Implementation of a Measurement-Device-Independent Entanglement Witness

Abstract

Entanglement, the essential resource in quantum information processing, should be witnessed in many tasks such as quantum computing and quantum communication. The conventional entanglement witness method, relying on an idealized implementation of measurements, could wrongly conclude a separable state to be entangled due to imperfect detections. Inspired by the idea of a time-shift attack, we construct an attack on the conventional entanglement witness process and demonstrate that a separable state can be falsely identified to be entangled. To close such detection loopholes, based on a recently proposed measurement-device-independent entanglement witness method, we design and experimentally demonstrate a measurement-device-independent entanglement witness for a variety of two-qubit states. By the new scheme, we show that an entanglement witness can be realized without detection loopholes. 2Quantum entanglement plays an important role in the nonclassical phenomenons of quantum mechanics. Being the key resource for many tasks in quantum information processing, such as quantum computation [1], quantum teleportation [2], and quantum cryptography [3,4], entanglement needs to be verified in many scenarios. There are several proposals to witness entanglement and we refer to Ref.[5] for a detailed review. A conventional way to detect entanglement, the entanglement witness (EW), gives one of two outcomes: "Yes" or "No", corresponding to the conclusive result that the state is entangled or to failure to draw a conclusion, respectively. Mathematically, for a given entangled quantum state ρ, a Hermitian operator W is called a witness, if tr[W ρ] < 0 (output of 'Yes') and tr[W σ] ≥ 0 (output of 'No') for any separable state σ. Note that there could also exist an entangled state ρ ′ such that tr[W ρ ′ ] ≥ 0 (output of 'No'). In the experimental verification, one can realize the conventional EW with only local measurements by decomposing W into a linear combination of product Hermitian observables [5].Focusing on the bipartite scenario, a general illustration of the conventional EW is shown in Fig. 1(a), where two parties, Alice and Bob, each receive one component of a bipartite state ρ AB from an untrusted third party Eve. They want to verify whether ρ AB is entangled or not, by performing local operations and measurements onThe correctness of such witness relies on implementation details of W . An unfaithful implementation of W , say, due to device imperfections, would render the witness results unreliable. For example, the measurement devices used by Alice and Bob might possibly be manufactured by another untrusted party, who could collaborate with Eve and deliberately fabricate devices to make the real implementation W ′ = W + δW deviate from W , such that W ′ is not a witness any more,That is, with the deviated witness W ′ , a separable state σ could be identified as an entangled one, which is more likely to happen when tr[W σ] is near zero. There is a strong similarity between the EW and the quantum key distribution (QKD)...

Reliable and robust entanglement witness

“…Theoretically, the MDIEW scheme prevents identifying separable states to be entangled. Such a reliable MDIEW has been experimentally demonstrated lately [9]. In practice, however, such a scheme can be inefficient, meaning that it witnesses very few entangled states despite that the observed data could actually provide more information.…”

“…The MDIEW scheme is based on an important discovery that any entangled state can be witnessed in a nonlocal game with quantum inputs [15]. In the MDIEW scheme, it is shown that an arbitrary conventional EW can be converted to be an MDIEW, which has been experimentally tested [9].…”

“…That is, there may exist some separable states σ, such that Tr[σW ′ ] < 0 ≤ Tr[σW ]. Practically, by exploiting device imperfections, an attack has been experimentally implemented for an entanglement witness procedure [9]. In cryptographic applications, such problem is regarded as a loophole, where one mistakes separable states to be entangled ones.…”

Measurement-Device-Independent Approach to Entanglement Measures

“…While this difficulty can be partially circumvented by making use of entanglement witnesses (EWs) when lower bounds on the entanglement are desired [14][15][16][17][18][19], errors and misalignments of the measurement devices can still lead to incorrect estimations of the quantities and thus, erroneous conclusions. A measurementdevice-independent approach is therefore desirable.Recent work by Buscemi [20] has introduced a new way to think about entanglement detection [21][22][23][24]. The idea is to map the problem onto a modified class of nonlocal games, called semiquantum nonlocal games (SQNLGs).…”

“…Recent work by Buscemi [20] has introduced a new way to think about entanglement detection [21][22][23][24]. The idea is to map the problem onto a modified class of nonlocal games, called semiquantum nonlocal games (SQNLGs).…”