124 Scientific American June 1997 Bringing Schrödinger’s Cat to Life

Trends in Physics

Bringing Schrödinger’s Cat to Life by Philip Yam, staff writer

Iam sorry that I ever had anything todo with quantum theory,” ErwinSchrödinger reportedly complained

to a colleague. The Austrian physicistwas not lamenting the fate of his nowfamous cat, which he figuratively placedin a box with a vial of poison in 1935.Rather he was commenting on thestrange implications of quantum me-chanics, the science behind electrons,atoms, photons and other things sub-microscopic. With his feline, Schröding-er attempted to illustrate the problem:according to quantum mechanics, par-ticles jump from point to point, occupyseveral places at once and seem to com-municate faster than the speed of light.So why don’t cats—or baseballs or plan-ets or people, for that matter—do thesame things? After all, they are made ofatoms. Instead they obey the predictable,classical laws quantified by Isaac New-ton. When does the quantum worldgive way to the physics of everyday life?“That’s one of the $64,000 questions,”chuckles David Pritchard of the Massa-chusetts Institute of Technology.

Pritchard and other experimentalistshave begun to peek at the boundary be-tween quantum and classical realms. Bycooling particles with laser beams or bymoving them through special cavities,physicists have in the past year createdsmall-scale Schrödinger’s cats. These“cats” were individual electrons andatoms made to reside in two places si-multaneously, and electromagnetic fieldsexcited to vibrate in two different waysat once. Not only do they show howreadily the weird gives way to the famil-iar, but in dramatic fashion they illus-trate a barrier to quantum computing—atechnology, still largely speculative, thatsome researchers hope could solve prob-lems that are now impossibly difficult.

The mystery about the quantum-clas-sical transition stems from a crucial qual-ity of quantum particles—they can un-dulate and travel like waves (and viceversa: light can bounce around as a par-ticle called a photon). As such, they can

be described by a wave function, whichSchrödinger devised in 1926. A sort ofquantum Social Security number, thewave function incorporates everythingthere is to know about a particle, sum-ming up its range of all possible posi-tions and movements.

Taken at face value, a wave functionindicates that a particle resides in allthose possibilities at once. Invariably,however, an observation reveals onlyone of those states. How or even why aparticular result emerges after a mea-surement is the point of Schrödinger’sthought experiment: in addition to thecat and the poison, a radioactive atom

goes into the box. Within an hour, theatom has an even chance of decaying;the decay would trigger a hammer thatsmashes open the vial of antifeline serum.

The Measurement Problem

According to quantum mechanics, theunobserved radioactive atom re-

mains in a funny state of being decayedand not decayed. This state, called a su-perposition, is something quantum ob-jects enter quite readily. Electrons canoccupy several energy levels, or orbitals,simultaneously; a single photon, afterpassing through a beam splitter, appears

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to traverse two paths at the same time.Particles in a well-defined superpositionare said to be coherent.

But what happens when quantum ob-jects are coupled to a macroscopic one,like a cat? Extending quantum logic,the cat should also remain in a coherentsuperposition of states and be dead andalive simultaneously. Obviously, this ispatently absurd: our senses tell us thatcats are either dead or alive, not both orneither. In prosaic terms, the cat is reallya measuring device, like a Geiger coun-ter or a voltmeter. The question is, then,Shouldn’t measuring devices enter thesame indefinite state that the quantum

particles they are designed to detect do?For the Danish physicist Niels Bohr,

a founder of quantum theory (and towhom Schrödinger’s regretful commentwas directed), the answer was that mea-surements must be made with a classicalapparatus. In what has come to be calledthe standard, or Copenhagen, interpre-tation of quantum mechanics, Bohr pos-tulated that macroscopic detectors neverachieve any fuzzy superposition, but hedid not explain exactly why not. “Hewanted to mandate ‘classical’ by hand,”says Wojciech Zurek of Los AlamosNational Laboratory. “Measurementssimply became.” Bohr also recognized

that the boundary between the classicaland the quantum can shift depending onhow the experiment is arranged. Fur-thermore, size doesn’t necessarily mat-ter: superpositions can persist on scalesmuch larger than the atomic.

