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arXiv:2006.05346 · Physical Review A

Quantifying entanglement preservability of experimental processes

Shih-Hsuan Chen, Meng-Lok Ng, Che‐Ming Li

Published Sep 8, 2021• 4 citations
arXivHTMLPDF

Abstract

Preserving entanglement is a crucial dynamical process for entanglement-based quantum computation and quantum-information processes, such as one-way quantum computing and quantum key distribution. However, the problem of quantifying the ability of an experimental process to preserve two-qubit entanglement in experimentally feasible ways is not well understood. Accordingly, herein, we consider the use of two measures, namely composition and robustness, for quantitatively characterizing the ability of a process to preserve entanglement, referred to henceforth as entanglement preservability. A fidelity benchmark is additionally derived to identify the ability of a process to preserve entanglement. We show that the measures and introduced benchmark are experimentally feasible and require only local measurements on single qubits and preparations of separable states. Moreover, they are applicable to all physical processes that can be described using the general theory of quantum operations, e.g., qubit dynamics in photonic and superconducting systems. Our method extends the existing tools for analyzing channels, e.g., channel resource theory, to quantify entanglement preservability for non-trace-preserving quantum processes. The results are of significant interest for applications in quantum-information processing in which entanglement preservation is required.

DOI
10.1103/physreva.104.032403

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Preserving entanglement is a crucial dynamical process for entanglement-based quantum computation and quantum-information processes, such as one-way quantum computing and quantum key distribution. However, the problem of quantifying the ability of an experimental process to preserve two-qubit entanglement in experimentally feasible ways is not well understood. Accordingly, herein, we consider the use of two measures, namely composition and robustness, for quantitatively characterizing the ability of a process to preserve entanglement, referred to henceforth as entanglement preservability. A fidelity benchmark is additionally derived to identify the ability of a process to preserve entanglement. We show that the measures and introduced benchmark are experimentally feasible and require only local measurements on single qubits and preparations of separable states. Moreover, they are applicable to all physical processes that can be described using the general theory of quantum operations, e.g., qubit dynamics in photonic and superconducting systems. Our method extends the existing tools for analyzing channels, e.g., channel resource theory, to quantify entanglement preservability for non-trace-preserving quantum processes. The results are of significant interest for applications in quantum-information processing in which entanglement preservation is required.
Quantum entanglement is a key physical resource in quantum information processing that allows for performing basic quantum tasks such as teleportation and quantum key distribution, which are impossible in the classical world. Ever since the rise of quantum information theory, it has been an open problem to quantify entanglement in an information-theoretically meaningful way. In particular, every previously defined entanglement measure bearing a precise information-theoretic meaning is not known to be efficiently computable, or if it is efficiently computable, then it is not known to have a precise information-theoretic meaning. In this Letter, we meet this challenge by introducing an entanglement measure that has a precise information-theoretic meaning as the exact cost required to prepare an entangled state when two distant parties are allowed to perform quantum operations that completely preserve the positivity of the partial transpose. Additionally, this entanglement measure is efficiently computable by means of a semidefinite program, and it bears a number of useful properties such as additivity and faithfulness. Our results bring key insights into the fundamental entanglement structure of arbitrary quantum states, and they can be used directly to assess and quantify the entanglement produced in quantum-physical experiments.
High-dimensional entanglement offers significant advantages over its low-dimensional counterpart in various information-processing tasks. However, to harness these advantages, it is crucial that the quantum channels used to store or transmit the subsystems of an entangled system not only preserve entanglement but also maintain its dimensionality above a certain threshold. The maximum entanglement dimension that a channel can preserve is referred to as its effective dimensionality, since the channel cannot be used to transmit information of dimension greater than that in a single use. In this work, we present a method to certify whether a quantum channel can preserve entanglement dimension above a given threshold. Unlike existing approaches, our method is faithful, i.e., it can be applied to any channel, and avoids common assumptions such as preparation of entangled states, auxiliary side channels, or perfect measurement devices. Moreover, the method can be extended to faithfully certify other classes of non-resource-breaking channels, such as non-nonpositive-partial-transpose-breaking channels (non-NPT-breaking channels). Finally, we discuss possible experimental realizations of our certification scheme through explicit examples.
The uncertainty principle is one of quantum theory's most foundational features. It underpins a quantum phenomenon called measurement incompatibility—two physical observables of a single quantum system may not always be measured simultaneously. Apart from being fundamentally important, measurement incompatibility is also a powerful resource in the broad quantum science and technologies, with wide applications to cryptography, communication, random number generation, and device-independent tasks. Since every physical system is unavoidably subject to noise, an important, yet still open, question is how to characterize the ability of noisy quantum dynamics to preserve measurement incompatibility. This work fills this gap by providing a resource theory of this ability, termed incompatibility preservability. We quantify incompatibility preservability by a robustness measure. Then, we introduce an operational task, entanglement-assisted filter game, to completely characterize both the robustness measure and the conversion of incompatibility preservability. Our results provide a general framework to describe how noisy dynamics affect the uncertainty principle's signature.
Entanglement fidelity quantifies how well a quantum channel preserves the correlations between a transmitted system and an inaccessible reference system. We derive closed-form expressions for the entanglement fidelity associated with several standard quantum noise models, including the random Pauli-X, dephasing, depolarizing, Werner-Holevo, generalized Pauli (Weyl), and amplitude-damping channels. For each model, we express the entanglement fidelity in terms of a general input density operator ρρρ, using Schumacher's Kraus-operator approach, which provides a channel-agnostic recipe applicable to any completely positive trace-preserving (CPTP) map with a finite Kraus representation. We then specialize to a communication scenario in which the source emits a two-letter parametric alphabet, thereby making explicit the dependence of entanglement preservation on both channel and source parameters. The resulting expressions enable direct comparisons of channel performance and rankings for representative families of input states, including common qubit states.
Quantum instruments describe both the classical outcome and the updated quantum state in a measurement process. To do this in a non-trivial way, instruments must have the capability to interact coherently with the state that they measure. Here, we develop a resource theory for instruments. We consider a relevant quantifier of the separation between interactive and non-interactive instruments and show that it admits three distinct operational interpretations in terms of quantum information tasks. These concern (i) the preservation of maximally entangled states after a local measurement, (ii) the average ability to preserve random states after measurement, and (iii) the ability to recover the classical information generated from measuring half of a maximally entangled state. We also introduce a natural set of allowed operations and show that the third task fully characterises the resource content of instruments. Our general framework reproduces as special cases established resource theories for channels and measurements.
Quantum coherence is an essential ingredient in quantum information processing and plays a central role in emergent fields such as nanoscale thermodynamics and quantum biology. However, our understanding and quantitative characterization of coherence as an operational resource are still very limited. Here we show that any degree of coherence with respect to some reference basis can be converted to entanglement via incoherent operations. This finding allows us to define a novel general class of measures of coherence for a quantum system of arbitrary dimension, in terms of the maximum bipartite entanglement that can be generated via incoherent operations applied to the system and an incoherent ancilla. The resulting measures are proven to be valid coherence monotones satisfying all the requirements dictated by the resource theory of quantum coherence. We demonstrate the usefulness of our approach by proving that the fidelity-based geometric measure of coherence is a full convex coherence monotone, and deriving a closed formula for it on arbitrary single-qubit states. Our work provides a clear quantitative and operational connection between coherence and entanglement, two landmark manifestations of quantum theory and both key enablers for quantum technologies.