High-dimensional Entangled States Research Articles

Automated gadget discovery in the quantum domain

In recent years, reinforcement learning (RL) has become increasingly successful in its application to the quantum domain and the process of scientific discovery in general. However, while RL algorithms learn to solve increasingly complex problems, interpreting the solutions they provide becomes ever more challenging. In this work, we gain insights into an RL agent’s learned behavior through a post-hoc analysis based on sequence mining and clustering. Specifically, frequent and compact subroutines, used by the agent to solve a given task, are distilled as gadgets and then grouped by various metrics. This process of gadget discovery develops in three stages: First, we use an RL agent to generate data, then, we employ a mining algorithm to extract gadgets and finally, the obtained gadgets are grouped by a density-based clustering algorithm. We demonstrate our method by applying it to two quantum-inspired RL environments. First, we consider simulated quantum optics experiments for the design of high-dimensional multipartite entangled states where the algorithm finds gadgets that correspond to modern interferometer setups. Second, we consider a circuit-based quantum computing environment where the algorithm discovers various gadgets for quantum information processing, such as quantum teleportation. This approach for analyzing the policy of a learned agent is agent and environment agnostic and can yield interesting insights into any agent’s policy.

State transfer and entanglement between two- and four-level atoms in a cavity

Qudits with a large Hilbert space to host quantum information are widely utilized in various applications, such as quantum simulation and quantum computation, but the manipulation and scalability of qudits still face challenges. Here, we propose a scheme to directly and locally transfer quantum information from multiple atomic qubits to a single qudit and vice versa in an optical cavity. With the qubit–qudit interaction induced by the cavity, our scheme can transfer quantum states efficiently and measurement-independently. In addition, this scheme can robustly generate a high-dimensional maximal entangled state with asymmetric particle numbers, showing its potential in realizing an entanglement channel. Such an information interface for qubits and qudit may have enlightening significance for future research on quantum systems in hybrid dimensions.

Equivalence between simulability of high-dimensional measurements and high-dimensional steering

The effect of quantum steering arises from the judicious combination of an entangled state with a set of incompatible measurements. Recently, it was shown that this form of quantum correlations can be quantified in terms of a dimension, leading to the notion of genuine high-dimensional steering. While this naturally connects to the dimensionality of entanglement (Schmidt number), we show that this effect also directly connects to a notion of dimension for measurement incompatibility. More generally, we present a general connection between the concepts of steering and measurement incompatibility, when quantified in terms of dimension. From this connection, we propose a novel twist on the problem of simulating quantum correlations. Specifically, we show how the correlations of certain high-dimensional entangled states can be exactly recovered using only shared randomness and lower-dimensional entanglement. Finally, we derive criteria for testing the dimension of measurement incompatibility, and discuss the extension of these ideas to quantum channels.

Spatial-spectral mapping to prepare frequency entangled qudits.

Entangled qudits, the high-dimensional entangled states, play an important role in the study of quantum information. How to prepare entangled qudits in an efficient and easy-to-operate manner is still a challenge in quantum technology. Here, we demonstrate a method to engineer frequency entangled qudits in a spontaneous parametric downconversion process. The proposal employs an angle-dependent phase-matching condition in a nonlinear crystal, which forms a classical-quantum mapping between the spatial (pump) and spectral (biphotons) degrees of freedom. In particular, the pump profile is separated into several bins in the spatial domain, and thus shapes the down-converted biphotons into discrete frequency modes in the joint spectral space. Our approach provides a feasible and efficient method to prepare a high-dimensional frequency entangled state. As an experimental demonstration, we generate a three-dimensional entangled state by using a homemade variable slit mask.

General scheme for complete high-dimensional Bell state measurement.

We theoretically propose a simple and efficient scheme for the complete analysis of high-dimensional Bell states in N dimensions. The mutually orthogonal high-dimensional entangled states can be unambiguously distinguished by obtaining the parity and relative phase information of entanglement independently. Based on this approach, we present the physical realization of photonic four-dimensional Bell state measurement with the current technology. The proposed scheme will be useful for quantum information processing tasks that utilize high-dimensional entanglement.