In November 1995 Pritchard and hisM.I.T. colleagues crystallized the fuzzi-ness of measurement. The team sent anarrow stream of sodium atoms throughan interferometer, a device that gives aparticle two paths to travel. The pathsrecombined, and each atom, acting as awave, “interfered” with itself, producinga pattern of light and dark fringes onan observing screen (identical to whatis seen when a laser shines through twoslits). The standard formulation of quan-tum mechanics states that the atomtook both paths simultaneously, so thatthe atom’s entire movement from sourceto screen was a superposition of anatom moving through two paths.

The team then directed a laser at oneof the paths. This process destroyed theinterference fringes, because a laser pho-ton scattering off the atom would indi-cate which path the atom took. (Quan-tum rules forbid “which-way” informa-tion and interference from coexisting.)

On the surface, this scattering wouldseem to constitute a measurement thatdestroys the coherence. Yet the teamshowed that the coherence could be “re-covered”—that is, the interference pat-tern restored—by changing the separa-tion between the paths to some quartermultiple of the laser photon’s wave-length. At those fractions, it was notpossible to tell from which path the pho-ton scattered. “Coherence is not reallylost,” Pritchard elucidates. “The atom

Scientific American June 1997 125

Recent experiments have begun to demonstrate how the weird world of quantum mechanics gives way

to the familiarity of everyday experience

Bringing Schrödinger’s Cat to Life

FRAMEWORK OF PHYSICS mustsomehow connect the exotica of quantummechanics—its dead-and-alive cats, or-bitals, oscillating ions and matter waves—

with the more intuitive counterparts fromclassical physics: probabilities, planetarymotions, pendulum swinging and double-slit, light-wave interference.

Copyright 1997 Scientific American, Inc.

became entangled with a larger system.”That is, the quantum state of the atombecame coupled with the measuring de-vice, which in this case was the photon.

Like many previous experiments,Pritchard’s work, which is a realizationof a proposal made by the late RichardFeynman many years ago, deepens themysteries underlying quantum physicsrather than resolving them. It demon-strates that the measuring apparatus canhave an ambiguous definition. In thecase of Schrödinger’s cat, then, is themeasurement the lifting of the lid? Orwhen light reaches the eye and is pro-cessed by the mind? Or a discharge ofstatic from the cat’s fur?

A recent spate of Schrödinger’s cat ex-periments have begun to address thesequestions. Not all physicists concur thatthey are looking at bona fide quantumcats—“kitten” is the term often used, de-pending on the desired level of cuteness.In any event, the attempts do indicatethat the quantum-classical changeover—sometimes called the collapse of thewave function or the state-vector reduc-tion—has finally begun to move out ofthe realm of thought experiments andinto real-world study.

Here, Kitty, Kitty

In 1991 Carlos Stroud and John Yea-zell of the University of Rochester

were experimenting with what are calledRydberg atoms, after the Swedish spec-troscopist Johannes Rydberg, discovererof the binding-energy relation betweenan electron and a nucleus. Ordinarily,electrons orbit the nucleus at a distanceof less than a nanometer; in Rydbergatoms the outer electron’s orbit has swol-len several 1,000-fold. This bloating canbe accomplished with brief bursts of la-ser light, which effectively put the elec-tron in many outer orbitals simultane-ously. Physically, the superposition ofenergy levels manifests itself as a “wavepacket” that circles the nucleus at anatomically huge distance of about half amicron. The packet represents the prob-ability of the excited electron’s location.

While swelling potassium atoms, theRochester workers noticed that after afew orbits, the wave packet would dis-perse, only to come back to life again astwo smaller packets on opposite endsof its large orbit. With his colleagueMichael W. Noel, Stroud showed lastSeptember that the two packets consti-tuted a Schrödinger’s cat state—a singleelectron in two locations.

Bringing Schrödinger’s Cat to Life

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FUZZINESS OF QUANTUM MEASUREMENT is demonstratedwith sodium atoms split and recombined to produce an interferencepattern (not shown). A laser deflecting off an atom would reveal whichpath the atom took and thereby eliminate interference. But the patternreemerges if the path lengths are varied, showing how deeply quantumsystems can become “entangled” with classical apparatus.

SCHRÖDINGER’S CAT made from a beryllium ion is first trapped byan electromagnetic field and then cooled with a laser. Laser “force”beams prepare the ion in a superposition of two spin states. Thesestates are then eased apart so that the ion resides in two places at once.

