# Decoherence and entanglement vs relationship

### The Role of Decoherence in Quantum Mechanics (Stanford Encyclopedia of Philosophy)

Nobody understands what consciousness is or how it works. Decoherence is expected to be extremely rapid in warm and wet might be placed in a special kind of superposition called an "entangled state". . Every line of thought on the relationship of consciousness to physics runs into deep trouble. The difference between superposition and entanglement. states, or in quantum theory terms, as a statistical mixture of pure states. . But now we can also see an interesting relation between entanglement and coherence. That of the second (the theory of 'decoherent histories' or 'consistent Section 3 then reviews the relation of decoherence to some of the main is because the electron has become entangled with the stray particles.

In the case of continuous models of decoherence based on the analogy of approximate joint measurements of position and momentum, one can do even better. In this case, the trajectories at the level of the components the trajectories of the preferred states will approximate surprisingly well the corresponding classical Newtonian trajectories.

As a matter of fact, one should expect slight deviations from Newtonian behaviour. These are due both to the tendency of the individual components to spread and to the detection-like nature of the interaction with the environment, which further enhances the collective spreading of the components a narrowing in position corresponds to a widening in momentum.

These deviations appear as noise, i. Other examples include trajectories of a harmonic oscillator in equilibrium with a thermal bath, and trajectories of particles in a gas without which the classical derivation of thermodynamics from statistical mechanics would make no sense; see below Section 4.

None of these features are claimed to obtain in all cases of interaction with some environment. It is a matter of detailed physical investigation to assess which systems exhibit which features, and how general the lessons are that we might learn from studying specific models. In particular, one should beware of common overgeneralisations.

True, middle-sized objects, say, on the Earth's surface will be very effectively decohered by the air in the atmosphere, and this is an excellent example of decoherence at work. On the other hand, there are also very good examples of decoherence-like interactions affecting microscopic systems, such as in the interaction of alpha particles with the gas in a bubble chamber. And further, there are arguably macroscopic systems for which interference effects are not suppressed.

For instance, it has been shown to be possible to sufficiently shield SQUIDS a type of superconducting devices from decoherence for the purpose of observing superpositions of different macroscopic currents—contrary to what one had expected see e.

Leggettand esp. Anglin, Paz and Zurek examine some less well-behaved models of decoherence and provide a useful corrective as to the limits of decoherence. In particular, we can assign probabilities to the alternative trajectories, so that probabilities for detection at the screen can be calculated by summing over intermediate events.

In a nutshell, the formalism is as follows. Such histories form a so-called alternative and exhaustive set of histories. We wish to define probabilities for the set of histories. But we can impose, as a consistency or weak decoherence condition, precisely that interference terms should vanish for any pair of distinct histories. If this is satisfied, we can view 2 as defining the distribution functions for a stochastic process with the histories as trajectories.

There are some differences between the various authors, but we shall gloss them over. Decoherence in the sense of this abstract formalism is thus defined simply by the condition that quantum probabilities for wave components at a later time may be calculated from quantum probabilities for wave components at an earlier time and quantum conditional probabilities according to the standard classical formula, i.

Models of dynamical decoherence fall under the scope of decoherence thus defined, but the abstract definition is much more general.

As such, it is particularly useful as a tool for describing decoherence in connection with attempts to solve the problem of the classical regime in the context of various different interpretational approaches to quantum mechanics.

The fact that interference is typically very well suppressed between localised states of macroscopic objects suggests that it is relevant to why macroscopic objects in fact appear to us to be in localised states.

A stronger claim is that decoherence is not only relevant to this question but by itself already provides the complete answer. In the special case of measuring apparatuses, it would explain why we never observe an apparatus pointing, say, to two different results, i.

As pointed out by many authors, however e. Adler ; Zehpp. The measurement problem, in a nutshell, runs as follows. Quantum mechanical systems are described by wave-like mathematical objects vectors of which sums superpositions can be formed see the entry on quantum mechanics. The problem is that, while we may accept the idea of microscopic systems being described by such sums, the meaning of such a sum for the composite of electron and apparatus is not immediately obvious.

Now, what happens if we include decoherence in the description? Decoherence tells us, among other things, that plenty of interactions are taking place all the time in which differently localised states of macroscopic systems couple to different states of their environment.

In particular, the differently localised states of the macroscopic system could be the states of the pointer of the apparatus registering the different x-spin values of the electron. Again, the meaning of such a sum for the composite system is not obvious. We are left with the following choice whether or not we include decoherence: Thus, decoherence as such does not provide a solution to the measurement problem, at least not unless it is combined with an appropriate interpretation of the theory whether this be one that attempts to solve the measurement problem, such as Bohm, Everett or GRW; or one that attempts to dissolve it, such as various versions of the Copenhagen interpretation.

