## 1 Introduction  
Distinguishability (or predictability) of paths in quantum interference experiments is closely linked with entanglement. For instance, to gain \"which-path\" information in a double-slit experiment, one should employ some kind of a measuring pointer (be it responsible for a strong, weak, partial measurement, etc.). The process of measuring the system's path involves entangling it with the device. For simplicity, one could assume the system is already entangled with another, similar system (in the desired basis); then, the \"which-path\" information is contained in the correlations between the two systems--i.e., knowing which slit the particle went through in one system supplies information regarding which slit the other particle went through in the other system. This approach was used by [PERSON] et al. in [1], where the authors proposed a quantitative measure for two-particle interference, denoted by \(v_{12}\), and proved a duality relation between one-particle interference visibility and two-particle interference visibility: \(v_{i}^{2}+v_{12}^{2}\leq 1\) (where \(v_{i}\) denotes the \(i\)th particle's interference visibility). This and other similar duality relations were studied in [2; 3; 4; 5]. For general definitions and discussion of interferometric quantities in multiple-slit scenarios, please see Appendix A. However, it seems to us that most of these works did not emphasize enough the state- and geometry-dependent quantitative relations between entanglement and interference of continuous variables (CV) such as position and momentum (or the corresponding quadratures of the electromagnetic field). The notions of nonlocality and entanglement in continuous-variable systems are intricate and subtle. Working in infinite-dimensional Hilbert spaces necessitates new theoretical methods (for entanglement and even quantumness quantification), new practical methods (like homodyne and heterodyne detectors), new tools (like Wigner functions, Q- and P-representations) and new conceptual ideas, but they also enable new opportunities for quantum communication and computation. Since the first entangled state to reach world-wide acclaim was the continuous-variable EPR state [6; 7], it is natural to ask whether complementarity relations similar to the aforementioned ones can be formulated in EPR-like states using continuous variables. However, in fact, our analysis here is more general, considering asymmetric configurations of Gaussian states, which reach the EPR state as a special, limiting case. Moreover, these CV states seem to offer richer relations between local and nonlocal observables than their discrete variables counterparts. While discrete variable systems benefit from high-fidelity operations, they are limited by the imperfect generation and detection of single quanta (e.g., photons), as well as the absence of deterministic interactions of single quanta [8]. In contrast, encoding of quantum information in continuous variables can achieve deterministic, unconditional operation of quantum protocols, albeit at the expense of lower fidelities [8; 9]. Although the high efficiency and unconditional preparation of CV entanglement is paid for with imperfection of the entanglement [10; 11; 12], the prepared Gaussian entangled states approach an ideal EPR state in the limit of infinite squeezing [13]. Thus, the practicality of continuous variables in quantum protocols is due to currently available highly efficient sources of squeezed laser light and existing techniques for preparing, unitarily manipulating, and measuring entangled quantum states, with the use of continuous quadrature amplitudes of the quantized electromagnetic field [10]. It is worth noting that in this paper we are mainly focused on theoretical aspects; experimental tests of complementarity using quantum optics may be found in [14; 15; 16; 17; 18; 19], as well as a recent experiment using complementarity for nonlocal erasure of phase objects [20].