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arXiv:2209.06849 · Physical Review A

Nondestructive verification of entangled states via fidelity witnessing

Ferran Riera-Sàbat, Jorge Miguel-Ramiro, Wolfgang Dür

Published Feb 10, 2023• 3 citations
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Abstract

Assessing the quality of an ensemble of noisy entangled states is a central task in quantum information processing. Usually, this is done by measuring and hence destroying multiple copies, from which state tomography or fidelity estimation can be employed to characterize states. Here we propose several methods to directly distinguish between two different sets of states, e.g., if their fidelity is above or below a certain threshold value. This turns out to be significantly more efficient and importantly keeps the verified states intact. We make use of auxiliary entanglement or an ensemble of larger size, where we operate on the whole ensemble, but measure only a small fraction where information has been concentrated. For certain state families, we demonstrate that such an approach can even outperform optimal methods that collectively measure directly a fixed fraction of the ensemble.

DOI
10.1103/physreva.107.022414

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Assessing the quality of an ensemble of noisy entangled states is a central task in quantum information processing. Usually, this is done by measuring and hence destroying multiple copies, from which state tomography or fidelity estimation can be employed to characterize states. Here we propose several methods to directly distinguish between two different sets of states, e.g., if their fidelity is above or below a certain threshold value. This turns out to be significantly more efficient and importantly keeps the verified states intact. We make use of auxiliary entanglement or an ensemble of larger size, where we operate on the whole ensemble, but measure only a small fraction where information has been concentrated. For certain state families, we demonstrate that such an approach can even outperform optimal methods that collectively measure directly a fixed fraction of the ensemble.
Consider the task of verifying that a given quantum device, designed to produce a particular entangled state, does indeed produce that state. One natural approach would be to characterize the output state by quantum state tomography, or alternatively, to perform some kind of Bell test, tailored to the state of interest. We show here that neither approach is optimal among local verification strategies for 2-qubit states. We find the optimal strategy in this case and show that quadratically fewer total measurements are needed to verify to within a given fidelity than in published results for quantum state tomography, Bell test, or fidelity estimation protocols. We also give efficient verification protocols for any stabilizer state. Additionally, we show that requiring that the strategy be constructed from local, nonadaptive, and noncollective measurements only incurs a constant-factor penalty over a strategy without these restrictions.
Maximally entangled states are a key resource in many quantum communication and computation tasks, and their certification is a crucial element to guarantee the desired functionality. We introduce collective strategies for the efficient, local verification of ensembles of Bell pairs that make use of an initial information and noise transfer to few copies prior to their measurement. In this way the number of entangled pairs that need to be measured and hence destroyed is significantly reduced as compared to previous, even optimal, approaches that operate on individual copies. Moreover, the remaining states are directly certified. We show that our tools can be extended to other problems and larger classes of multipartite states.
Entanglement is one of the most fascinating features of quantum theory, as it fundamentally distinguishes quantum systems from classical systems. It not only might play a role in natural processes, but provides an especially powerful resource for a plethora of quantum information protocols, including quantum state teleportation, superdense coding as well as quantum computation schemes. However, for larger systems involving more than two parties, it is a challenging task to verify and characterize entanglement. In this thesis, efficient means for detecting genuine multipartite entanglement in multiqubit quantum systems will be derived, demonstrated, and discussed. Beyond that, methods for quantum state and process tomography will be introduced, which allow to analyze and investigate prepared multipartite states or even the performance of whole setups. Some typical obstacles for reliable state tomography will be pointed out, together with new means to understand experimentally obtained data. Finally, the measurement problem, which describes the unavoidable backaction of a measurement process to the quantum state under investigation, will be illustrated. Together with the discussion of different methods of quantum measurements, the optimal measurement instruments for binary qubit measurements will be derived. These optimal measurement instruments allow to perform a quantum measurement, providing a tunable amount of information about the quantum state, while avoiding any unnecessary disturbance to the state. This set of optimal instruments will be compared to other measurement schemes, such as measurements based on the optimal quantum cloning protocol.
The efficient and reliable characterization of quantum states plays a vital role in most, if not all, quantum information processing tasks. In this work, we present a universally optimal protocol for verifying entangled states by employing the so-called quantum nondemolition measurements, such that the verification efficiency is equivalent to that of the optimal global strategy. Instead of being probabilistic as the standard verification strategies, our protocol is constructed sequentially, which is thus more favorable for experimental realizations. In addition, the target states are preserved in the protocol after each measurement, so can be reused in any subsequent tasks. We demonstrate the power of our protocol for the optimal verification of Bell states, arbitrary two-qubit pure states, and stabilizer states. We also prove that our protocol is able to perform tasks including fidelity estimation and state preparation.
So-called direct measurements of entanglement are collective measurements on multiple copies of a (bipartite or multipartite) quantum system that directly provide one with a value for some entanglement measure, such as the concurrence for bipartite states. Multiple copies are needed since the entanglement of a mixed state is not a linear function of the density matrix. The procedures proposed and implemented so far make certain assumptions about the states generated. This feature distinguishes direct measurements from standard entanglement verification tests such as Bell inequalities, entanglement witnesses, and quantum-state tomography, which make no such assumptions. I discuss how a direct measurement can be turned into a quantitative entanglement verification test without such assumptions by exploiting a recent theorem by Renner [Nature Phys. 3, 645 (2007)10.1038/nphys684].