CAT-AND-MOUSE EXPERIMENT is done with a trapped electro-magnetic field (confined photons). A rubidium atom is excited by mi-crowaves into a superposition of two states. As it passes through thecenter cavity, it relays its superposed state to the electromagnetic field.A second atom serves as the “mouse” that probes the resulting state ofthe field. (The second microwave cavity, identical to the first, providesa way to create quantum interference and is essential to measurements.)

Copyright 1997 Scientific American, Inc.

An electron, though, is essentially amere point. Closer to the macroscopicrealm is an ion (a charged atom), whichconsists of many elementary particles.In May 1996 Chris Monroe, David J.Wineland and their colleagues at theNational Institute of Standards andTechnology (NIST) in Boulder, Colo., cre-ated a Schrödinger’s cat out of a berylli-um ion. They first trapped the ion withelectromagnetic fields, then hit it with alaser beam that stifled the ion’s thermaljitters and thereby cooled it to within amillikelvin of absolute zero. Then theresearchers fired two laser beams, eachof a slightly different frequency, at theion to manipulate its spin, an intrinsic,quantum feature that points either upor down. With the lasers, the research-ers made the ion take on a superposi-tion of spin-up and spin-down states.

So much for the preparations; nextcame the more macroscopic part. Bymanipulating the tuning of the two la-sers, the NIST team could swing the spin-up state to and fro in space, and thespin-down state fro and to. A snapshotwould show the ion in the spin-up stateat one physical location and simultane-ously in the spin-down state at a secondposition. The states were 80 nanometersapart—large on the atomic scale. “Wemade one ion occupy two places that arevery far separated compared with thesize of the original ion,” Monroe says.

Last December, Michel Brune, SergeHaroche, Jean-Michel Raimond andtheir colleagues at the Ecole NormaleSupérieure (ENS) in Paris took mattersa step further. “We were able to monitorthe washing-out of quantum features,”Haroche explains. To see how the super-position collapsed to one state or anoth-er, they in effect dangled a quantummouse in front of their Schrödinger’s catto check whether it was alive or dead.

The cat was a trapped electromagnet-ic field (a bunch of microwave photonsin a cavity). The researchers sent into thecavity a Rydberg atom that had beenexcited into a superposition of two dif-ferent energy states. The Rydberg atomtransferred its superposed state to theresident electromagnetic field, putting itinto a superposition of two differentphase, or vibrational, states. With itstwo phases, the field thus resembled theSchrödinger’s cat in its odd superposi-tion between life and death.

For the mouse, the ENS team firedanother Rydberg atom into the cavity.The electromagnetic field then trans-ferred information about its superposed

phases to the atom. The physicists com-pared the second atom with the first toglean superposition information aboutthe electromagnetic field.

More interesting, however, was theteam’s ability to control crucial variablesand to determine how coherent statesbecome classical ones. By varying the in-terval between the two atoms sent intothe cavity (from 30 to 250 microsec-onds), they could see how the collapseof the superposition varied as a functionof time, and by enlarging the electro-magnetic field (by putting more photonsin the cavity), they could see how thecollapse changed with size. “This is thefirst time we can observe the progres-sive evolution of quantum to classicalbehavior,” Haroche says.

“This is a breathtaking experiment,”Zurek enthuses. “Seeing a Schrödinger’scat is always surprising, but being ableto see the cat forced to make a choice be-tween ‘dead’ and ‘alive,’ to observe forthe first time quantum weirdness goingaway, is the real coup.” Moreover, theENS results jibed with most theorists’technical expectations. “What it tellsme,” Zurek remarks, “is that the simpleequations we’ve been writing down seemto be a good approximation.”

Losing Coherence

Zurek is the leading advocate of atheory called decoherence, which

is based on the idea that the environ-ment destroys quantum coherence. Heformulated it in the 1980s (althoughsome of it harkens back to Bohr and

other quantum founders) and with var-ious collaborators has been investigat-ing its consequences ever since.

The destabilizing environment essen-tially refers to anything that could beaffected by—and hence inadvertently“measure”—the state of the quantumsystem: a single photon, a vibration of amolecule, particles of air. The environ-ment is not simply “noise” in this theo-ry; it acts as an apparatus that constant-ly monitors the system.

The ENS experiment makes that effectclear. “The system decoheres becausethe system leaks information,” Zureknotes. Some photons can escape the cav-ity and hence betray the state of the re-maining ones to the rest of the universe.“So in a sense, Schrödinger’s cat is hav-ing kittens crawling out,” Zurek says.