Characterizing and Tailoring Spatial Correlations in Multimode Parametric Down-Conversion

Photons entangled in their position-momentum degrees of freedom serve as an elegant manifestation of the Einstein-Podolsky-Rosen paradox, while also enhancing quantum technologies for communication, imaging, and computation. The multimode nature of photons generated in parametric down-conversion has inspired a generation of experiments on high-dimensional entanglement, ranging from complete quantum state teleportation to exotic multipartite entanglement. However, precise characterization of the underlying position-momentum state is notoriously difficult due to limitations in detector technology, resulting in a slow and inaccurate reconstruction riddled with noise. Furthermore, theoretical models for the generated two-photon state often forgo the importance of the measurement system, resulting in a discrepancy between theory and experiment. Here we formalize a description of the two-photon wave function in the spatial domain, referred to as the collected joint-transverse momentum amplitude (JTMA), which incorporates both the generation and measurement system involved. We go on to propose and demonstrate a practical and efficient method to accurately reconstruct the collected JTMA using a simple phase-step scan known as the $2D\ensuremath{\pi}$ measurement. Finally, we discuss how precise knowledge of the collected JTMA enables us to generate tailored high-dimensional entangled states that maximize discrete-variable entanglement measures such as entanglement of formation or entanglement dimensionality, and optimize critical experimental parameters such as photon heralding efficiency. By accurately and efficiently characterizing photonic position-momentum entanglement, our results unlock its full potential for discrete-variable quantum information science and lay the groundwork for future quantum technologies based on multimode entanglement.

Experimental optimal verification of three-dimensional entanglement on a silicon chip

High-dimensional entanglement is significant for the fundamental studies of quantum physics and offers unique advantages in various quantum information processing tasks. Integrated quantum devices have recently emerged as a promising platform for creating, processing, and detecting complex high-dimensional entangled states. A crucial step toward practical quantum technologies is to verify that these devices work reliably with an optimal strategy. In this work, we experimentally implement an optimal quantum verification strategy on a three-dimensional maximally entangled state using local projective measurements on a silicon photonic chip. A 95% confidence is achieved from 1190 copies to verify the target quantum state. The obtained scaling of infidelity as a function of the number of copies is −0.5497 ± 0.0002, exceeding the standard quantum limit of −0.5 with 248 standard deviations. Our results indicate that quantum state verification could serve as an efficient tool for complex quantum measurement tasks.

Verifying angular-position entanglement by Hardy's paradox with multisetting high-dimensional systems

High-dimensional entangled states are of crucial importance, as they provide higher channels for quantum information. Angular position, as a continuous variable, provides an infinite Hilbert space theoretically. It is usually represented in discrete bases experimentally because of the convenient modulation of the width of the angular aperture. Thus the combination of the angular apertures will conveniently shape the two photon states. And the entanglement of the two photon states can be naturally demonstrated by Hardy's paradox. Here, by testing Hardy's paradox for two-setting high-dimensional angular subspaces with dimension ranging from 2 to 7 and for multisetting three-dimensional subspaces with setting ranging from 3 to 5, we reveal the high-dimensional entanglement in the angular-position degree of freedom. We show that the high-dimensional angular-position entanglement can yield a much sharper contradiction between the quantum mechanics and classical theories. Our work shows that the angular variable can be considered as an alternative discrete base to provide the high-dimensional entangled states. Thus it may be used as a new platform for quantum information.

Metrology-assisted entanglement distribution in noisy quantum networks

We consider the distribution of high-dimensional entangled states to multiple parties via noisy channels and the subsequent probabilistic conversion of these states to desired target states using stochastic local operations and classical communication. We show that such state-conversion protocols can be enhanced by embedded channel-estimation routines at no additional cost in terms of the number of copies of the distributed states. The defining characteristic of our strategy is the use of those copies for which the conversion was unsuccessful for the estimation of the noise, thus allowing one to counteract its detrimental effect on the successfully converted copies. Although this idea generalizes to various more complex situations, we focus on the realistic scenario, where only finitely many copies are distributed and where the parties are not required to process multiple copies simultaneously. In particular, we investigate the performance of so-called one-successful-branch protocols, applied sequentially to single copies and an adaptive Bayesian estimation strategy. Finally, we compare our strategy to more general but less easily practically implementable strategies involving distillation and the use of quantum memories to process multiple copies simultaneously.

Tripartite high-dimensional magnon-photon entanglement in phases with broken PT -symmetry of a non-Hermitian hybrid system

Hybrid systems that combine spin ensembles and superconducting circuits provide a promising platform for implementing quantum information processing. We propose a non-Hermitian magnon-circuit-QED hybrid model consisting of two cavities and an yttrium iron garnet (YIG) sphere placed in one of the cavities. Abundant exceptional points (EPs), parity-time ($\mathcal{PT}$)-symmetry phases, and $\mathcal{PT}$-symmetry broken phases are investigated in the parameter space. Tripartite high-dimensional entangled states can be generated steadily among modes of the magnon and photons in $\mathcal{PT}$-symmetry broken phases, corresponding to which the stable quantum coherence exists. Results show that the tripartite high-dimensional entangled state is robust against the dissipation of hybrid system, independent of a certain initial state, and insensitive to the fluctuation of magnon-photon coupling. Further, we propose to simulate the hybrid model with an equivalent $LCR$ circuit. This paper may provide prospects for realizing multipartite high-dimensional entangled states in the magnon-circuit-QED hybrid system.