Some of the main workers in the field such as Zeh and perhaps Zurek suggest that decoherence is most naturally understood in terms of Everett-like interpretations see below Section 3. Pearle and philosophers e. As such it has much to offer to the philosophy of quantum mechanics. At first, however, it seems that discussion of environmental interactions should actually exacerbate the existing problems. Intuitively, if the environment is carrying out, without our intervention, lots of approximate position measurements, then the measurement problem ought to apply more widely, also to these spontaneously occurring measurements.

Although the different components that couple to the environment will be individually incredibly localised, collectively they can have a spread that is many orders of magnitude larger. That is, the state of the object and the environment could be a superposition of zillions of very well localised terms, each with slightly different positions, and that are collectively spread over a macroscopic distance, even in the case of everyday objects.

To put it crudely: And indeed, discussing the measurement problem without taking decoherence fully into account may not be enough, as we shall illustrate by the case of some versions of the modal interpretation in Section 3. The question is then whether, if viewed in the context of any of the main foundational approaches to quantum mechanics, these classical aspects can be taken to explain corresponding classical aspects of the phenomena.

The answer, perhaps unsurprisingly, turns out to depend on the chosen approach, and in the next section we shall discuss in turn the relation between decoherence and several of the main approaches to the foundations of quantum mechanics. Even more generally, one can ask whether the results of decoherence could thus be used to explain the emergence of the entire classicality of the everyday world, i.

## The Role of Decoherence in Quantum Mechanics

As we have mentioned already, there are cases in which a classical description is not a good description of a phenomenon, even if the phenomenon involves macroscopic systems. There are also cases, notably quantum measurements, in which the classical aspects of the everyday world are only kinematical definiteness of pointer readingswhile the dynamics is highly non-classical indeterministic response of the apparatus.

The question of explaining the classicality of the everyday world becomes the question of whether one can derive from within quantum mechanics the conditions necessary to discover and practise quantum mechanics itself, and thus, in Shimony's words, close the epistemological circle. In this generality the question is clearly too hard to answer, depending as it does on how far the physical programme of decoherence Zehp.

We shall thus postpone the partly speculative discussion of how far this programme might go until Section 4. Decoherence and Approaches to Quantum Mechanics There is a wide range of approaches to the foundations of quantum mechanics.

A convenient way of classifying these approaches is in terms of their strategies for dealing with the measurement problem. Such approaches may have intuitively little to do with decoherence since they seek to suppress precisely those superpositions that are created by decoherence. Nevertheless their relation to decoherence is interesting.

Among collapse approaches Section 3. Of these, the most developed are the so-called pilot-wave theories Section 3.

Finally, there are approaches that seek to solve or dissolve the measurement problem strictly by providing an appropriate interpretation of the theory. Slightly tongue in cheek, one can group together under this heading approaches as diverse as Everett interpretations see the entries on Everett's relative-state interpretation and on the many-worlds interpretationmodal interpretations and the Copenhagen interpretation.

We shall be analysing these approaches specifically in their relation to decoherence we discuss the Everett interpretation in Section 3. There is some ambiguity in how to interpret von Neumann.

### quantum mechanics - Entanglement and coherence - Physics Stack Exchange

He may have been advocating some sort of special access to our own consciousness that makes it appear to us that the wave function has collapsed; this would suggest a phenomenological reading of Process I. Alternatively, he may have proposed that consciousness plays some causal role in precipitating the collapse; this would suggest that Process I is a physical process taking place in the world on a par with Process II.

This is often referred to as the movability of the von Neumann cut between the subject and the object, or some similar phrase. Collapse could occur anywhere along the so-called von Neumann chain: Von Neumann thus needs to show that all of these models are equivalent, as far as the final predictions are concerned, so that he can indeed maintain that collapse is related to consciousness, while in practice applying the projection postulate at a much earlier and more practical stage in the description.

Von Neumann poses this problem in Section VI. Then in Section VI. Converting one to the other In a paper to be published in Physical Review Letters, physicists led by Gerardo Adesso, Associate Professor at the University of Nottingham in the UK, with coauthors from Spain and India, have provided a simple yet powerful answer to the question of how these two resources are related: The physicists arrived at this result by showing that, in general, any nonzero amount of coherence in a system can be converted into an equal amount of entanglement between that system and another initially incoherent one.

This discovery of the conversion between coherence and entanglement has several important implications. For one, it means that quantum coherence can be measured through entanglement. Consequently, all of the comprehensive knowledge that researchers have obtained about entanglement can now be directly applied to coherence, which in general is not nearly as well-researched outside of the area of quantum optics.

