrained by the inequality 2 + 2 ≤ 1 . Generalizing this relation to the case of more than two slits is still an unsolved problem. A new definition for predictability for multi-slit interference is introduced. It is shown that this predictability and quantum coherence follow a duality relation 2 + 2 ≤ 1 , which saturates for all pure states. For the case of two slits, this relation reduces to the previously known one.
Complementarity, or more specifically, the wave-particle duality, and quantum coherence are two fundamental concepts in quantum mechanics. Recently, motivated by the progress of the quantification of quantum coherence, the complementary relation between coherence and path information is investigated by many authors, and various duality relations between them are established. Such relations not only provide insights into fundamental problems of quantum mechanics, such as the understanding of quantum coherence and wave-particle duality; but also are important in applications of quantum technologies. In this paper, based on the Bures distance and unambiguous quantum state discrimination, systematic analysis of the complementarity between the quantum coherence and path information in two path interferometers is carried out. Similarly as other related works, the wave aspect, or the visibility of the interferometer, is quantified by the l1-norm measure of quantum coherence, and the path information is considered via unambiguous quantum state discrimination. In this way, a novel duality relation in two path interferometers is obtained. Compared with known results, our work considers mixed states as well as pure states; considers the path predictability resulting from the intrinsic path asymmetry of the quantum state, as well as the path distinguishability resulting from the use of a which-path detector. Therefore, our work systematically generalizes known results in two path interferometers by removing all the unnecessary restrictions. Specifically, the most general form of quantum states in two path interferometers is considered and the duality relation between quantum coherence and path information is proved based on the positivity property of density matrices. The cases of path predictability and path distinguishability are considered separately. For path predictability, the proof is straightforward; whereas some advanced mathematical techniques, such as the Schur-Weyl inequality, properties of the fidelity and properties of positive matrices, are required in order to give a rigorous proof of the duality relation between coherence and path distinguishability. Concrete examples are provided to illustrate the abstract method and results. Our work concerns about two path interferometers exclusively and depends heavily that the dimensionality is two, therefore it would be an interesting task to generalize the results in this paper to n-path interferometers.
The interference observed for a quanton, traversing more than one path, is believed to characterize its wave nature. Conventionally, the sharpness of interference has been quantified by its visibility or contrast, as defined in optics. Based on this visibility, wave-particle duality relations have been formulated for two-path interference. However, as one generalizes the situation to multi-path interference, it is found that conventional interference visibility is not a good quantifier. A recently introduced measure of quantum coherence has been shown to be a good quantifier of the wave nature. The subject of quantum coherence, in relation to the wave nature of quantons and to interference visibility, is reviewed here. It is argued that coherence can be construed as a more general form of interference visibility, if the visibility is measured in a different manner, and not as contrast. Quanta 2019; 8: 24–35.
It is well known that fringe contrast is not a good quantifier of the wave nature of a quanton in multipath interference. An alternative interference visibility, based on the Hilbert-Schmidt coherence is introduced. It is demonstrated that this visibility is a good quantifier of wave nature and can be experimentally measured. A generalized path predictability is introduced, which reduces to the predictability of Greenberger and Yasin for the case of two paths. In a multipath, which-way interference experiment, the new visibility, the predictability, and the I concurrence (quantifying the entanglement between the quanton and the path detector) are shown to follow a tight triality relation. It quantifies the essential role that entanglement plays in multipath quantum complementarity.