Having the environment define thequantum-classical boundary has the ad-vantage of removing some of the mysti-cal aspects of quantum theory that cer-tain authors have promulgated. It doesaway with any special need for a con-sciousness or new physical forces to ef-fect a classical outcome. It also explainswhy size per se is not the cause of deco-herence: large systems, like real-life cats,would never enter a superposition, be-cause all the particles that make up a fe-line influence a vast number of environ-mental parameters that make coherenceimpossible. Given a one-gram bob on apendulum and a few reasonable assump-tions, the interference terms in the sys-tem’s wave function drop to about2.7–1,000 of their original value in ananosecond—a virtually instantaneousdisappearance of quantum weirdness.“The old intuition going back to Bohris on the money,” although now there isa physical mechanism to substantiatehis mandate, Zurek concludes.

Still, Zurek’s decoherence model isflawed in some eyes. “In my view, deco-herence doesn’t select a particular out-come,” opines Anthony J. Leggett of theUniversity of Illinois. “In real life, youget definite macroscopic outcomes.”

Zurek argues that the environmentdoes indeed dictate the quantum possi-bilities that end up in the real world. Theprocess, which he refers to as environ-ment-induced superselection, or einse-lection, tosses out the unrealistic, quan-tum states and retains only those statesthat can withstand the scrutiny of theenvironment and thus might becomeclassical. “The selection is done by theenvironment, so you will not be able topredict which of the allowed possibili-

Bringing Schrödinger’s Cat to Life Scientific American June 1997 127

WRITING ON AN ATOM is theo-retically plausible. An electron in asuperposition of 2,500 energy levelshas a wave function sufficiently com-plex to encode a message. Words arewritten by assigning color and satu-ration to the amplitude and phaseof the wave function.

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ties will become real,” Zurekobserves.

The explanation feels less thansatisfying. Zurek’s approach is“very appealing. It allows youto calculate things, to see howthe interference fringes wash outas the superposition gets big-ger,” NIST’s Monroe says. “Butthere’s still something funnyabout it. He’s sweeping thingsunder the rug, but it’s hard tosay what rug.” The problem isthat decoherence—and in factany theory about the quantum-classical transition—is necessari-ly ad hoc. Quantum superposi-tions must somehow yield out-comes that conform to oureveryday sense of reality. Thatleads to circuitous logic: the re-sults seen in the macroscopicworld arise out of the quantumworld because those results arethe ones we see. A solution of sorts, ad-vocated by a few prominent cosmolo-gists, is the unwieldy “many worlds”interpretation, which holds that all pos-sibilities stipulated by the wave functiondo in fact happen. They go on to exist inparallel universes. The idea, however, isuntestable, for the parallel universes re-main forever inaccessible to one another.

Radical Reworkings

The problems with decoherence andthe many-worlds idea have led a

sizable minority to support a view calledGRW theory, according to Leggett. Theconcept was put forward in 1986 byGianCarlo Ghirardi and Tullio Weberof the University of Trieste and AlbertoRimini of the University of Pavia.

In the GRW scheme, the wave func-tion of a particle spreads out over time.But there is a small probability that thespreading wave “hits” a mysterious“something” in the background. Thewave function suddenly becomes local-ized. Individual particles have only asmall chance of a hit, about once every100 million years. But for a macroscop-ic cat, the chance that at least one of itsroughly 1027 particles makes a hit is high,at least once every 100 picoseconds. Thecat never really has a chance to enterany kind of superposition. Hence, thereis no need for decoherence: the macro-scopic state of the cat results from spon-taneous microscopic collapses.

A few problems plague this model.One is that the timing factor that trig-

gers the hit is entirely arbitrary; propo-nents simply choose one that producesreasonable results. More important,though, is the source of the trigger. “Ba-sically, [there is] a sort of universalbackground noise that cannot itself bedescribed by quantum mechanics,” Leg-gett explains. The noise is not simplyrandom processes in the environment;it has a distinct mathematical flavor.Roger Penrose of the University of Ox-ford argues in his book Shadows of theMind that the trigger may be gravity,which would neatly sidestep certaintechnical objections.

