At the heart of the history of quantum
entanglement lies a famous debate between two groups of physicists, a
clever paradox and an iconoclastic way out of it.
If quantum mechanics
is a true theory of nature, does it mean god plays dice with the univese?
Credit: johanl/Flickr, CC BY 2.0
God does not
play dice with the universe. He plays an ineffable game of his own devising,
which might be compared, from the perspective of any of the other players, to
being involved in an obscure and complex version of poker in a pitch dark room,
with blank cards, for infinite stakes, with a dealer who won’t tell you the
rules, and who smiles all the time.
– Terry
Pratchett
In June
2017, a group of scientists in China announced that they had used the country’s
Micius satellite, launched a year earlier, to teleport information from Earth
to space in an instant. In other words, they had moved it across over
500 km in literally no time. To achieve this, they had relied on a natural
phenomenon called quantum entanglement. The name itself correctly suggests that
it belongs in the realm of quantum mechanics, the realm of subatomic particles.
The Chinese scientists’ experiment had bested a previous record, when in 2012
their leader himself had lead a team that had teleported information
across 97 km.
Very few
ideas in science enjoy the popularity that teleportation does: it has been
equally awe-inspiring among scientists and laypeople. To the more inspired,
what is fascinating is not how an object “leaves” one point in
space and “arrives” at another but that it traverses the intervening distance
in an instant. The implications of such travel are significant at first sight.
The day when we will be able to “beam” a person up and down across space –
a la Star Trek – might
still be very far away but in the meantime we could use quantum entanglement
to, for example, teleport digital security keys between two computers and
prevent most forms of eavesdropping by hackers.
In the
earlier experiment, Jian-Wei Pan, a physics professor at the University of
Science and Technology of China, Hefei, and his colleagues used quantum
entanglement to teleport information across Qinghai Lake in the country’s
west. Using an ultraviolet laser pointed at a barium crystal, Pan’s team
generated pairs of entangled photons. Each photon of a pair was transmitted
using a telescope to two parties on either sides of the lake.
The nature
of quantum entanglement
Let’s call
the parties A and B.
Making a
measurement on the photons yields a good description of the state the
photons are in. It refers to the values of a few fixed variables. If the
variables have a particular combination of values, then the system is
said to be in a particular state. States are usually independent of extrinsic
properties like mass. So, A’s and B’s goals are to see if a third party
interacting with these photons ends up in a state similar to the control group
even when separated by 97 km of free-space.
To measure
this, the researchers at A let photons generated locally – i.e. at A itself –
to interact with the incoming modified photons in a fixed, predictable way.
This changed state is then measured and compared with the state of the photons
at B. Pan & co. found that the states of the modified photons at A and
those of the unmodified photons at B were the same 80% of the time.
What is
wonderful is that the particles didn’t have to end up with the
same state. Eighty per cent is a value large enough to rule out any
coincidence. This long-distance “communication” between minuscule, fragile
particles is proof that their pre-travel entanglement was durable and
resulted in a predictability of state that let the particles behave similarly
in two very different measurement experiments.
The
precise nature of this entanglement, which Albert Einstein called “spooky
action at a distance”, that baffles most scientists. When two groups of photons
are said to be quantum-entangled, it means that the states that the groups are
in are related to each other by means of a variable. If the variable changes,
then the properties of the photons change, too. However, how the groups
themselves are related to each other does not change.
The
existence of this variable is not as much disputed as it is hoped into
existence. We haven’t found it yet – assuming it exists. And because it
remains outside the realm of human control, experiments with teleportation tend
to leave this variable alone and instead focus on how much the measurement
sites can be separated by, how efficiently large molecules can be entangled,
etc. That is, they stick to testing its limits.
To do this,
the photons are subjected to a simplified treatment, one conceived with
the fewest assumptions as well as the fewest sources of error.
Instead of groups of photons, physicists address them two at a time. The state
that each half of this pair can exist is in is defined thus. Let’s say the
two particles are ‘a’ and ‘b’ and the states are ‘0’ and ‘1’. The
four possible combinations of states then are:
{0, 0}
{0, 1}
{1, 0}
{1, 1}
Entanglement
is said to have occurred when b is in a particular state when a
is in a particular state. That is, if b is 1 every time a is 0,
then a and b could be entangled. Since this property is
commutative, a will be 0 every time b is 1 as well. Further, the
change occurs instantaneously irrespective of the distance between the two
particles, giving the impression that they’re “communicating” at a speed faster
than that of light. The presence of such an order, together with the four
possible outcomes, makes each outcome a particular state of the system.