Experimental High-Dimensional Greenberger-Horne-Zeilinger Entanglement with Superconducting Transmon Qutrits

Multipartite entanglement is one of the core concepts in quantum information science with broad applications that span from condensed matter physics to quantum physics foundation tests. Although its most studied and tested forms encompass two-dimensional systems, current quantum platforms technically allow the manipulation of additional quantum levels. We report the experimental demonstration and certification of a high-dimensional multipartite entangled state in a superconducting quantum processor. We generate the three-qutrit Greenberger-Horne-Zeilinger state by designing the necessary pulses to perform high-dimensional quantum operations. We obtain the fidelity of $76\mathrm{%}\ifmmode\pm\else\textpm\fi{}1\mathrm{%}$, proving the generation of a genuine three-partite and three-dimensional entangled state. To this date, only photonic devices have been able to create and certify the entanglement of these high-dimensional states. Our work demonstrates that another platform, superconducting systems, is ready to exploit genuine high-dimensional entanglement and that a programmable quantum device accessed on the cloud can be used to design and execute experiments beyond binary quantum computation.

Correlations in Entanglement-Assisted Prepare-and-Measure Scenarios

We investigate the correlations that can arise between Alice and Bob in prepare-and-measure communication scenarios where the source (Alice) and the measurement device (Bob) can share prior entanglement. The paradigmatic example of such a scenario is the quantum dense coding protocol, where the communication capacity of a qudit can be doubled if a two-qudit entangled state is shared between Alice and Bob. We provide examples of correlations that actually require more general protocols based on higher-dimensional entangled states. This motivates us to investigate the set of correlations that can be obtained from communicating either a classical or a quantum $d$-dimensional system in the presence of an unlimited amount of entanglement. We show how such correlations can be characterized by a hierarchy of semidefinite programming relaxations by reducing the problem to a non-commutative polynomial optimization problem. We also introduce an alternative relaxation hierarchy based on the notion of informationally-restricted quantum correlations, which, though it represents a strict (non-converging) relaxation scheme, is less computationally demanding. As an application, we introduce device-independent tests of the dimension of classical and quantum systems that, in contrast to previous results, do not make the implicit assumption that Alice and Bob share no entanglement. We also establish several relations between communication with and without entanglement as resources for creating correlations.

High dimensional quantum network coding based on prediction mechanism over the butterfly network

The high-dimensional quantum system greatly improve the quantum channel capacity and information storage space, and achieve high-dimensional quantum information transmission, which enhance the speed of quantum computing and quantum information processing. In this paper, a high-dimensional quantum teleportation protocol without information loss is proposed. We consider pre-sharing a high-dimensional non-maximum entangled state as a quantum channel between sender and receiver. By adding auxiliary particle and performing high-dimensional local operations, it is possible to achieve high-dimensional quantum teleportation without information loss. Simultaneously, we apply the protocol to butterfly network, and propose a novel high-dimensional quantum network coding based on prediction mechanism. In our scheme, we use Z-{|0⟩, |1⟩} basis to predict the transmission of high dimensional states over the butterfly network. When the prediction is successful, the deterministic transmission of high-dimensional quantum states can be realized over the butterfly network. Our scheme greatly saves the usage of quantum and classical channels, which improves the utilization efficiency of both channels.

Probabilistic hierarchically controlled teleportation of anarbitrary <italic>m</italic>-qudit state with a pure entangledquantum channel

<p indent=0mm>Quantum teleportation is a unique quantum information processing method in quantum communication. Researchers have shown considerable interest in hierarchically controlled teleportation by using quantum entangled states as the quantum channel. Protocols for the hierarchically controlled teleportation of an arbitrary single-qubit via a four-qubit χ state and a four-qubit cluster state have been proposed. We present a protocol for the hierarchically controlled teleportation of an arbitrary <italic>m</italic>-qudit (<italic>d</italic>-dimensional quantum system) state by using a partially entangled quantum state as the quantum channel. The sender performs <italic>m</italic> generalized Bell-state measurements on her <sc>2<italic>m</italic></sc> particles. To reconstruct the original state, the upper-grade receiver only needs to apply a unitary operation in accordance with one of the receivers’ measurement results, and the lower-grade receivers need to perform a unitary operation according to all the other receivers’ measurement results. The receivers can reconstruct the original state probabilistically by introducing an auxiliary qubit and performing a collective unitary transformation. The protocol has the advantage of having high channel capacity by using a high-dimensional entangled state as the quantum channel.

Speeding up measurements of entangled states

New approach much faster than previous methods Researchers at the University of the Witwatersrand’s School of Physics, in South Africa, have developed a technique that provides a simple, fast and direct approach for the measurement of dimensionality and purity of high-dimensional entangled states.

