Entanglement is a “quantum correlation” between the properties of particles.Shutterstock, and are often in the news these days. Articles about them inevitably refer to entanglement, a property of quantum physics that makes all these magical devices possible.Einstein called entanglement “,” a name that has stuck and become. Beyond just building better, understanding and harnessing entanglement is also useful in other ways.For example, it can be used to make more accurate measurements of, and to better understand the properties of. It also subtly shows up in other places: I have been studying how atoms bumping into each other become entangled, to understand how this affects the accuracy of atomic clocks.But what is entanglement? Is there some way to understand this “spooky” phenomenon?
I will try to explain it by bringing together two notions from physics: conservation laws and quantum superpositions. Conservation lawsare some of the deepest and most pervasive concepts in all of physics. The law of conservation of energy states that the total amount of energy in an isolated system remains fixed (although it can be converted from electrical energy to mechanical energy to heat, and so on). This law underlies the workings of all of our machines, whether they are steam engines or electric cars. Conservation laws are a kind of accounting statement: you can exchange bits of energy around, but the total amount has to stay the same.(momentum being mass times velocity) is the reason why, when two ice skaters with different masses push off from each other, the lighter one moves away faster than the heavier. This law also underlies the famous dictum that “every action has an equal and opposite reaction.” Conservation of angular momentum is why — going back to ice skaters again — a whirling by drawing her arms closer to her body. France’s Gabriella Papadakis and Guillaume Cizeron demonstrate the effects of conservation laws during the 2019 ISU European Figure Skating Championships in Belarus.
ShutterstockThese conservation laws have been experimentally verified to work across an extraordinary range of scales in the universe, from all the way down to the tiniest. Quantum additionPicture yourself on a nice hike through the woods. You come to a fork in the trail, but you find yourself struggling to decide whether to go left or right.
The path to the left looks dark and gloomy but is reputed to lead to some nice views, while the one to the right looks sunny but steep. You finally decide to go right,. In a quantum world, you could have chosen both.For systems described by quantum mechanics (that is, things that are sufficiently well isolated from heat and external disturbances), the rules are more interesting.
The principle that was supposed to make quantum entanglement impossible is known as local-realism, which conforms to Einsteinian physics by establishing that any signal from any sender to any.
Like a spinning top, an electron for example can be in a state where it spins clockwise, or in another state where it spins anticlockwise. Unlike a spinning top though, it can also be in a state that is clockwise spinning + anticlockwise spinning.The states of quantum systems can be added together and subtracted from each other. Mathematically, the rules for combining quantum states can be described in the same way as the rules for. The word for such a combination of quantum states is a superposition. This is really what is behind strange quantum effects that you may have heard about, such as the double-slit experiment, or particle-wave duality. PBS Studios: The Double-Slit Experiment.Say you decide to force an electron in the clockwise spinning + anticlockwise spinning superposition state to yield a definite answer. Then the electron randomly ends up either in the clockwise spinning state or in the anticlockwise spinning state.
The odds of one outcome versus the other are easy to calculate (with a at hand). The intrinsic randomness of this process may bother you if your worldview requires the universe to behave in a way, but c'est la (experimentally tested) vie. Conservation laws and quantum mechanicsLet’s put these two ideas together now, and apply the law of conservation of energy to a pair of quantum particles.Imagine a pair of quantum particles (say atoms) that start off with a total of 100 units of energy. You and your friend separate the pair, taking one each. You find that yours has 40 units of energy. Using the law of conservation of energy, you deduce that the one your friend has must have 60 units of energy. As soon as you know the energy of your atom, you immediately also know the energy of your friend’s atom.
You would know this even if your friend never revealed any information to you. And you would know this even if your friend was off on the other side of the galaxy at the time you measured the energy of your atom. Nothing spooky about it (once you realize this is just correlation, not causation).But the quantum states of a pair of atoms can be more interesting.