These states are called Bell states, named for the Scottish physicist
John Stuart Bell.
To find out
what the current Bell state of a particle is, a Bell measurement is made.
However, Heisenberg’s uncertainty principle, however, messes this up: the
principles dictates that the act of making the measurement will
change the state of the system. This is how, for example, the principle
prohibits us from knowing an electron’s position and momentum at the same time.
However, this alteration does not matter as long as the pre-measurement state
is observed and recorded. In Pan’s experiment, with six initial possible
states, the Bell measurement was made not by a direct observation per se but by
observing how the local and incoming photons interacted.
Earlier,
another experiment had been conducted that demonstrated the teleportation of
quantum information across 16 km. The principal shortcoming of that experiment
was that the photons to be teleported had been specially generated within the
lab under careful conditions. In practice, this is a highly ideal condition
that could make it difficult to be used as ‘everyday technology’. Pan and
his colleagues had eliminated this necessity in their 97-km experiment by
generating local photons with random states.
Between the
classical and the quantum
The history
of quantum entanglement is as entertaining as teleportation itself is. At its
heart lies a furious debate between two groups of physicists, a clever
paradox and an iconoclastic way out of it.
To ease into
it, consider an experiment. Imagine two devices separated by a large
distance. These are devices that receive inputs and spit out results.
There are two kinds of inputs: classical inputs, which are governed by
classical physics, and quantum-mechanical inputs, defined by the rules of
quantum mechanics. An input is generated by a common source and is
delivered to the devices in an instant.
Now,
a pair of inputs is generated at the source such that each input may
instruct the device to yield a result ‘x’ or ‘y’. The device
called A reads the instructions and yields a result, A*. The device called B
reads the instructions and yields a result, B*. If A* and B* are in the
same state, then they may be said to be entangled. To have achieved this,
A and B – the devices that yielded them – must have communicated in some way
to, if nothing else, come to an ‘agreement’. Alternatively, they could have
been in possession of some information since before the observation
phase.
If it so
happened that A and B communicated instantaneously – i.e., exchanged
information at faster than the speed of light – then they may be said to be
entangled. Let’s remember that, in a quantum mechanical context, the results
are found to be identical only after they are observed. Thus, ‘the
act of observing the result’ also participates in the measurement process.
This is
because Heisenberg’s uncertainty principle kicks in when the particles are
observed. When we make the measurement, we are changing the value of some state
variable of the particle, so it is the final state that we end up
observing. Bell was the first to make this observation and added that the act
of observation was somehow tied in with quantum entanglement. In fact, he
concluded that the results were entangled in some way because
of the act of observing.
Now, the
act of observing is a classical phenomenon because the devices A and B that
enable the measurement are classical devices. That said, Bell argued that this
is where the line between classical mechanics and quantum mechanics blurred. He
wrote in 1971:
Theoretical
physicists live in a classical world, looking out into a quantum-mechanical
world. The latter we describe only subjectively, in terms of procedures and
results in our classical domain. … Now nobody knows just where the boundary
between the classical and the quantum domain is situated. … More plausible to
me is that we will find that there is no boundary. The wave functions would
prove to be a provisional or incomplete description of the quantum-mechanical
part. It is this possibility, of a homogeneous account of the world, which is
for me the chief motivation of the study of the so-called “hidden variable”
possibility.
That we
often call quantum mechanics ‘quirky’ is because it allows
things like entanglement to occur. However, the people who first
noticed that this was possible were also hoping to use it to make the
point that quantum mechanics could not be a true theory of nature. They were
Einstein, Boris Podolsky and Nathan Rosen, commonly referred to as EPR.
The
principal target of their ire was the wave function, a mathematical
function that adherents of quantum mechanics thought could describe the
properties of a quantum mechanical entity, like a particle. For example, by
‘solving’ a wave function, physicists could elicit some of a particle’s
states. While a wave function could ‘encode’ a particle, the particle
itself could not influence its own wave function. Physicists also believed that
each wave function depended on the whole configuration of the universe.