Other, more radical proposals abound.The most well known was put forth bythe late David Bohm, who postulatedthat “hidden variables” underpin quan-tum mechanics. These variables—de-scribing properties that in a way renderwave functions as real forces—wouldeliminate the notion of superpositionsand restore a deterministic reality. Likethe many-worlds idea, Bohm’s theorycannot be verified: the hidden variablesby definition remain, well, hidden.

Given such choices, many workingphysicists are subscribing to decoher-ence, which makes the fewest leaps offaith even if it arguably fails to resolvethe measurement problem fully. “Deco-herence does answer the physical as-pects of the questions,” Zurek says, butdoes not get to the metaphysical ones,such as how a conscious mind perceivesan outcome. “It’s not clear if you havethe right to expect the answer to allquestions, at least until we develop a

better understanding of how brain andmind are related,” he muses.

Bigger superpositions may enable re-searchers to start ruling out some theo-ries—GRW and decoherence predictthem on different scales, for instance.“What we would like to do is to go tomore complex systems and entanglemore and more particles” than just themere 10 trapped before, Haroche of theENS says. Future NIST experiments areparticularly suited to serve as “decoher-ence monitors,” Monroe contends. “Wecan simulate noise to deliberately causethe superposition to decay.” Leggett hasproposed using sensors made from su-perconducting rings (called SQUIDs): itshould be possible to set up large cur-rents flowing in opposite directionsaround the ring simultaneously.

Still, there’s a long way to go. “Evenin the most spectacular experiments, atmost you’ve shown a superposition formaybe 5,000 particles. That’s a longway from the 1023 characteristic of themacroscopic world,” says Leggett, whononetheless remains supportive. “Myown attitude is that one should just tryto do experiments to see if quantummechanics is still working.”

Shrinking transistors, now with fea-tures less than a micron in size, may alsolead to insights about the quantum-clas-sical changeover. In a few years they mayreach dimensions of tens of nanometers,a realm sometimes called the mesoscopicscale. Da Hsuan Feng of Drexel Univer-sity speculates that quantum mechanicsperhaps really doesn’t lead to classical

Bringing Schrödinger’s Cat to Life128 Scientific American June 1997

Jobs for Quantum Cats

Researchers have proposed and demonstrated several technologies exploiting entan-gled and superposed quantum states, such as quantum computing. A few other

schemes include the following:

Using lasers, researchers can place mole-cules in a superposition of reaction path-ways; then they can control the chemicalprocess by adjusting the degree of interfer-ence. Last December workers separated

isotopes with asimilar technique.Obstacles includeless than practicalefficiency levelsand difficulty incontrolling phasecharacteristics ofthe laser.

Quantum Key Cryptography

A much betterprospect than quan-tum computing isquantum key cryp-tography. Legitimatecommunicators cre-ate shared keys us-ing the polarizationof photons. Eaves-dropping on these keys would immediatelybe noticed, because it would disrupt thekey photons’ states. Quantum cryptogra-phy has been shown to function over sev-eral kilometers in optical fibers.

Quantum Chemistry

Copyright 1997 Scientific American, Inc.

mechanics; rather both descriptionsspring from still undiscovered conceptsin the physical realm between them.

Quantum Computing

Even if experiments cannot yet tacklethe measurement problem fully, they

have much to contribute to a very hotfield: quantum computing. A classicalcomputer is built of transistors thatswitch between 0 or 1. In a quantumcomputer, however, the “transistors” re-main in a superposition of 0 and 1(called a quantum bit, or qubit); calcu-lations proceed via interactions betweensuperposed states until a measurementis performed. Then the superpositionscollapse, and the machine delivers a finalresult. In theory, because it could processmany possible answers simultaneously,a quantum computer would accomplishin seconds tasks, such as factoring largenumbers to break codes, that wouldtake years for a classical machine.

In December 1995 researchers suc-cessfully created quantum two-bit sys-tems. Monroe and his colleagues craft-ed a logic element called a controlled-NOT gate out of a beryllium ion. Theion is trapped and cooled to its lowestvibrational state. This state and the firstexcited vibrational state constitute onebit. The second bit is the spin of one ofthe ion’s electrons. Laser pulses can forcethe bits into superpositions and flip thesecond bit depending on the state of thefirst bit. Other variations of gates coupletwo photons via an atom in a cavity or

transmit an entangled pair of photonsthrough a network of detectors.