The energy of the pair can be partitioned in many possible ways (consistent with energy conservation, of course). The combined state of the pair of atoms can be in a superposition, for example:your atom: 60 units; friend’s atom: 40 units + your atom: 70 units; friend’s atom: 30 units.This is an entangled state of the two atoms. Neither your atom, nor your friend’s, has a definite energy in this superposition.
Nevertheless, the properties of the two atoms are correlated because of conservation of energy: their energies always add up to 100 units.For example, if you measure your atom and find it in a state with 70 units of energy, you can be certain that your friend’s atom has 30 units of energy. You would know this even if your friend never revealed any information to you. And thanks to energy conservation, you would know this even if your friend was off on the other side of the galaxy.Nothing spooky about it., Assistant Professor of Physics,This article is republished from under a Creative Commons license.
I.Entanglement is often regarded as a uniquely quantum-mechanical phenomenon, but it is not. In fact, it is enlightening, though somewhat unconventional, to consider a simple non-quantum (or “classical”) version of entanglement first. This enables us to pry the subtlety of entanglement itself apart from the general oddity of quantum theory.
QuantizedA in which top researchers explore the process of discovery. This month’s columnist, Frank Wilczek, is a Nobel Prize-winning physicist at the Massachusetts Institute of Technology.Entanglement arises in situations where we have partial knowledge of the state of two systems. For example, our systems can be two objects that we’ll call c-ons. The “c” is meant to suggest “classical,” but if you’d prefer to have something specific and pleasant in mind, you can think of our c-ons as cakes.Our c-ons come in two shapes, square or circular, which we identify as their possible states. Then the four possible joint states, for two c-ons, are (square, square), (square, circle), (circle, square), (circle, circle). The following tables show two examples of what the probabilities could be for finding the system in each of those four states.
We say that the c-ons are “independent” if knowledge of the state of one of them does not give useful information about the state of the other. Our first table has this property. If the first c-on (or cake) is square, we’re still in the dark about the shape of the second. Similarly, the shape of the second does not reveal anything useful about the shape of the first.On the other hand, we say our two c-ons are entangled when information about one improves our knowledge of the other.
Our second table demonstrates extreme entanglement. In that case, whenever the first c-on is circular, we know the second is circular too. And when the first c-on is square, so is the second. Knowing the shape of one, we can infer the shape of the other with certainty.
The quantum version of entanglement is essentially the same phenomenon — that is, lack of independence. In quantum theory, states are described by mathematical objects called wave functions. The rules connecting wave functions to physical probabilities introduce very interesting complications, as we will discuss, but the central concept of entangled knowledge, which we have seen already for classical probabilities, carries over.Cakes don’t count as quantum systems, of course, but entanglement between quantum systems arises naturally — for example, in the aftermath of particle collisions. In practice, unentangled (independent) states are rare exceptions, for whenever systems interact, the interaction creates correlations between them.Consider, for example, molecules. They are composites of subsystems, namely electrons and nuclei. A molecule’s lowest energy state, in which it is most usually found, is a highly entangled state of its electrons and nuclei, for the positions of those constituent particles are by no means independent.
II.Now I will describe two classic — though far from classical! — illustrations of quantum theory’s strangeness. Both have been checked in rigorous experiments. (In the actual experiments, people measure properties like the angular momentum of electrons rather than shapes or colors of cakes.)Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) described a startling effect that can arise when two quantum systems are entangled. The EPR effect marries a specific, experimentally realizable form of quantum entanglement with complementarity.An EPR pair consists of two q-ons, each of which can be measured either for its shape or for its color (but not for both). We assume that we have access to many such pairs, all identical, and that we can choose which measurements to make of their components. If we measure the shape of one member of an EPR pair, we find it is equally likely to be square or circular.
If we measure the color, we find it is equally likely to be red or blue.The interesting effects, which EPR considered paradoxical, arise when we make measurements of both members of the pair. When we measure both members for color, or both members for shape, we find that the results always agree. Thus if we find that one is red, and later measure the color of the other, we will discover that it too is red, and so forth.