According to EPR, these properties, among others, meant that any interpretation
of quantum mechanics that included the wave function would allow Heisenberg’s
uncertainty principle to be violated.
The EPR
paradox
In 1935, the
trio published a paper describing a paradox – a
phenomenon – that has since been called quantum entanglement. EPR tried to
refute quantum mechanics by showing up the flaws of quantum entanglement
(objects that are entangled share the same wave function). In their paper, they
argued that, since entanglement occurred only on conjugate entities – particles
that are somehow, but surely, paired – then the measurement of one of the
A*-state variables should have rendered the corresponding state variable
in B* indeterminate (because of the uncertainty principle). However,
entanglement has already been observed. This means that either the two
particles should have communicated or that they should have had the information
necessary to generate the same outcome.
EPR preferred
the latter explanation, asserting that some “hidden local variable” was
responsible for controlling the outcome of the ‘act of observing’. They had
made two assumptions to come to this conclusion: locality and realism. The
principle of locality states that an object is affected directly only by its
immediate surroundings, not by an event that is occurring a large distance away
and at the same time. Realism is the ability to assume the existence of objects
and parameters even when they have not been observed. Together, they made for a
classical way to explain a quantum mechanical effect, and so remove one of
the features that made quantum mechanics weird and make it more palatable
to Einstein. After all, it was he who had asserted “god does not play dice with
the universe” in response to quantum mechanics’ whimsy. (E.g., we can’t know
the state of a particle before observing it, so it could be in any state,
including in both
states at once).
In 1964,
Bell proposed a now-famous theorem that
refuted the EPR paradox’s preferred explanation. He observed that any local
realist theories are incompatible with quantum mechanics. Essentially, this
means that since a great number of experiments agree with the predictions of
quantum mechanics, and since many of the results are stronger than to be
explicable by just local hidden variables, either locality or realism is in
conflict with quantum mechanics. Specifically, in his theorem, Bell had
posited that locality had been violated and that faster-than-light communication
was happening.
Bell’s
hypothesis was based on the de Broglie-Bohm theory (initially rejected because
of Bohm’s support for communism), which interpreted quantum mechanical effects
as being caused by the wave function. This, we now understand, immediately
requires that the principle of locality be violated (because a wave function
was influenced by the entire universe). We also see that teleportation (of
quantum information) is an instance of non-locality because it implies instantaneous
communication. If two particles can communicate faster than at the speed of
light to replicate quantum mechanical effects, then perhaps complex
objects can someday be replicated instantaneously across large distances by
simultaneously reproducing the quantum states of the particles associated with
the object.
Of course,
such a possibility is hinged on Bell’s theorem being true and on the EPR
paradox’s implied existence of locality being false. To date, numerous
experiments have been conducted that have neither conclusively validated
nor invalidated Bell’s theorem. Reactions to the theorem itself have
ranged from apathetic to celebratory, with one physicist stating, “Anybody
who’s not bothered by Bell’s theorem has to have rocks in his head.” The
difficulty lies in what it implied for the real world: it made quantum
mechanics and local realism mutually exclusive. Either quantum mechanics
was falling short of explaining some physical parameters or superluminal
information transfer was happening. (Bell told BBC in 1985 that if the latter
is to be disallowed, then we should assume the more-disconcerting notion that
there is no such thing as free-will in the universe.)
If looking
behind the curtain kills some of the fantasy, that is not the case with
teleportation at least. Entanglement continues to elude understanding,
and simplifying something so enigmatic to problems in linear algebra
– as we have seen – is simply not enough to make sense of whatever is allowing
it. With their paper in 2012, Pan and his team were sitting pretty at
the forefront of quantum mechanical teleportation – as they are today in 2017.
Even if we still have a long way go, the knowledge of Pan’s experiments
have given us the best shot at ultimately achieving the teleportation of
more sophisticated information systems. But as Bell and EPR have helped
elucidate, what they have achieved may be awesome but it brings with it an
implication that many of us continue to find difficult to accept.
This article
was originally published on the author’s blog in 2012, and has been reproduced
here with edits.
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