Measuring dimensionality and purity of high-dimensional entangled states

High-dimensional entangled states are promising candidates for increasing the security and encoding capacity of quantum systems. While it is possible to witness and set bounds for the entanglement, precisely quantifying the dimensionality and purity in a fast and accurate manner remains an open challenge. Here, we report an approach that simultaneously returns the dimensionality and purity of high-dimensional entangled states by simple projective measurements. We show that the outcome of a conditional measurement returns a visibility that scales monotonically with state dimensionality and purity, allowing for quantitative measurements for general photonic quantum systems. We illustrate our method using two separate bases, the orbital angular momentum and pixels bases, and quantify the state dimensionality by a variety of definitions over a wide range of noise levels, highlighting its usefulness in practical situations. Importantly, the number of measurements needed in our approach scale linearly with dimensions, reducing data acquisition time significantly. Our technique provides a simple, fast and direct measurement approach.

Entanglement purification by counting and locating errors with entangling measurements

We consider entanglement purification protocols for multiple copies of qubit states. We use high-dimensional auxiliary entangled systems to learn about the number and positions of errors in the noisy ensemble in an explicit and controlled way, thereby reducing the amount of noise in the ensemble and purifying the remaining states. This allows us to design entanglement purification protocols for any number of copies that work particularly well for a small number of expected errors, i.e., high fidelity of initial states. The main tool is a counter gate with which the required nonlocal information can be transferred into the high-dimensional entangled qudit auxiliary states. We compare our schemes to standard recurrence protocols that operate on pairs of copies, and hashing and breeding protocols that operate on a (asymptotically) large number of copies. Our protocols interpolate between these two regimes, leading to higher achievable fidelity and yield. We illustrate our approach for bipartite qubit states and generalize it to purify multiparty GHZ states.

Justifying the thin-crystal approximation in spontaneous parametric down-conversion for collinear phase matching

Spatially engineered photons from spontaneous parametric down-conversion (SPDC) are a valuable tool for studying and applying photonic entanglement. An advantage of SPDC is that simple expressions for the two-photon state can be obtained using justified approximations. In particular, the thin-crystal approximation has often been invoked in the engineering of high-dimensional entangled states. Knowledge of the conditions under which the thin-crystal approximation remains valid is essential for the realization of experimental setups. We provide a quantitative guideline on the validity of the thin-crystal approximation in calculating the two-photon spatial state. In particular, we show that the applicability of this regime is related to the focusing parameter ${\overline{w}}_{p}={w}_{p}/\sqrt{{\ensuremath{\lambda}}_{p}\phantom{\rule{0.16em}{0ex}}L}$, where ${w}_{p}$ and ${\ensuremath{\lambda}}_{p}$ are the beam waist and wavelength of the pump beam, respectively, and $L$ is the length of the nonlinear crystal. Additionally, the validity of the thin-crystal regime is investigated concerning the size of a subspace in the Laguerre Gaussian basis, into which the two-photon state can be projected in a given experiment.

Is high-dimensional photonic entanglement robust to noise?

High-dimensional entangled states are of significant interest in quantum science as they increase the information content per photon and can remain entangled in the presence of significant noise. The authors develop the analytical theory and show experimentally that the noise tolerance of high-dimensional entanglement can be significantly increased by a modest increase in the size of the Hilbert space. For example, doubling the size of a Hilbert space with a local dimension of d = 300 leads to a reduction in the threshold detector efficiencies required for entanglement certification by two orders of magnitude. This work is developed in the context of spatial entanglement in the few-photon limit, but it can easily be translated to photonic states entangled in different degrees of freedom. The authors also demonstrate that knowledge of a single parameter, the signal-to-noise ratio, precisely links measures of entanglement to a range of experimental parameters quantifying noise in a quantum communication system, enabling accurate predictions of its performance. This work serves to answer a simple question: “Is high-dimensional photonic entanglement robust to noise?” Here, the authors show that the answer is more nuanced than a simple “yes” or “no” and involves a complex interplay between the noise characteristics of the state, channel, and detection system.

Unified monogamy relation of entanglement measures

The monogamy of quantum entanglement captures the property of limitation in the distribution of entanglement. Various monogamy relations exist for different entanglement measures that are important in quantum information processing. Our goal in this work is to propose general monogamy inequalities for several entanglement measures on entangled qubit systems. The present results provide a unified model for various entanglement measures including the concurrence, the negativity, the entanglement of formation, Tsallis-q entropy, Renyi-q entropy, and Unified-(q, s) entropy. We then propose tightened monogamy inequalities for multipartite qubit systems and derive upper bounds of aforementioned entanglement measures for multipartite pure state under generalized bipartitions. We finally prove a generic result that most of tripartite high-dimensional entangled pure states have no entanglement monogamy. These results are useful for exploring the entanglement theory, quantum information processing and secure quantum communication.