On the other hand, if we measure the shape of one, and then the color of the other, there is no correlation. Thus if the first is square, the second is equally likely to be red or to be blue.We will, according to quantum theory, get those results even if great distances separate the two systems, and the measurements are performed nearly simultaneously. The choice of measurement in one location appears to be affecting the state of the system in the other location. This “spooky action at a distance,” as Einstein called it, might seem to require transmission of information — in this case, information about what measurement was performed — at a rate faster than the speed of light.But does it?
Until I know the result you obtained, I don’t know what to expect. I gain useful information when I learn the result you’ve measured, not at the moment you measure it. And any message revealing the result you measured must be transmitted in some concrete physical way, slower (presumably) than the speed of light.Upon deeper reflection, the paradox dissolves further. Indeed, let us consider again the state of the second system, given that the first has been measured to be red.
If we choose to measure the second q-on’s color, we will surely get red. But as we discussed earlier, when introducing complementarity, if we choose to measure a q-on’s shape, when it is in the “red” state, we will have equal probability to find a square or a circle. Thus, far from introducing a paradox, the EPR outcome is logically forced. It is, in essence, simply a repackaging of complementarity.Nor is it paradoxical to find that distant events are correlated. After all, if I put each member of a pair of gloves in boxes, and mail them to opposite sides of the earth, I should not be surprised that by looking inside one box I can determine the handedness of the glove in the other. Similarly, in all known cases the correlations between an EPR pair must be imprinted when its members are close together, though of course they can survive subsequent separation, as though they had memories.
Again, the peculiarity of EPR is not correlation as such, but its possible embodiment in complementary forms. III., and discovered another. It involves three of our q-ons, prepared in a special, entangled state (the GHZ state). We distribute the three q-ons to three distant experimenters.
Each experimenter chooses, independently and at random, whether to measure shape or color, and records the result. The experiment gets repeated many times, always with the three q-ons starting out in the GHZ state.Each experimenter, separately, finds maximally random results. When she measures a q-on’s shape, she is equally likely to find a square or a circle; when she measures its color, red or blue are equally likely.
So far, so mundane.But later, when the experimenters come together and compare their measurements, a bit of analysis reveals a stunning result. Let us call square shapes and red colors “good,” and circular shapes and blue colors “evil.” The experimenters discover that whenever two of them chose to measure shape but the third measured color, they found that exactly 0 or 2 results were “evil” (that is, circular or blue).
But when all three chose to measure color, they found that exactly 1 or 3 measurements were evil. That is what quantum mechanics predicts, and that is what is observed.So: Is the quantity of evil even or odd? Both possibilities are realized, with certainty, in different sorts of measurements. We are forced to reject the question. It makes no sense to speak of the quantity of evil in our system, independent of how it is measured. Indeed, it leads to contradictions.The GHZ effect is, in the physicist Sidney Coleman’s words, “quantum mechanics in your face.” It demolishes a deeply embedded prejudice, rooted in everyday experience, that physical systems have definite properties, independent of whether those properties are measured.
For if they did, then the balance between good and evil would be unaffected by measurement choices. Once internalized, the message of the GHZ effect is unforgettable and mind-expanding. IV.Thus far we have considered how entanglement can make it impossible to assign unique, independent states to several q-ons. Similar considerations apply to the evolution of a single q-on in time.We say we have “entangled histories” when it is impossible to assign a definite state to our system at. Similarly to how we got conventional entanglement by eliminating some possibilities, we can create entangled histories by making measurements that gather partial information about what happened. In the simplest entangled histories, we have just one q-on, which we monitor at two different times.
We can imagine situations where we determine that the shape of our q-on was either square at both times or that it was circular at both times, but that our observations leave both alternatives in play. This is a quantum temporal analogue of the simplest entanglement situations illustrated above.