Quantum Computers and Schrödinger’s Cat

Schrödinger’s Cat

Readers:

Believe it or not, this is not the first blog entry I am making regarding Schrödinger’s cat. I blogged about it first in October 2009 on the blog site I do for my friend’s toy store, Toy Anxiety (http://www.toyanxiety.com).

I have been reading the cover story of the February 17, 2014 issue of Time Magazine. The story is about The Infinity Machine, which promises to solve some of humanity’s most complex problems. Financial backers include Jeff Bezos of Amazon.com, NASA and the CIA.

The infinity machine, called the D-Wave Two, is a quantum computer that is so powerful, people are still figuring out how best to use it. But, it has the power to solve problems that would take conventional computers (referred to in the article as classical computers) centuries to solve. Some of the fields of study that would benefit from this quantum computer are cryptography, nanotechnology, pharmaceuticals to artificial intelligence.

Quantum computing is a marriage of quantum physics and digital computing. At the very basis of understanding quantum physics is the theory of Schrödinger’s cat, a famous thought experiment by Erwin Schrödinger.

I encourage you to read the entire article in Time Magazine. For now, though, I will provide an explanation of Schrödinger’s cat. The great visual above, from HowStuffWorks, helps in understanding this theory.

Best regards,

Michael

Schrödinger’s Cat

Schrödinger’s cat is a thought experiment, often described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The thought experiment presents a cat that might be alive or dead, depending on an earlier random event. In the course of developing this experiment, he coined the term Verschränkung — literally, entanglement.

Origin and motivation

Schrödinger’s thought experiment was intended as a discussion of the EPR article, named after its authors — Einstein, Podolsky, and Rosen — in 1935. The EPR article had highlighted the strange nature of quantum superpositions. Broadly stated, a quantum superposition is the combination of all the possible states of a system (for example, the possible positions of a subatomic particle). The Copenhagen interpretation implies that the superposition undergoes collapse into a definite state only at the exact moment of quantum measurement.

Schrödinger and Einstein had exchanged letters about Einstein’s EPR article, in the course of which Einstein had pointed out that the quantum superposition of an unstable keg of gunpowder will, after a while, contain both exploded and unexploded components.

To further illustrate the putative incompleteness of quantum mechanics, Schrödinger applied quantum mechanics to a living entity that may or may not be conscious. In Schrödinger’s original thought experiment, he describes how one could, in principle, transform a superposition inside an atom to a large-scale superposition of a live and dead cat by coupling cat and atom with the help of a “diabolical mechanism”. He proposed a scenario with a cat in a sealed box, wherein the cat’s life or death was dependent on the state of a subatomic particle. According to Schrödinger, the Copenhagen interpretation implies that the cat remains both alive and dead (to the universe outside the box) until the box is opened.

Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; quite the reverse. The thought experiment serves to illustrate the bizarreness of quantum mechanics and the mathematics necessary to describe quantum states. Intended as a critique of just the Copenhagen interpretation (the prevailing orthodoxy in 1935), the Schrödinger cat thought experiment remains a topical touchstone for all interpretations of quantum mechanics. How each interpretation deals with Schrödinger’s cat is often used as a way of illustrating and comparing each interpretation’s particular features, strengths, and weaknesses.

The thought experiment

Schrödinger wrote:

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small that perhaps in the course of the hour, one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges, and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a “blurred model” for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

The above text is a translation of two paragraphs from a much larger original article that appeared in the German magazine Naturwissenschaften (“Natural Sciences”) in 1935.

Schrödinger’s famous thought experiment poses the question, when does a quantum system stop existing as a mixture of states and become one or the other? (More technically, when does the actual quantum state stop being a linear combination of states, each of which resembles different classical states, and instead begins to have a unique classical description?) If the cat survives, it remembers only being alive. But explanations of the EPR experiments that are consistent with standard microscopic quantum mechanics require that macroscopic objects, such as cats and notebooks, do not always have unique classical descriptions. The purpose of the thought experiment is to illustrate this apparent paradox. Our intuition says that no observer can be in a mixture of states; yet the cat, it seems from the thought experiment, can be such a mixture. Is the cat required to be an observer, or does its existence in a single well-defined classical state require another external observer? Each alternative seemed absurd to Albert Einstein, who was impressed by the ability of the thought experiment to highlight these issues. In a letter to Schrödinger dated 1950, he wrote:

You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality, if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established. Their interpretation is, however, refuted most elegantly by your system of radioactive atom + amplifier + charge of gunpowder + cat in a box, in which the psi-function of the system contains both the cat alive and blown to bits. Nobody really doubts that the presence or absence of the cat is something independent of the act of observation.

Note that no charge of gunpowder is mentioned in Schrödinger’s setup, which uses a Geiger counter as an amplifier and hydrocyanic poison instead of gunpowder. The gunpowder had been mentioned in Einstein’s original suggestion to Schrödinger 15 years before, and apparently Einstein had carried it forward to the present discussion.

Copenhagen interpretation

In the Copenhagen interpretation of quantum mechanics, a system stops being a superposition of states and becomes either one or the other when an observation takes place. This experiment makes apparent the fact that the nature of measurement, or observation, is not well-defined in this interpretation. Some interpret the experiment to mean that while the box is closed, the system simultaneously exists in a superposition of the states “decayed nucleus/dead cat” and “undecayed nucleus/living cat”, and that only when the box is opened and an observation performed does the wave function collapse into one of the two states. More intuitively, some feel that the “observation” is taken when a particle from the nucleus hits the detector. This line of thinking can be developed into objective collapse theories. In contrast, the many worlds approach denies that collapse ever occurs.

