Quantum Coherence Witness with Untrusted Measurement Devices

Abstract

Coherence is a fundamental resource in quantum information processing, which can be certified by a coherence witness. Due to the imperfection of measurement devices, a conventional coherence witness may lead to fallacious results. We show that the conventional witness could mistake an incoherent state as a state with coherence due to the inaccurate settings of measurement bases. In order to make the witness result reliable, we propose a measurement-device-independent coherence witness scheme without any assumptions on the measurement settings. We introduce the decoy-state method to significantly increase the capability of recognizing states with coherence. Furthermore, we experimentally demonstrate the scheme in a time-bin encoding optical system. Superposition explains many striking phenomena of quantum mechanics, such as the interference in the double-slit experiment of electrons and Schrödinger's cat gedanken experiment. According to Born's rule, measuring a superposed system would lead to a random projection, whose outcome cannot be predicted in principle. This feature can be employed in quantum information processing for designing quantum random number generators (QRNGs) [1,2]. Recently, the strength of superposition is quantified under the framework of quantum coherence [3,4], which is a rapidly developing field in quantum foundation. Quantum coherence has close connections with entanglement and other quantum correlations in many-body systems, and interestingly these measures can be transformed into each other [5][6][7][8]. Also, various concepts can be mapped from quantum entanglement to quantum coherence, such as coherence of assistance [9], coherence distillation and cost [10][11][12][13][14], and coherence evolutions [15]. It turns out that coherence, as an essential resource, plays an important role in various tasks including quantum algorithms [16], quantum biology [17], and quantum thermodynamics [18].In reality, it is crucial to judge whether a quantum source is capable for certain quantum information processing tasks. Coherence witness has been introduced to detect the existence of coherence for an unknown state [19]. A valid coherence witness W is a Hermitian operator which is positive semidefinite after dephasing on the coherence computational basis ∆(W ) ≥ 0. This condition is equivalent to that of tr(ρW ) ≥ 0 for all incoherent states. Then, tr(ρW ) < 0 shows coherence in ρ. Coherence witness has a close connection with a coherence measure called robustness of coherence C R (ρ) [19]. If we optimize the observable W to maximize −tr(ρW ), the maximum value is the robustness of coherence of ρ. In other words, the witness can be used to lower bound the coherence of an unknown system [20]; i.e., the relation C R (ρ) ≥ −tr(ρW ) always holds for a valid witness W [19]. This property can also be applied to construct a source-independent QRNG [21]. Several experiments relevant to coherence witness have been reported recently [20,22,23].The key problem is that the correctness of coherence witness highly ...

Estimating Coherence Measures with Untrusted Devices

“…In a recent work of ref. [84], a proof‐of‐principle demonstration has been given showing that there are coherent states of which the relative entropy of coherence can be estimated by the scenario. However, the discussion there is mainly focused on randomness generation, and the scenario's strength of coherence witness and estimation is not very clear.…”

“…First, we briefly review the result in ref. [84]. In this work, the relative entropy of coherence is taken as the coherence measure for the research of randomness generation.…”

“…To deal with the optimization, in [84] an optimization method in ref. [2] based on Lagrange duality has been applied.…”

“…Little is known whether we can perform (semi) DI tests in the study of single party coherence. An exception is a recent work [ 84 ] where it is shown that coherence can be witnessed by uncharacterized measurement devices in a prepare‐and‐measure scenario. However, only the relative entropy of coherence is considered, and it is not known if all coherent states can be (robustly) witnessed by the scenario.…”

Manipulation of Multi‐Level Quantum Systems via Unsharp Measurements and Feedback Operations

“…Recent years have witnessed remarkable progress in the manipulation of quantum system in both theories and experiments . The ability to precisely control dynamical evolutions is the prerequisite for the development of quantum‐enabled technologies.…”