Abstract
Entanglement sources that produce many entangled states act as a main component in applications exploiting quantum physics such as quantum communication and cryptography. Realistic sources are inherently noisy, cannot run for an infinitely long time, and do not necessarily behave in an independent and identically distributed manner. An important question then arises—how can one test, or certify, that a realistic source produces high amounts of entanglement? Crucially, a meaningful and operational solution should allow us to certify the entanglement which is available for further applications after performing the test itself (in contrast to assuming the availability of an additional source which can produce more entangled states, identical to those which were tested). To answer the above question and lower bound the amount of entanglement produced by an uncharacterised source, we present a protocol that can be run by interacting classically with uncharacterised (but not entangled to one another) measurement devices used to measure the states produced by the source. A successful run of the protocol implies that the remaining quantum state has high amounts of one-shot distillable entanglement. That is, one can distill many maximally entangled states out of the single remaining state. Importantly, our protocol can tolerate noise and, thus, certify entanglement produced by realistic sources. With the above properties, the protocol acts as the first ‘operational device-independent entanglement certification protocol’ and allows one to test and benchmark uncharacterised entanglement sources which may be otherwise incomparable.
Highlights
Entanglement is one of the most fundamental concepts of quantum physics, distinguishing it from classical physics [HHHH09]. It plays a crucial role in the advantages gained by considering applications of quantum physics such as quantum computation [Wil10], communication [DW02], and cryptography [BS16]
How should one quantify the amount of entanglement produced by a source? Secondly, how can one compare, or benchmark, different types of entanglement sources? Thirdly, how can one test, or certify, that high amounts of entanglement are being produced by the source?
Given an uncharacterised source of entanglement producing n bipartite systems globally described by the state φ ∈ HA⊗ ̃n ⊗ HB⊗ ̃n for some Hilbert spaces HA and HB and two measurement devices not entangled to one another but otherwise uncharacterised, our goal is to find a Device-independent entanglement certification (DIEC) protocol, employing only local operations and classical communication (LOCC), that certifies that φ is highly entangled in a meaningful operational way
Summary
Entanglement is one of the most fundamental concepts of quantum physics, distinguishing it from classical physics [HHHH09]. The devices can be assumed to be “malicious”[1]; as long as a violation of a Bell inequality is observed, the observer, or verifier, can be sure of the quantum nature of the systems without placing significant trust in the manufacture of the devices Most previous works, both theoretical and experimental, that can be seen as DI entanglement certification (DIEC) procedures work only under the IID assumption and fail to be operational in the sense defined above.[2] This includes tests concerned with the demonstration of entanglement via an entanglement witness (i.e. answering a yes-no question) [GT09, BBS+13, Ban14], as well as more quantitative analyses of entanglement measures such as the negativity and dimension witness [MBL+13]. As far as we are aware, the only self-testing works where this is not the case are [CRSV16, NV17]
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