Here’s a nice sur­prise: quan­tum phys­ics is less com­pli­cat­ed than we thought, ac­cord­ing to new re­search. The work links two strange fea­tures of the quan­tum world—or na­ture at the small­est scales, such as that of sub­a­tom­ic par­t­i­cles—call­ing them dif­fer­ent man­i­festa­t­ions of the same thing.

Quan­tum phys­ics says that par­t­i­cles can be­have like waves, and vi­ce versa. Re­search­ers have now con­clud­ed that this ‘wave-particle du­al­i­ty’ is simp­ly the quan­tum un­cer­tain­ty prin­ci­ple in dis­guise. (Cred­it: Tim­o­thy Yeo / CQT, Na­tion­al U. of Sin­ga­pore )

These fea­tures go by the names “wave-par­t­i­cle du­al­ity” and the “uncer­tainty prin­ci­ple.” In work pub­lished Dec. 19 in the jour­nal Na­ture Com­mu­nica­t­ions, the re­search­ers, who did the work at the Na­t­ional Uni­vers­ity of Sin­ga­pore, say the first is just the sec­ond in dis­guise.

The con­nec­tion “comes out very nat­u­rally when you con­sid­er them as ques­tions about what in­forma­t­ion you can gain about a sys­tem,” said one of the sci­en­tists, Steph­a­nie Weh­ner, who is now at the Delft Uni­vers­ity of Tech­nol­o­gy in the Neth­er­lands.

Wave-par­t­i­cle du­al­ity is the idea that a quan­tum ob­ject can be­have like a wave, but that the wave be­hav­ior stops if you try to lo­cate the ob­ject.

The duality is seen in ex­pe­ri­ments in which sub­a­tom­ic par­t­i­cles, such as elec­trons, are fired one by one at a screen with two thin slits. The par­t­i­cles pile up be­hind the slits not in two heaps, but in a striped pat­tern as you’d ex­pect for waves that “in­ter­fere” with each oth­er. An ever­yday ex­am­ple of wave in­ter­fer­ence oc­curs when you toss two peb­bles in a pond at once a small dis­tance away from each oth­er: when the two sets of rip­ples meet, they form char­ac­ter­is­tic pat­terns as their effects add up.

How­ev­er, in the quan­tum case, the pat­tern van­ishes if you sneak a look at which slit a par­t­i­cle goes through—at which point the par­t­i­cles start to act like par­t­i­cles and not waves.

The quan­tum un­cer­tain­ty prin­ci­ple is the idea that it’s im­pos­si­ble to know cer­tain pairs of things about a quan­tum par­t­i­cle at once. For ex­am­ple, the more pre­cisely you know the po­si­tion of an at­om, the less pre­cisely you can know its speed. It’s a lim­it on the fun­da­men­tal know­a­bil­ity of na­ture, not a state­ment on meas­ure­ment skill. The new work finds that there is an ident­ical sort of limit on how much you can learn about a sys­tem’s wave ver­sus the par­t­i­cle be­hav­ior.

Wave-par­t­i­cle du­al­ity and un­cer­tain­ty have been fun­da­men­tal con­cepts in quan­tum phys­ics since the early 1900s. “We were guid­ed by a gut feel­ing, and only a gut feel­ing, that there should be a con­nec­tion,” said co-re­searcher Pat­rick Coles, who is now at the In­sti­tute for Quan­tum Com­put­ing in Wa­ter­loo, Can­a­da.

One can write equa­t­ions that cap­ture how much can be learn­ed about pairs of prop­er­ties subject to the un­cer­tain­ty prin­ci­ple. Coles, Weh­ner and co-author Je­drzej Kan­iew­ski work with a form of such equa­t­ions known as “en­tropic un­cer­tain­ty rela­t­ions,” and they found that all the maths pre­vi­ously used to de­scribe wave-par­t­i­cle du­al­ity could be re­for­mu­lat­ed in terms of these rela­t­ions.

“It was like we had dis­cov­ered the ‘Rosetta Stone’ that con­nect­ed two dif­fer­ent lan­guages,” said Coles. “The lit­er­a­ture on wave-par­t­i­cle du­al­ity was like hi­er­o­glyph­ that we could now trans­late in­to our na­tive tongue.”

Be­cause the en­tropic un­cer­tain­ty rela­t­ions used in their transla­t­ion have al­so been used in de­mon­strat­ing the se­cur­ity of quan­tum cryp­tog­ra­phy—schemes for se­cure com­mu­nica­t­ion us­ing quan­tum par­t­i­cles—the re­search­ers sug­gest the work could help in­spire new cryp­tog­ra­phy methods.

In ear­li­er pa­pers, Wehner and col­la­bo­ra­tors found con­nec­tions be­tween the un­cer­tain­ty prin­ci­ple and oth­er as­pects of phys­ics, namely quan­tum “non-local­ity” and the sec­ond law of ther­mo­dy­nam­ics. The first deals with par­t­i­cles’ abil­ity to act as though they can com­mu­ni­cate in­stan­ta­ne­ously over long dis­tances; the sec­ond states that dis­or­der in the uni­verse can al­ways in­crease but not de­crease. The re­search­ers say their next goal is to think about how all this fits into a big­ger pic­ture of how na­ture works.

Courtesy of the Centre for Quantum Technologies 
at the National University of Singapore
and World Science staff