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Register a new userDistributed Quantum Metrology and the Entangling Power of Linear Networks
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We derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality.
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Notions of circuit complexity and cost play a key role in quantum computing and simulation where they capture the (weighted) minimal number of gates that is required to implement a unitary. Similar notions also become increasingly prominent in high energy physics in the study of holography. While notions of entanglement have in general little implications for the quantum circuit complexity and the cost of a unitary, in this note, we discuss a simple such relationship when both the entanglement of a state and the cost of a unitary take small values, building on ideas on how values of entangling power of quantum gates add up. This bound implies that if entanglement entropies grow linearly in time, so does the cost. The implications are two-fold: It provides insights into complexity growth for short times. In the context of quantum simulation, it allows to compare digital and analog quantum simulators. The main technical contribution is a continuous-variable small incremental entangling bound.
Generative adversarial networks (GANs) are one of the most widely adopted semisupervised and unsupervised machine learning methods for high-definition image, video, and audio generation. In this work, we propose a new type of architecture for quantum generative adversarial networks (entangling quantum GAN, EQ-GAN) that overcomes some limitations of previously proposed quantum GANs. Leveraging the entangling power of quantum circuits, EQ-GAN guarantees the convergence to a Nash equilibrium under minimax optimization of the discriminator and generator circuits by performing entangling operations between both the generator output and true quantum data. We show that EQ-GAN has additional robustness against coherent errors and demonstrate the effectiveness of EQ-GAN experimentally in a Google Sycamore superconducting quantum processor. By adversarially learning efficient representations of quantum states, we prepare an approximate quantum random access memory (QRAM) and demonstrate its use in applications including the training of quantum neural networks.
The capacity of a quantum gate to produce entangled states on a bipartite system is quantified in terms of the entangling power. This quantity is defined as the average of the linear entropy of entanglement of the states produced after applying a quantum gate over the whole set of separable states. Here we focus on symmetric two-qubit quantum gates, acting on the symmetric two-qubit space, and calculate the entangling power in terms of the appropriate local-invariant. A geometric description of the local equivalence classes of gates is given in terms of the $mathfrak{su}(3)$ Lie algebra root vectors. These vectors define a primitive cell with hexagonal symmetry on a plane, and through the Weyl group the minimum area on the plane containing the whole set of locally equivalent quantum gates is identified. We give conditions to determine when a given quantum gate produces maximally entangled states from separable ones (perfect entanglers). We found that these gates correspond to one fourth of the whole set of locally-distinct quantum gates. The theory developed here is applicable to three-level systems in general, where the non-locality of a quantum gate is related to its capacity to perform non-rigid transformations on the Majorana constellation of a state. The results are illustrated by an anisotropic Heisenberg model, the Lipkin-Meshkov-Glick model, and two coupled quantized oscillators with cross-Kerr interaction.
We show that entanglement can be used to detect spacetime curvature. Quantum fields in the Minkowski vacuum are entangled with respect to local field modes. This entanglement can be swapped to spatially separated quantum systems using standard local couplings. A single, inertial field detector in the exponentially expanding (de Sitter) vacuum responds as if it were bathed in thermal radiation in a Minkowski universe. We show that using two inertial detectors, interactions with the field in the thermal case will entangle certain detector pairs that would not become entangled in the corresponding de Sitter case. The two universes can thus be distinguished by their entangling power.
We study the entangling properties of multipartite unitary gates with respect to the measure of entanglement called one-tangle. Putting special emphasis on the case of three parties, we derive an analytical expression for the entangling power of an $n$-partite gate as an explicit function of the gate, linking the entangling power of gates acting on $n$-partite Hilbert space of dimension $d_1 ldots d_n$ to the entanglement of pure states in the Hilbert space of dimension $(d_1 ldots d_n)^2$. Furthermore, we evaluate its mean value averaged over the unitary and orthogonal groups, analyze the maximal entangling power and relate it to the absolutely maximally entangled (AME) states of a system with $2n$ parties. Finally, we provide a detailed analysis of the entangling properties of three-qubit unitary and orthogonal gates.
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