Physicists find quantum coherence and quantum entanglement are two sides of the same coin

June 25, 2015 by Lisa Zyga, report

(a) Input states that are fully incoherent (S and A) cannot be converted to entanglement via incoherent operations. (b) On the other hand, when the input state of S has any nonzero coherence, the coherence can be converted to entanglement via incoherent operations. The new results show that, in such a scenario, the input coherence and the output entanglement are quantitatively equivalent. Credit: Streltsov, et al.
(—Quantum coherence and quantum entanglement are two landmark features of quantum physics, and now physicists have demonstrated that the two phenomena are "operationally equivalent"—that is, equivalent for all practical purposes, though still conceptually distinct. This finding allows physicists to apply decades of research on entanglement to the more fundamental but less-well-researched concept of coherence, offering the possibility of advancing a wide range of quantum technologies.

Close relatives with the same roots

Although physicists have known that coherence and are close relatives, the exact relationship between the two resources has not been clear.

It's well-known that and are both rooted in the superposition principle—the phenomenon in which a single quantum state simultaneously consists of multiple states—but in different ways. Quantum coherence deals with the idea that all objects have wave-like properties. If an object's wave-like nature is split in two, then the two waves may coherently interfere with each other in such a way as to form a single state that is a superposition of the two states. This concept of superposition is famously represented by Schrödinger's cat, which is both dead and alive at the same time when in its coherent state inside a closed box. Coherence also lies at the heart of quantum computing, in which a qubit is in a superposition of the "0" and "1" states, resulting in a speed-up over various classical algorithms. When such a state experiences decoherence, however, all of its quantumness is typically lost and the advantage vanishes.

The second phenomenon, quantum entanglement, also involves superposition. But in this case, the states in a superposition are the shared states of two entangled particles rather than those of the two split waves of a single particle. The intrigue of entanglement lies in the fact that the two entangled particles are so intimately correlated that a measurement on one particle instantly affects the other particle, even when separated by a large distance. Like coherence, quantum entanglement also plays an essential role in , such as quantum teleportation, quantum cryptography, and super dense coding.

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 scientists show that coherence and entanglement are quantitatively, or operationally, equivalent, based on their behavior arising from their respective resource theories.

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: since the geometric measure of entanglement is a "full convex monotone," the same can be said of the associated coherence measure. As the scientists explained, this is possible because the new results allowed them to define and quantify one resource in terms of the other.

"The significance of our work lies in the fact that we prove the close relation between entanglement and coherence not only qualitatively, but on a quantitative level," coauthor Alex Streltsov, of ICFO-The Institute of Photonic Sciences in Barcelona, told "More precisely, we show that any quantifier of entanglement gives rise to a quantifier of coherence. 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."

While the results show that coherence and entanglement are operationally equivalent, the physicists explain that this doesn't mean that are the exact same thing, as they are still conceptually different ideas.

"Despite having the same roots of origin, namely , coherence and entanglement are conceptually different," said coauthors Uttam Singh, Himadri Dhar, and Manabendra Bera at the Harish-Chandra Research Institute in Allahabad, India. "For example, coherence can be present in single quantum systems, where entanglement is not well-defined. Also, coherence is defined with respect to a given basis, while entanglement is invariant under local basis changes. In all, we believe coherence and entanglement are operationally equivalent but conceptually different."

Future quantum connections

The operational equivalence of coherence and entanglement will likely have a far-reaching impact on areas ranging from quantum information theory to more nascent fields such as quantum biology and nanoscale thermodynamics. In the future, the plan to investigate whether coherence and entanglement might also be interconverted into a third resource—that of quantum discord, which, like entanglement, is another type of quantum correlation between two systems.

"Our future plans are diverse," Adesso said. "On the theoretical side, we are working to construct a unified framework to interpret, classify and quantify all different forms of quantum resources, including and beyond entanglement and coherence, and highlight the interlinks among them from an operational perspective. This will allow us to navigate the hierarchy of quantumness indicators in composite systems with a common pilot, and to appreciate which particular ingredients are needed in various informational tasks.