For example, the new knowledge has already allowed the physicists to settle an important open question concerning the geometric measure of coherence: As the scientists explained, this is possible because the new results allowed them to define and quantify one resource in terms of the other.

This concept allowed us to prove that the geometric measure of coherence is a valid coherence quantifier, thus answering a question left open in several previous works. Also, coherence is defined with respect to a given basis, while entanglement is invariant under local basis changes. When this "observer effect" was first noticed by the early pioneers of quantum theory, they were deeply troubled.

It seemed to undermine the basic assumption behind all science: If the way the world behaves depends on how — or if — we look at it, what can "reality" really mean?

The most famous intrusion of the mind into quantum mechanics comes in the "double-slit experiment" Some of those researchers felt forced to conclude that objectivity was an illusion, and that consciousness has to be allowed an active role in quantum theory.

To others, that did not make sense. Surely, Albert Einstein once complained, the Moon does not exist only when we look at it! Today some physicists suspect that, whether or not consciousness influences quantum mechanics, it might in fact arise because of it. They think that quantum theory might be needed to fully understand how the brain works. Might it be that, just as quantum objects can apparently be in two places at once, so a quantum brain can hold onto two mutually-exclusive ideas at the same time?

These ideas are speculative, and it may turn out that quantum physics has no fundamental role either for or in the workings of the mind. But if nothing else, these possibilities show just how strangely quantum theory forces us to think. View image of The famous double-slit experiment Credit: Imagine shining a beam of light at a screen that contains two closely-spaced parallel slits.

Some of the light passes through the slits, whereupon it strikes another screen. Light can be thought of as a kind of wave, and when waves emerge from two slits like this they can interfere with each other.

If their peaks coincide, they reinforce each other, whereas if a peak and a trough coincide, they cancel out. This wave interference is called diffraction, and it produces a series of alternating bright and dark stripes on the back screen, where the light waves are either reinforced or cancelled out. The implication seems to be that each particle passes simultaneously through both slits This experiment was understood to be a characteristic of wave behaviour over years ago, well before quantum theory existed.

The double slit experiment can also be performed with quantum particles like electrons; tiny charged particles that are components of atoms.

In a counter-intuitive twist, these particles can behave like waves. That means they can undergo diffraction when a stream of them passes through the two slits, producing an interference pattern. Now suppose that the quantum particles are sent through the slits one by one, and their arrival at the screen is likewise seen one by one. Now there is apparently nothing for each particle to interfere with along its route — yet nevertheless the pattern of particle impacts that builds up over time reveals interference bands.

The implication seems to be that each particle passes simultaneously through both slits and interferes with itself. This combination of "both paths at once" is known as a superposition state. But here is the really odd thing. View image of The double-slit experiment Credit: In that case, however, the interference vanishes.

Simply by observing a particle's path — even if that observation should not disturb the particle's motion — we change the outcome. The physicist Pascual Jordan, who worked with quantum guru Niels Bohr in Copenhagen in the s, put it like this: And it gets even stranger. View image of Particles can be in two states Credit: To do so, we could measure which path a particle took through the double slits, but only after it has passed through them.

By then, it ought to have "decided" whether to take one path or both. The sheer act of noticing, rather than any physical disturbance caused by measuring, can cause the collapse An experiment for doing this was proposed in the s by the American physicist John Wheeler, and this "delayed choice" experiment was performed in the following decade. It uses clever techniques to make measurements on the paths of quantum particles generally, particles of light, called photons after they should have chosen whether to take one path or a superposition of two.

It turns out that, just as Bohr confidently predicted, it makes no difference whether we delay the measurement or not. As long as we measure the photon's path before its arrival at a detector is finally registered, we lose all interference.

It is as if nature "knows" not just if we are looking, but if we are planning to look. View image of Credit: What's more, the delayed-choice experiment implies that the sheer act of noticing, rather than any physical disturbance caused by measuring, can cause the collapse. But does this mean that true collapse has only happened when the result of a measurement impinges on our consciousness? It is hard to avoid the implication that consciousness and quantum mechanics are somehow linked That possibility was admitted in the s by the Hungarian physicist Eugene Wigner.

In this sense, Wheeler said, we become participants in the evolution of the Universe since its very beginning. In his words, we live in a "participatory universe. But one way or another, it is hard to avoid the implication that consciousness and quantum mechanics are somehow linked. Beginning in the s, the British physicist Roger Penrose suggested that the link might work in the other direction.

Whether or not consciousness can affect quantum mechanics, he said, perhaps quantum mechanics is involved in consciousness. View image of Physicist and mathematician Roger Penrose Credit: Could not these structures then adopt a superposition state, just like the particles in the double slit experiment?