A quantum cryptographic protocol is device-independent if its security does not rely on trusting that the quantum devices used are truthful. Thus the security analysis of such a protocol needs to consider scenarios of imperfect or even malicious devices. Several important problems have been shown to admit unconditional secure and device-independent protocols. A closely related topic (that is not discussed in this article) is measurement-device independent quantum key distribution.

Overview and history

Mayers and Yao proposed the idea of designing quantum protocols using "self-testing" quantum apparatus, the internal operations of which can be uniquely determined by their input-output statistics. Subsequently, Roger Colbeck in his Thesis proposed the use of

Bell test A Bell test, also known as Bell inequality test or Bell experiment, is a real-world physics experiment designed to test the theory of quantum mechanics in relation to Albert Einstein's concept of local realism. Named for John Stewart Bell, the e ...

s for checking the honesty of the devices. Since then, several problems have been shown to admit unconditional secure and device-independent protocols, even when the actual devices performing the Bell test are substantially "noisy," i.e., far from being ideal. These problems include

quantum key distribution Quantum key distribution (QKD) is a secure communication method which implements a cryptographic protocol involving components of quantum mechanics. It enables two parties to produce a shared random secret key known only to them, which can then b ...

randomness expansion In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual rando ...

, and

randomness amplification In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual rando ...

Key distribution

The goal of

is for two parties, Alice and Bob, to share a common secret string through communications over public channels. This was a problem of central interest in quantum cryptography. It was also the motivating problem in Mayers and Yao's paper. A long sequence of works aim to prove unconditional security with robustness. Vazirani and Vidick were the first to reach this goal. Subsequently, Miller and Shi proved a similar result using a different approach.

Randomness expansion

The goal of randomness expansion is to generate a longer private random string starting from a uniform input string and using untrusted quantum devices. The idea of using

to achieve this goal was first proposed by Roger Colbeck in his Ph.D. Thesis. Subsequent works have aimed to prove unconditional security with robustness and the increase the rate of expansion. Vazrani and Vidick were the first to prove full quantum security for an exponentially expanding protocol. Miller and Shi achieved several additional features, including cryptographic level security, robustness, and a single-qubit requirement on the quantum memory. The approach was subsequently extended by the same authors to show that the noise level can approach the obvious upper bound, when the output may become deterministic.

Randomness amplification

The goal of randomness amplification is to generate near-perfect randomness (approximating a fair coin toss) starting from a single source of weak randomness (a coin each of whose tosses is somewhat unpredictable, though it may be biased and correlated with previous tosses). This is known to be impossible classically. However, by using quantum devices, it becomes possible even if the devices are untrusted. Roger Colbeck and

Renato Renner Renato Renner (born 11 December 1974) is a Swiss professor for Theoretical Physics at the Swiss Federal Institute of Technology (ETH) in Zurich, where he is head of the Research Group for Quantum Information Theory. His research interests incl ...

were motivated by physics considerations to ask the question first. Their construction and the subsequent improvement by Gallego et al. are secure against a non-signalling adversary, and have significant physical interpretations. The first construction that does not require any structural assumptions on the weak source is due to Chung, Shi, and Wu.

References

{{reflist, 30em, refs= {{Cite conference , last1=Mayers, first1=Dominic , last2=Yao, first2=Andrew C.-C. , title=Quantum Cryptography with Imperfect Apparatus , conference=IEEE Symposium on Foundations of Computer Science (FOCS) , year =1998 , arxiv=quant-ph/9809039 , bibcode=1998quant.ph..9039M {{ Cite thesis , last=Colbeck , first=Roger , title=Quantum And Relativistic Protocols For Secure Multi-Party Computation , chapter=Chapter 5 , arxiv=0911.3814, date=December 2006 , publisher=University of Cambridge {{Cite journal , title = Fully Device-Independent Quantum Key Distribution , last1=Vazirani , first1 = Umesh , last2=Vidick , first2=Thomas , journal = Physical Review Letters , year = 2014 , volume = 113 , issue=14 , pages =140501 , doi=10.1103/physrevlett.113.140501 , pmid=25325625 , arxiv=1210.1810, bibcode=2014PhRvL.113n0501V, s2cid=119299119 {{Cite journal , last1=Miller , first1=Carl , last2=Shi , first2=Yaoyun , year=2016 , title = Robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices , journal=Journal of the ACM , volume=63 , issue=4 , page=33 , arxiv=1402.0489, doi=10.1145/2885493 , s2cid=53234710 {{Cite journal , last1=Miller , first1=Carl , last2=Shi , first2=Yaoyun , year=2017 , title=Universal security for randomness expansion , journal=SIAM Journal on Computing , volume=46 , issue=4 , pages=1304–1335 , arxiv=1411.6608 , doi=10.1137/15m1044333 , s2cid = 6792482 {{cite arXiv , title=Physical Randomness Extractors: Generating Random Numbers with Minimal Assumptions , last1=Chung, first1=Kai-Min, last2=Shi, first2=Yaoyun, last3=Wu, first3=Xiaodi , eprint=1402.4797 , year=2014 , class=quant-ph {{cite book , chapter =Certifiable quantum dice: or, true random number generation secure against quantum adversaries , last1=Vazirani , first1 = Umesh , last2=Vidick , first2=Thomas , year = 2012 , title=The 44th Symposium on Theory of Computing (STOC) , pages =61–76 , chapter-url = http://dl.acm.org/citation.cfm?id=2213977 {{cite journal , title=Free randomness can be amplified , last1=Colbeck, first1=Roger, last2=Renner, first2=Roger , year=2012 , arxiv=1105.3195 , journal=Nature Physics , volume=8 , issue=6, pages=450–453 , doi=10.1038/nphys2300 , bibcode=2012NatPh...8..450C, s2cid=118309394 {{cite journal , title=Full randomness from arbitrarily deterministic events , first1=Rodrigo, last1=Gallego, first2=Lluis, last2=Masanes, first3=Gonzalo, last3=De La Torre, first4=Chirag, last4=Dhara, first5=Leandro, last5=Aolita, first6=Antonio, last6=Acín , journal=Nature Communications , year=2014 , pages=2654 , volume=4 , arxiv=1210.6514 , doi=10.1038/ncomms3654, pmid=24173040 , bibcode=2013NatCo...4.2654G, s2cid=14630558 Quantum cryptography