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arXiv:1407.6460 · Physical Review A

Interference visibility, entanglement, and quantum correlation

Lin Zhang, Arun Kumar Pati, Junde Wu

Published Aug 7, 2015• 10 citations
arXivHTMLPDF

Abstract

In quantum information and communication two fundamental nonclassical features that one exploits in harnessing the true power of composite quantum systems are the interference and quantum correlations. We show how a concept akin to interference can be connected to entanglement and quantum correlation. In particular, we prove that the difference in the squared visibility for the density operator before and after a complete measurement, averaged over all unitary evolutions, is related to the quantum correlation measure based on the measurement disturbance. For pure and mixed bipartite states the unitary average of the squared visibility is related to the entanglement measure. This may provide a method to detect entanglement and quantum correlation with quantum interference setups. Furthermore, we prove that for a fixed purity of the subsystem state, there is a complementarity relation between the linear entanglement of formation and the measurement disturbance. This brings out a quantitative difference between two kinds of quantum correlations and suggests that the origins of these two can be different.

DOI
10.1103/physreva.92.022316

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Complementary relationships exist among interference properties of particles such as pattern visibility, predictability, and distinguishability. Additionally relationships between average information gain Ḡ and measurement disturbance F for entangled spin pairs are well established. This article examines whether a similar complementary relationship exists between entanglement and measurement. For qubit systems, both measurements on a single system and measurements on a bipartite system are considered in regard to entanglement. It is proven that Ē + D ≤ 1 holds, where Ē is the average entanglement after a measurement is made and D is a measure of the measurement disturbance of a single measurement. Assuming measurements on a bipartite system shared by Alice and Bob, it is shown that Ē + Ḡ ≤ 1, where Ḡ is the maximum average information gain that Bob can obtain regarding Alice’s result. These results are generalized to arbitrary initial mixed states and non-Hermitian operators. In the case of maximally entangled initial states, it is found that D ≤ EL and Ḡ ≤ EL, where EL is the loss of entanglement due to measurement by Alice. We conclude that the amount of disturbance and average information gain one can achieve is strictly limited by entanglement.
We study the quantumness of correlations for ensembles of bi- and multi-partite systems and relate it to the task of quantum data hiding. Quantumness is here intended in the sense of minimum average disturbance under local measurements. We consider a very general framework, but focus on local complete von Neumann measurements as cause of the disturbance, and, later on, on the trace-distance as quantifier of the disturbance. We discuss connections with entanglement and previously defined notions of quantumness of correlations. We prove that a large class of quantifiers of the quantumness of correlations are entanglement monotones for pure bipartite states. In particular, we define an entanglement of disturbance for pure states, for which we give an analytical expression. Such a measure coincides with negativity and concurrence for the case of two qubits. We compute general bounds on disturbance for both single states and ensembles, and consider several examples, including the uniform Haar ensemble of pure states, and pairs of qubit states. Finally, we show that the notion of ensemble quantumness of correlations is most relevant in quantum data hiding. Indeed, while it is known that entanglement is not necessary for a good quantum data hiding scheme, we prove that ensemble quantumness of correlations is.
We study the quantumness of correlations for ensembles of bi- and multi-partite systems and relate it to the task of quantum data hiding. Quantumness is here intended in the sense of minimum average disturbance under local measurements. We consider a very general framework, but focus on local complete von Neumann measurements as the cause of the disturbance, and, later on, on the trace-distance as a quantifier of the disturbance. We discuss connections with entanglement and previously defined notions of quantumness of correlations. We prove that a large class of quantifiers of the quantumness of correlations are entanglement monotones for pure bipartite states. In particular, we define an entanglement of disturbance for pure states, for which we give an analytical expression. Such a measure coincides with negativity and concurrence for the case of two qubits. We compute general bounds on disturbance for both single states and ensembles, and consider several examples, including the uniform Haar ensemble of pure states, and pairs of qubit states. Finally, we show that the notion of ensemble quantumness of correlations is most relevant in quantum data hiding. Indeed, while it is known that entanglement is not necessary for a good quantum data-hiding scheme, we prove that ensemble quantumness of correlations is necessary.
Abstract We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we study the bipartite case and the connection of two typically applied and distinctively different concepts of nonclassicality in quantum optics and quantum information. Our investigation includes the representation of correlated states in terms of quasiprobability matrices, a comparative study of joint and conditional quantum correlations, and an entanglement characterization. It is, for example, shown that our composition approach always includes entanglement as one form of quantum correlations. Yet, other forms of quantum correlations can also occur without entanglement. Finally, we give an outlook towards multimode systems and temporal correlations.
Entanglement verification and measurement is essential for experimental tests of quantum mechanics and also for quantum communication and information science. Standard methods of verifying entanglement in a bipartite mixed state require detection of both particles and involve coincidence measurement. We present a method that enables us to verify and measure entanglement in a two-photon mixed state without detecting one of the photons, i.e., without performing any coincidence measurement or postselection. We consider two identical sources, each of which can generate the same two-photon mixed state but they never emit simultaneously. We show that one can produce a set of single-photon interference patterns, which contain information about entanglement in the two-photon mixed state. We prove that it is possible to retrieve the information about entanglement from the visibility of the interference patterns. Our method reveals a distinct avenue for verifying and measuring entanglement in mixed states.