"On the practical side, we are investigating experimentally friendly schemes to detect, quantify, and preserve , entanglement and other quantum correlations in noisy environments. More fundamentally, we hope these results will inspire us to devise scalable and efficient methods to convert between different quantum resources for technological applications, and bring us closer to understanding where the boundaries of the quantum world ultimately lie in realistic scenarios."

Explore further: Physicists show 'quantum freezing phenomenon' is universal

More information: Alexander Streltsov, et al. "Measuring Quantum Coherence with Entanglement." Physical Review Letters. To be published.
Also at arXiv:1502.05876 [quant-ph]

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not rated yet Jun 25, 2015
So all this time i did not truly understand quantum coherence... okay. Interesting.... this doesn't do much to advance QC's though. Coherence is still an issue.
not rated yet Jun 25, 2015
What they say that QE and QC are different concepts but impossible to experimentally distinguish since operationally they are equivalent it means that they produce identical or similar observables. It might be true but this post span interpretation of this beyond the appropriate scope.

An interesting take on misinterpretations of QM phenomena put forward in popular media I found at:

not rated yet Jun 25, 2015
No problem with the math, but the physics alludes me. If particles and waves have the same properties, walking through walls would be a cinch. Waves are always associated with particles and waves infer relative particle motion, two different things. But you can test your idea with oppositely charged particles. When they collide, to they travel through each other or do they recoil? Two different field responses based upon the line of collision. So, mathematically, surely it allows +/.-, i.e. reflections, so how do you separate the two? So maybe it's the quanta of energy definition through Planks Constant, quanta, not a plus or minus charge. So quanta as ... Or rather a well defined point in space-time?
5 / 5 (2) Jun 25, 2015
You are not a single particle. You are a vast ensemble of quantum particles all interacting with each other. Thus the wavepackets are so tightly constrained that walking through walls on a macroscopic scale is pretty much impossible. Just like you also won't diffract into two copies of yourself when you walk through a door.

The rest of your questions are pretty much covered by a solid course in Quantum Mechanics or Quantum Field Theory for the more advanced approach. We can calculate (or at least approximate) the results of particle collisions to a pretty solid degree of accuracy through those methods.
5 / 5 (1) Jun 25, 2015
Hmmm ... I thought this was already "known" ... it is certainly very close to the way we talk about loss of coherence in the density matrix formulation of Q.M. ... perhaps there was a mathematical theorem that hadn't been proven yet?
not rated yet Jun 25, 2015
So I define a particle, electron, or proton, only as a + or - point within a 4D space. The field at each point is deterministic, not a mathematical query using QM. Using this space each event is determined at each point and described by the relative E&H fields, only. Simply a calculation using a properly defined space. Within a controlled environment the field is totally defined.

Definition: Coherence among particles, polarity of particle, polarity of light, spin, and among wavelets? Choose the range of coherence in time and space or control it! Is the use of quanta really necessary in the 21st century with massive computers.

juz sa'n
not rated yet Jun 25, 2015
Thought we threw the slide rules away long ago; else, they are in a museum.
not rated yet Jun 25, 2015
So yeah, not about playing with matter for the light show; today, we use data, both calculable and measurable and inferred from measurement and so on, using a well defined physics as our measure. You may name the measurement anything you wish, but its simply the field and + and - particles, nothing else! What are your tools?
not rated yet Jun 25, 2015
Can we define that the near field is laminar then ... but near a particle, the force ( better E field magnitude) is a measure of the inverse surface area of the sphere defined with the radius defined as the distance between the two particles. How about the absolute value of R as a four dimensional vector as the radius? I haven't worked that out, i.e. really! What are the possibilities? So, if space is the field then ...
5 / 5 (3) Jun 25, 2015
Rufus... you're using words that I suspect mean something different to you than they do to scientists who study the subject. The thing you're talking about as "a point in 4D space..." that's field theory, in a way. Except that in addition to the EM field, there's an "electron field" that has various electrons in it like the EM field has photons in it. And those two fields interact with each other. And then there are quark fields, and gluon fields, and so on and so on.

And to a degree, those calculations are "deterministic" as you might say.... but the maths to solve them are TREMENDOUSLY difficult. Like insane levels of difficulty. Not something you can just pop into a computer and have it pop out an answer.

