We experimentally verify the link existing between entanglement and the amount of wave-particle duality in a bipartite quantum system with superconducting qubits in the IBM Q quantum computer. We consider both pure and mixed states, and study the influence of state purity on the observation of the complementarity triality relation of Jakob and Bergou [arXiv:quant-ph/0302075; Opt. Commun. 283, 827 (2010)]. This work confirms the quantitative completion of local Bohr's complementarity principle by the nonlocal quantum entanglement typical of a truly bipartite quantum system.
We experimentally verify the link existing between entanglement and the amount of wave-particle duality in a bipartite quantum system with superconducting qubits in the IBM Q quantum computer. We consider both pure and mixed states, and study the influence of state purity on the observation of the complementarity triality relation of Jakob and Bergou [arXiv:quant-ph/0302075; Opt. Commun. 283, 827 (2010)]. This work confirms the quantitative completion of local Bohr's complementarity principle by the nonlocal quantum entanglement typical of a truly bipartite quantum system.
We introduce a complete set of complementary quantities in bipartite, two-dimensional systems. Complementarity then relates the quantitative entanglement measure concurrence which is a bipartite property to the single-particle quantum properties predictability and visibility, for the most general quantum state of two qubits. Consequently, from an interferometric point of view, the usual wave-particle duality relation must be extended to a ``triality'' relation containing, in addition, the quantitative entanglement measure concurrence, which has no classical counterpart and manifests a genuine quantum aspect of bipartite systems. A generalized duality relation, that also governs possible violations of the Bell's inequality, arises between single- and bipartite properties.
In bipartite quantum systems, entanglement correlations between the parties exerts direct influence in the phenomenon of wave-particle duality. This effect has been quantitatively analyzed in the context of two qubits by Jakob and Bergou [Opt. Commun. 283, 827 (2010)]. Employing a description of the K-meson propagation in free space where its weak decay states are included as a second party, we study here this effect in the kaon-antikaon oscillations. We show that a new quantitative ``triality'' relation holds, similar to the one considered by Jakob and Bergou. In our case, it relates the distinguishability between the decay-product states corresponding to the distinct kaon propagation modes KS,KL, the amount of wave-like path interference between these states, and the amount of entanglement given by the reduced von Neumann entropy. The inequality can account for the complementarity between strangeness oscillations and lifetime information previously considered in the literature, therefore allowing one to see how it is affected by entanglement correlations. As we will discuss, it allows one to visualize clearly through the ${K}^{0}\ensuremath{-}\overline{K}{\phantom{\rule{0.16em}{0ex}}}^{0}$ oscillations the fundamental role of entanglement in quantum complementarity.
In this work, we will deal with pure, bipartite quantum systems of two q-dits (arbitrary dimensions). In these systems, we will study the complementarity between the local entities Predictability and Visibility (that quantifie the properties of particle and wave of each subsystem) and the Concurrence, (that quantifies the entanglement between the q-dits). In a previous work [Quantitative complementarity relations in bipartite systems. Optics Communications, Vol 283, (2010); and arXiv.org, e-print quant-ph/0302075 (2003)] concerning systems of two q-bits (2x2), Jakob and Bergou have found that this complementarity can be quantified by a beautiful equality to one. But when the system is two q-dits there is a disagreement in the literature concerning the normalization of the local information (Preditability and Visibility) of the subsystems [Quantitative wave-particle duality in multibeam interferometers. Phys. Rev. A, Vol 64, 042113 (2001)] e [Complementarity and entanglement in bipartite qudit systems. Phys. Rev. A, Vol 76, 052107 (2007)]. In this last paper, Jakob and Bergou have chosen the non-normalization and have found an expression that quantifies the complementarity between local and non-local information, but not a so simple one, like it has been found in the two q-bits case. We have tried to see what happens if we choose normalized versions of the Preditability, Visibility and Concurrence and we have found an alternative relation that quantifies the complementarity, in terms of an equality to one
Abstract Quantum entanglement between an interfering particle and a detector for acquiring the which-path information plays a central role for enforcing Bohr’s complementary principle, but the quantitative relation between this entanglement and the fringe visibility remains untouched upon for an initial mixed state. Here we find an equality for quantifying this relation. Our equality characterizes how well the interference pattern can be preserved when an interfering particle, initially carrying a definite amount of coherence, is entangled with a which-path detector to a certain degree. This equality provides a connection between entanglement and interference in the unified framework of coherence, revealing the quantitative entanglement-interference complementarity. We experimentally demonstrate this relation with a superconducting circuit, where a resonator serves as a which-path detector for an interfering qubit. The results demonstrate quantum entanglement is the mechanism for prohibiting any detector from acquiring which-path information without deteriorating the interference pattern, which was not confirmed previously.
Abstract Bohr’s complementarity and Schrödinger’s entanglement are two prominent physical characters of quantum systems. In this article, we formally connect them. It is known that complementarity relations for wave-particle duality are saturated only for pure, single-quanton, quantum states. For mixed states, the wave-particle quantifiers never saturate a complementarity relation and can even reach zero for a maximally mixed state. To fully characterize a quanton, it is not enough to consider its wave-particle aspect; we have also to regard its quantum correlations with other systems. Here we prove that for any complete complementarity relation involving predictability and visibility measures that satisfy the criteria established in the literature, the corresponding quantum correlations are entanglement monotones. Therefore, we formally connect entanglement monotones with complementarity relations without appealing to a particular measure.
Besides Heisenberg uncertainty, entanglement is another mechanism that can enforce complementarity in multipartite quantum systems. Analysing its effects in a bipartite system of two qubits, M. Jakob and J. Bergou had shown that the usual wave-particle duality relation, in interferometric systems, regarding which-way information and interference visibility, should be extended to a ¿triality¿ relation containing, in addition, a quantitative entanglement measure. Employing a model for the neutral K-meson propagation in free space in which its weak decay products are included as a second party, we study its effect in the neutral kaon interferometry. We show that a new quantitative triality relation can also be established in this case. The state of the total system remains pure in the course of dynamics, so, we can use the von Neumann entropy of a reduced party as a quantitative measure of entanglement. The other two quantities in the triality relation are the distinguishability between the decay products states corresponding to the two distinct kaon propagation modes KS and KL, and the wave-like path interference between these states. These two distinct modes are the analogues to the two separated paths in usual interferometric devices. The inequality obtained here can account for the complementarity between strangeness oscillations and lifetime information previously considered in the literature. Moreover, it allows us to visualise through the K0 ¿ K0 oscillations the fundamental role of entanglement in quantum complementarity.