Yet the creation of a useful quantumcomputer, relying on superpositions ofthousands of ions performing billions ofoperations, remains dubious. The prob-lem? Loss of superposition. The logicgates must be fast enough to work be-fore the qubits lose coherence. Usingdata from the NIST gate experiment,Haroche and Raimond calculated in anAugust 1996 Physics Today article thatgiven the gate speed of 0.1 millisecond,the bits would have to remain in a su-perposition for at least a year to com-plete a meaningful computation (in thiscase, factoring a 200-digit number).

Other physicists are less pessimistic,since error-correcting codes (which areindispensable in classical computing)might be the solution. “It gives you in-structions on how to repair the dam-age,” says David DiVincenzo of theIBM Thomas J. Watson Research Cen-ter in Yorktown Heights, N.Y.

Moreover, DiVincenzo points out thata new method of quantum computation,making use of nuclear magnetic reso-nance (NMR) techniques, could raisecoherence times to a second or more.Say a liquid—a cup of coffee—is placedin a magnetic field; because of thermalvibration and other forces, only one outof every million nuclei in the caffeinemolecules would line up with the mag-netic field. These standouts can be ma-nipulated with radio waves to put theirspins in a superposition of up and down.Maintaining coherence is easier here

than in the other techniques be-cause the nuclear spins undergo-ing the superpositions are wellprotected from the environmentby the surrounding turmoil ofseething molecules, the madscramble of which averages outto zero. The calculating caffeinesits effectively in the calm eye ofa hurricane. Two groups haverecently demonstrated quan-tum computing by NMR, usinga four-qubit version to sum 1and 1. More complex systems,using perhaps 10 qubits, couldbe had by the end of the year.

The drawback is readout.With no way to detect individ-ual spins, researchers must mea-sure all the molecules’ spins—

both qubit and nonqubit ones.Complex molecules capable ofsustaining many spins aretherefore “noisier” than sim-

pler ones. “They’ll be able to do somenice stuff,” Monroe says, “but beyondabout 10 bits, they’ll run into funda-mental problems.” The output from 10bits is only 0.001 as strong as that froma single bit; for 20, the output is downby one million. So the NMR techniquemay not enter a meaningful computa-tional realm of at least 50 bits.

There might be other uses for quan-tum superpositions, though. Stroud pro-poses data storage on an atom, becausean electron in a Rydberg atom could bemade to inhabit a superposition of 2,500different energy levels. “That means thatthe electron’s wave function can be quitecomplex, encoding a great deal of infor-mation,” Stroud expounds. He demon-strated the possibility theoretically bywriting “OPTICS” on an atom. Otheruses for quantum superposition, suchas in cryptography, chemistry and eventeleportation, have been demonstrated.Schrödinger’s boxed cat may have out-witted the best philosophical minds sofar, but it seems to have found plenty oftechnological reasons to stay put.

Bringing Schrödinger’s Cat to Life Scientific American June 1997 129

The idea has less to dowith Star Trek than withreconstructing destroyedinformation. The crux isthe Einstein-Podolsky-Ro-sen effect, which showsthat two photons can re-main entangled, no mat-

ter how far apart they are, until a measurementis made (which instantaneously puts both in adefinite state). Alice takes one EPR photon, Bobthe other. Later, Alice measures her EPR photonwith respect to a third photon. Bob can use therelational measurement to re-create Alice’snon-EPR photon. Whether Bob truly remateri-alized the photon or just created an indistin-guishable clone is unclear. Researchers at theUniversity of Innsbruck reportedly demonstrat-ed the phenomenon, which might have use inquantum cryptography.

Lasers ordinarily require a populationinversion, a condition in which atoms inan excited state outnumber those in theground state; the excited atoms emit la-ser photons as they drop to the groundstate. In 1995 researchers sidestepped thisrequirement. In lasing without inversion,two coupling lasers give ground-stateatoms two paths to one higher energylevel. Interference between the paths ren-ders the ground-state atoms invisible, andso fewer excitedatoms are need-ed. Such lasersdo not requireas much powerand in principlecould emit lightin the desirablex-ray region.

Quantum Laser OpticsQuantum Teleportation

Further Reading

Decoherence and the Transition fromQuantum to Classical. Wojciech Zurekin Physics Today, Vol. 44, No. 10, pages36–44; October 1991.

Where Does the Weirdness Go? DavidLindley. BasicBooks, 1996.

Schrödinger’s Machines. Gerard J. Mil-burn. W. H. Freeman and Co., 1997.

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