Why? Because the fields evolve over *every conceivable* possibility. An electron may travel in a straight line. Or it may emit and then reabsorb a photon. Or it may split into a photon pair and recombine to an electron. And so much more. And you have to add all that up.
not rated yet Jun 25, 2015
How about time travel, within a container of control, any particle moving backward in time would appear as an antiparticle, but the motion from event one to event two would appear causal. So time travel and observe-ability has not been reconciled, for locations, and times within our reference frame. But yes, we could build an object that travels ahead of us and a propulsion system such that our bodies see Fp - Fo, propulsion - gravity pull. The gravity pull object would be immune to the g forces and provide a tractor beam, i.e. +/-E field simulating a gigantic mass, best to maintain G by orbiting. But I think this only goes from A to B with allowed acceleration of the host, minimum time t. To travel to a time before but maintain position, then we do not move. So we would have to reconfigure the entire field. Einstein allows this! In other words, every point in space time is singular but not fixed until the event. As an intelligent group of + & -, we can create
5 / 5 (3) Jun 25, 2015
Well, again, you're using words in different ways than they mean to the scientists who use them, to some degree...

So let me clarify my previous point. See, even all the various "particle paths" stuff... that's still a lie. The real reality is that QFT has a very very complicated integral at its heart. And if you break it into pieces you get mathematical pieces that are very similar to the mathematics of moving particles. So we create a cute story about all these particle paths. But that's just a neat way to represent very complex mathematics.

that's what is meant by antiparticles "travelling back in time." They don't *actually* travel back in time... there's just a piece of the mathematical puzzle that looks similar to how a particle travelling back in time would.

So I'd say that, realistically, it's fun to have fun ideas.... but you really need to learn what we already "know" about things before being able to really advance it a step further.
not rated yet Jun 26, 2015
The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the Wave-Particle Duality and the electron's spin also, building the Bridge between the Classical and Quantum Theories. The Planck Distribution Law of the electromagnetic oscillators explains the electron/proton mass rate and the Weak and Strong Interactions by the diffraction patterns. The Weak Interaction changes the diffraction patterns by moving the electric charge from one side to the other side of the diffraction pattern, which violates the CP and Time reversal symmetry. The diffraction patterns and the locality of the self-maintaining electromagnetic potential explains also the Quantum Entanglement, giving it as a natural part of the relativistic quantum theory.
not rated yet Jun 26, 2015
The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the Wave-Particle Duality and the electron's spin also, building the Bridge between the Classical and Quantum Theories. The Planck Distribution Law of the electromagnetic oscillators explains the electron/proton mass rate and the Weak and Strong Interactions by the diffraction patterns. The Weak Interaction changes the diffraction patterns by moving the electric charge from one side to the other side of the diffraction pattern, which violates the CP and Time reversal symmetry. The diffraction patterns and the locality of the self-maintaining electromagnetic potential explains also the Quantum Entanglement, giving it as a natural part of the relativistic quantum theory.
not rated yet Jun 26, 2015
not rated yet Jun 26, 2015
Such collapse of superposition by gravity and heat was previously presented by RBL in Dec 2005 via sciprint and later published in vixRa in Dec 2012 and later published in IJPS in Jan 2015: "A Theory of the Relativistic Fermionic Spinrevorbital" Seehttp://www.academ...B049585. click 'Full Text PDF' for full manuscript. Therein I thoroughly discover, define (page 1), describe, govern (page 1-2) and predict discontinuum submicroscopic states (as governed by Little Rule 2) of quantum mechanics and intervening continuum submicroscopic states (as govern by Little Rule 3) of a hidden nature and how gravity and heat can disrupt discontinuum states to form continuum states to manifest gravity.
not rated yet Jun 28, 2015
Well, when we grow up, our kids will think it's child's play at pre-K. It's just block assembly based upon stability. You may place any block into a field and define it's stability or in-stability and disruption to the field and atomic structure, from +,-, to molecules and galaxies! probably will be a holographic learning tool into a language the kids can understand. By the time they finish High School, they will have a BS filter built-in and through away all this BS!

GR, BB, SM will be lectures in false logic!

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