Steven Weinberg said:

All this familiar story is true, but it leaves out an irony. Bohr’s version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong; physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wave function (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?

Considerable progress has been made in recent years toward the resolution of the problem, which I cannot go into here. It is enough to say that neither Bohr nor Einstein had focused on the real problem with quantum mechanics. The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wave function, the Schrödinger equation, to observers and their apparatus.

Everett’s many-worlds interpretation & consistent histories

In 1957, Hugh Everett formulated the many-worlds interpretation of quantum mechanics, which does not single out observation as a special process. In the many-worlds interpretation, both alive and dead states of the cat persist, but are decoherent from each other. In other words, when the box is opened, that part of the universe containing the observer and cat is split into two separate universes: one containing an observer looking at a box with a dead cat, and one containing an observer looking at a box with a live cat.

Since the dead and alive states are decoherent, there is no effective communication or interaction between them. When an observer opens the box, he becomes entangled with the cat, so “observer states” corresponding to the cat’s being alive and dead are formed, and each can have no interaction with the other. The same mechanism of quantum decoherence is also important for the interpretation in terms of consistent histories. Only the “dead cat” or “alive cat” can be a part of a consistent history in this interpretation.

Roger Penrose criticises this:

“I wish to make it clear that, as it stands, this is far from a resolution of the cat paradox. For there is nothing in the formalism of quantum mechanics that demands that a state of consciousness cannot involve the simultaneous perception of a live and a dead cat”,

although the mainstream view (without necessarily endorsing many-worlds) is that decoherence is the mechanism that forbids such simultaneous perception.

A variant of the Schrödinger’s Cat experiment, known as the quantum suicide machine, has been proposed by cosmologist Max Tegmark. It examines the Schrödinger’s Cat experiment from the point of view of the cat, and argues that by using this approach, one may be able to distinguish between the Copenhagen interpretation and many-worlds.

Ensemble interpretation

The ensemble interpretation states that superpositions are nothing but subensembles of a larger statistical ensemble. That being the case, the state vector would not apply to individual cat experiments, but only to the statistics of many similarly prepared cat experiments. Proponents of this interpretation state that this makes the Schrödinger’s Cat paradox a trivial nonissue.

This interpretation serves to discard the idea that a single physical system in quantum mechanics has a mathematical description that corresponds to it in any way; the problem should be renamed Schrödinger’s cats.

Objective collapse theories

According to objective collapse theories, superpositions are destroyed spontaneously (irrespective of external observation) when some objective physical threshold (of time, mass, temperature, irreversibility, etc.) is reached. Thus, the cat would be expected to have settled into a definite state long before the box is opened. This could loosely be phrased as “the cat observes itself”, or “the environment observes the cat”.

Objective collapse theories require a modification of standard quantum mechanics to allow superpositions to be destroyed by the process of time evolution.

Practical applications

The experiment is a purely theoretical one, and the machine proposed is not known to have been constructed. Analogous effects, however, have some practical use in quantum computing and quantum cryptography. It is possible to send light that is in a superposition of states down a fiber optic cable. Placing a wiretap in the middle of the cable that intercepts and retransmits the transmission will collapse the wave function (in the Copenhagen interpretation, “perform an observation”) and cause the light to fall into one state or another. By performing statistical tests on the light received at the other end of the cable, one can tell whether it remains in the superposition of states or has already been observed and retransmitted. In principle, this allows the development of communication systems that cannot be tapped without the tap being noticed at the other end. This experiment can be argued to illustrate that “observation” in the Copenhagen interpretation has nothing to do with consciousness (unless some version of panpsychism is true), in that a perfectly unconscious wiretap will cause the statistics at the end of the wire to be different. Such a test would only work if the collapse occurs after (as opposed to before) observation; otherwise, it would appear collapsed whether it had been wiretapped or not.

In quantum computing, the phrase “cat state” often refers to the special entanglement of qubits wherein the qubits are in an equal superposition of all being 0 and all being 1;

i.e., |00...0\rangle + |11...1\rangle.

Extensions

Although discussion of this thought experiment talks about two possible states (cat alive and cat dead), in reality, there would be a huge number of possible states, since the temperature and degree and state of decomposition of the cat would depend on exactly when and how (as well as if) the mechanism was triggered, as well as the state of the cat prior to death.

In another extension, prominent physicists have gone so far as to suggest that astronomers observing dark matter in the universe in 1998 may have “reduced its life expectancy” through a pseudo-Schrödinger’s Cat scenario, although this is a controversial viewpoint.

Another variant on the experiment is Wigner’s friend, in which there are two external observers, the first of whom opens and inspects the box and then communicates his observations to a second observer. The issue here is, does the wave function collapse when the first observer opens the box, or only when the second observer is informed of the first observer’s observations? Another extension is a scenario wherein the inside of the box is videotaped and played to an audience at a later time, or played back to the cat while in the box. If dead, there would be no observer to cause disentanglement; if alive, disentanglement would occur.

—————————————————————————-

Sources:

[1] Wikipedia, Schrödinger’s cat.

[2] Lev Grossman, Quantum Leap, Time Magazine, February 17, 2014.

[3] Image, Schrödinger’s cat, HowStuffWorks, 2007.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s