Entanglement is an essential ingredient for building a quantum network that can have many applications. Understanding how entanglement is distributed in a network is a crucial step to move forward. Here we study the conservation and distribution of Gaussian entanglement in a linear network using a new quantifier for bipartite entanglement. We show that the entanglement can be distributed through a beam splitter in the same way as the transmittance and reflectance. The requirements on the entangled states and the type of networks to satisfy this relation are presented explicitly. Our results provide a useful quantification for quantum entanglement and further insights into the structure of entanglement in a network.
Entanglement is an essential ingredient for building a quantum network that can have many applications. Understanding how entanglement is distributed in a network is a crucial step to move forward. Here we study the conservation and distribution of Gaussian entanglement in a linear network using a new quantifier for bipartite entanglement. We show that the entanglement can be distributed through a beam splitter in the same way as the transmittance and reflectance. The requirements on the entangled states and the type of networks to satisfy this relation are presented explicitly. Our results provide a useful quantification for quantum entanglement and further insights into the structure of entanglement in a network.
The generation and quantification of quantum entanglement is crucial for quantum information processing. Here we study the transition of Gaussian correlation under the effect of linear optical beam-splitters. We find the single-mode Gaussian coherence acts as the resource in generating Gaussian entanglement for two squeezed states as the input states. With the help of consecutive beam-splitters, single-mode coherence and quantum entanglement can be converted to each other. Our results reveal that by using finite number of beam-splitters, it is possible to extract all the entanglement from the single-mode coherence even if the entanglement is wiped out before each beam-splitter.
Preparation of entangled states of photons are useful for quantum computing and communication. In this paper, we present a simplistic protocol of entanglement generation using beam splitters with suitable reflectivity. The photons in an initial state with fully classical probability distribution pass through an optical network, made up of sequential beam splitters and are prepared in maximally entangled states. We also present the detailed theoretical analysis of entangled state generation, for an arbitrary number of photons, fed through the input ports of the beam splitters with equal probability.
Abstract Quantum optics connects fundamental phenomena such as entanglement and superposition with practical applications like metrology and communication. Throughout, there is an interplay between information theoretic concepts such as entropy and physical considerations such as quantum system design, noise, and loss. Therefore, a result at the heart of these fields can have numerous ramifications in development of applications and advancing our understanding of quantum physics. Our recent proof for the entanglement properties of states interfering with the vacuum on a beam splitter led to monotonicity and convexity properties for quantum states undergoing photon loss [Lupu-Gladstein et al., PRA 112 , 033722 (2025)] by breathing life into a decades-old conjecture. In this work, we extend these fundamental properties to measures of similarity between states, provide inequalities for creation and annihilation operators beyond the Cauchy–Bunyakovsky–Schwarz inequality, prove a conjecture [Hertz et al., PRA 110 , 012408 (2024)] dictating that nonclassicality through the quadrature coherence scale is uncertifiable beyond a loss of 50%, place constraints on quasiprobability distributions of all physical states, and explore entanglement generation optimized over all input states and linear optical networks. These ideas can now be used throughout quantum optics.
We review the theory of continuous-variable entanglement with special emphasis on foundational aspects, conceptual structures and mathematical methods. Much attention is devoted to the discussion of separability criteria and entanglement properties of Gaussian states, for their great practical relevance in applications to quantum optics and quantum information, as well as for the very clean framework that they allow for the study of the structure of nonlocal correlations. We give a self-contained introduction to phase-space and symplectic methods in the study of Gaussian states of infinite-dimensional bosonic systems. We review the most important results on the separability and distillability of Gaussian states and discuss the main properties of bipartite entanglement. These include the extremal entanglement, minimal and maximal, of two-mode mixed Gaussian states, the ordering of two-mode Gaussian states according to different measures of entanglement, the unitary (reversible) localization and the scaling of bipartite entanglement in multimode Gaussian states. We then discuss recent advances in the understanding of entanglement sharing in multimode Gaussian states, including the proof of the monogamy inequality of distributed entanglement for all Gaussian states. Multipartite entanglement of Gaussian states is reviewed by discussing its qualification by different classes of separability, and the main consequences of the monogamy inequality, such as the quantification of genuine tripartite entanglement in three-mode Gaussian states, the promiscuous nature of entanglement sharing in symmetric Gaussian states and the possible coexistence of unlimited bipartite and multipartite entanglement. We finally review recent advances and discuss possible perspectives on the qualification and quantification of entanglement in non-Gaussian states, a field of research that is to a large extent yet to be explored.
A beam splitter is a basic linear optical element appearing in many optics experiments and is frequently used as a continuous-variable entangler transforming a pair of input modes from a separable Gaussian state into an entangled state. However, a beam splitter is a passive operation that can create entanglement from Gaussian states only under certain conditions. One such condition is that the input light is suitably squeezed. We demonstrate, experimentally, that a beam splitter can create entanglement even from modes which do not possess such a squeezing provided that they are correlated to, but not entangled with, a third mode. Specifically, we show that a beam splitter can create three-mode entanglement by acting on two modes of a three-mode fully separable Gaussian state without entangling the two modes themselves. This beam splitter property is a key mechanism behind the performance of the protocol for entanglement distribution by separable states. Moreover, the property also finds application in collaborative quantum dense coding in which decoding of transmitted information is assisted by interference with a mode of the collaborating party.
Large-scale quantum networks have been employed to overcome practical constraints of transmission and storage for single entangled systems. Our goal in this paper is to explore the strong entanglement distribution of quantum networks. We firstly show that any connected network consisting of generalized Einstein-Podolsky-Rosen states and Greenberger-Horne-Zeilinger states satisfies the strong Coffman-Kundu-Wootters monogamy inequality in terms of the bipartite entanglement measure; in addition, the monogamy inequalities are also considered for generic entangled quantum networks. This reveals the interesting feature of high-dimensional entanglement with local tensor decomposition going beyond qubit entanglement. We then apply the entanglement distribution relation in entangled networks to get a quantum maximum-flow minimum-cut theorem in terms of von Neumann entropy and R\'enyi-$\ensuremath{\alpha}$ entropy. We finally classify entangled quantum networks by distinguishing network configurations under local unitary operations. These results provide insights into characterizing quantum networks in quantum information processing.