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arXiv:2204.11310 · Physical Review Applied

Universal device for two-qubit entangled measurements via photonic quantum walks

Wen-Zhe Yan, Zhibo Hou, Jun-Feng Tang, Guo‐Yong Xiang, Chuan‐Feng Li, Guang‐Can Guo, Marc-Olivier Renou

Published Oct 12, 2023• 2 citations
arXivHTMLPDF

Abstract

Sophisticated positive-operator-valued measures (POVMs) are fundamental to obtain a quantum advantage in many informational problems but are difficult to implement. We design a universal measurement device composed of cascaded quantum-walk modules able to realize arbitrary entangled POVMs on two qubits. Only parameters in the modules need reprogramming for different POVMs. We apply our device to the task of direction guessing, realizing nine different five-outcome entangled measurements (fidelities above 0.9850) via nine-step photonic quantum walks, recovering optimal direction guessing from nonideal input states. Our work marks an important step toward building a universal versatile quantum measurement device able to implement optimal measurements for various quantum information tasks.

DOI
10.1103/physrevapplied.20.044032

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Sophisticated positive-operator-valued measures (POVMs) are fundamental to obtain a quantum advantage in many informational problems but are difficult to implement. We design a universal measurement device composed of cascaded quantum-walk modules able to realize arbitrary entangled POVMs on two qubits. Only parameters in the modules need reprogramming for different POVMs. We apply our device to the task of direction guessing, realizing nine different five-outcome entangled measurements (fidelities above 0.9850) via nine-step photonic quantum walks, recovering optimal direction guessing from nonideal input states. Our work marks an important step toward building a universal versatile quantum measurement device able to implement optimal measurements for various quantum information tasks.
We report an experimental implementation of a single-qubit generalized measurement scenario, the positive-operator valued measure (POVM), based on a quantum walk model. The qubit is encoded in a single-photon polarization. The photon performs a quantum walk on an array of optical elements, where the polarization-dependent translation is performed via birefringent beam displacers and a change of the polarization is implemented with the help of wave plates. We implement: (i) trine POVM, i.e., the POVM elements uniformly distributed on an equatorial plane of the Bloch sphere; (ii) symmetric-informationally-complete (SIC) POVM; and (iii) unambiguous discrimination of two nonorthogonal qubit states.
Abstract Direct measurement of entanglement is an efficient method for obtaining the degree of entanglement without full reconstruction of the quantum state. But most of the current entanglement direct measurement schemes are designed for the states in specific physical systems, and are not universal for different physical systems. So, in this paper, we want to design a universal direct measurement algorithm for the entanglement of two-qubit states, where universal means that the algorithm does not depend on specific physical systems. Although the conventional quantum walk (QW) model does not have this universal property, we find that by introducing auxiliary qubits and CNOT gates in quantum circuits, a generalized QW model can be realized in any qubit system, i.e. it is universal for different physical systems. Inspired by the universal property of this generalized QW model, a universal quantum algorithm is designed for directly measuring the entanglement degree of two-qubit states, which we call the QW inspired algorithm. To demonstrate the feasibility of the algorithm, analytical calculations and numerical simulations for three representative quantum states are studied. The results show that the algorithm can be used to directly measure two-qubit entanglement, and the universality of the algorithm guarantees that it works not only in optical systems but also in any other physical system. Furthermore, this algorithm may find more applications in other quantum information tasks necessitating qubit–qubit coupling.
Symmetric informationally complete positive operator-valued measurement (SIC-POVM) is one important class of quantum measurement which is crucial for various quantum information processing tasks. SIC-POVMs have the advantage of providing an unbiased estimator for quantum states with the minimal number of outcomes needed for full tomography. We present an experimental approach on a photonic quantum walk which can be used to implement SIC-POVMs on a single-qbubit. The projection measurements of single-photons' positions correspond to elements of SIC-POVM on the polarization of single-photons.
This thesis describes a linear-optical device for performing generalized quantum measurements \non quantum bits (qubits) encoded in photon polarization, the implementation \nof said device, and its use in two diff erent but related experiments. The device works by \ncoupling the polarization degree of freedom of a single photon to a `mode' or `path' degree \nof freedom, and performing a projective measurement in this enlarged state space in order \nto implement a tunable four-outcome positive operator-valued measure (POVM) on the \ninitial quantum bit. In both experiments, this POVM is performed on one photon from a \ntwo-photon entangled state created through spontaneous parametric down-conversion. \nIn the fi rst experiment, this entangled state is viewed as a two-qubit photonic cluster \nstate, and the POVM as a means of increasing the computational power of a given resource \nstate in the cluster-state model of quantum computing. This model traditionally \nachieves deterministic outputs to quantum computations via successive projective measurements, \nalong with classical feedforward to choose measurement bases, on qubits in a highly entangled \nresource called a cluster state; we show that `virtual qubits' can be appended to a \ngiven cluster by replacing some projective measurements with POVMs. Our experimental \ndemonstration fully realizes an arbitrary three-qubit cluster computation by implementing \nthe POVM, as well as fast active feed-forward, on our two-qubit photonic cluster state. \nOver 206 diff erent computations, the average output delity is 0.9832 +/- 0.0002; furthermore \nthe error contribution from our POVM device and feedforward is only of order 10^-3, less \nthan some recent thresholds for fault-tolerant cluster computing. \nIn the second experiment, the POVM device is used to implement a deterministic \nprotocol for remote state preparation (RSP) of arbitrary photon polarization qubits. RSP \nis the act of preparing a quantum state at a remote location without actually transmitting \nthe state itself. We are able to remotely prepare 178 diff erent pure and mixed qubit \nstates with an average delity of 0.995. Furthermore, we study the the fidelity achievable \nby RSP protocols permitting only classical communication, without shared entanglement, \nand compare the resulting benchmarks for average fidelity against our experimental results. \nOur experimentally-achieved average fi delities surpass the classical thresholds whenever \nclassical communication alone does not trivially allow for perfect RSP.
Positive-operator-value measurement (POVM) is the most general class of quantum measurement. We propose a scheme to deterministically implement arbitrary POVMs of single atomic qubit via cavity QED catalysed by only one ancilla atomic qubit. By appropriately entangling two atomic qubits and sequentially measuring the ancilla qubit, any POVM can be implemented step by step. As an application of our scheme, the realization of a specific POVM for optimal unambiguous discrimination (OUD) between two nonorthogonal states is given.
Quantum measurements play a fundamental role in quantum mechanics. Especially, generalized quantum measurements provide a powerful and versatile tool to extract information from quantum systems. However, how to realize them on an arbitrary higher-dimensional quantum system remains a challenging task. Here we propose a simple recipe for the implementation of a general positive-operator valued measurement (POVM) on a higher-dimensional quantum system via a one-dimensional discrete-time quantum walk with a two-dimensional coin. Furthermore, using single photons and linear optics, we realize experimentally a symmetric, informationally complete (SIC) POVM on a three-dimensional system with high fidelity. As an application, we realize a qutrit state tomography with SIC-POVM and confirm that the infidelity scaling achieved by the qutrit SIC-POVM is as good as that based on mutually unbiased bases. Our study paves the way to explore physics and information in higher-dimensional quantum systems and finds applications in various quantum information processing tasks that rely on generalized quantum measurements.