Quantum entanglement
Quantum entanglement (rarely quantum correlation) is a physical phenomenon in the field of quantum mechanics. Two or more particles can enter into a non-local connection with each other, which is called entanglement. Measurements of certain observables entangled particles are correlated. That is, we measure a quantum property of particles in A (eg, spin), the correlated to property (eg, negative spin) can be found without delay even with particles B. Between the measurable properties ( observables ) of the systems seem to insist, therefore, relationships that have not been adopted in classical physics and in classical natural philosophical views; related interpretation controversies concerning, inter alia, the so-called Einstein - Podolsky-Rosen paradox. The entangled particles can therefore not be described as single particles with defined states, but only the overall system as such. However, the dependencies between the individual occurring in a measurement states of the individual particles can specify.
Overview
Due to the possibility of quantum entanglement, the general state of a composite system in general not determined by the states of its subsystems, ie, it does not separate into substates. An entangled state can not be produced by preparation of all individual systems in each case appropriate conditions. The entanglement is a consequence of the superposition. In contrast to the classical addition of intensities as in optics and electrodynamics in quantum mechanics (similar to the coherence in classical optics ) amplitudes and phases superimposed ( superposition of wave crests and troughs → interference ), with additional ( multiplicative ) admixtures nichtkommutierender ( not commuting ) states ( complex wave functions or vectors in Hilbert space ) lead to further complications. For spatially separated subsystems quantum entanglement is quantum non-locality, ie, the state of the entangled system is not localized, but extends over the whole system spatially distributed. Originally only supposed to be relevant for microscopic systems, quantum entanglement has been demonstrated directly in recent times over macroscopic distances and for mesoscopic systems.
Due to the Born's probability interpretation of quantum theory, the Entanglement has long been misunderstood and therefore less " trivialized " as a purely statistical correlation, even by Erwin Schrödinger, who coined the term. Entangled states describe individual characteristics such as the total angular momentum of a system of two or more particles. The scope of the term has seemingly only Albert Einstein recognized in 1935 in the work associated with the EPR effect, although he misinterpreted the true meaning ( see below). The importance of entanglement has only been confirmed by the fact that John Stewart Bell in 1964 found that quantum mechanics violates the requirement imposed by him famous Bell's inequality. This is excluded an unknown, described by hidden variables local reality as opposed to the basic assumptions of Einstein.
Therefore, the quantum non-locality is also no need ( in Einstein's words ) "spooky action at a distance "; Nor need the so-called quantum teleportation of Transportation of anything. This means that the phenomenon of entanglement is not based on so-called hidden variables that we just not (yet) able to discover.
The fact that the entanglement (as opposed to classical physics ) does not allow locally - realist interpretation, it means that either the locality must be abandoned ( for example, if one accorded the nonlocal wave function itself a real character - this happens especially in collapse theories in the many-worlds interpretation, or the de Broglie -Bohm theory ) or the concept of a microscopic reality - or both; the most radical departure this is represented by the classical realism in the Copenhagen interpretation; according to this interpretation, which is regarded by physicists for decades as the standard quantum mechanics is not real - as a measurement the state does not determine, but prepared - even locally - because the state vector, the probability amplitudes determines simultaneously at all points, for example.
History
The possibility of entanglement is probably one of those consequences of quantum mechanics that generated the most resistance to this theory as such. Albert Einstein, Boris Podolsky and Nathan Rosen formulated the EPR effect in 1935, according to the quantum entanglement injury to the classical principle of local realism would lead what was described by Einstein in a famous quote "spooky action at a distance ".
On the other hand, the predictions of quantum mechanics could be assigned highly successful experimentally, even Einstein's "spooky action at a distance " was observed. Many scientists felt that this was in error (see below) to unknown, deterministic "hidden variables", which are subject to local realism, but at the same time could explain all quantum phenomena.
1964 showed John Stewart Bell, that the effects of quantum entanglement can be experimentally distinguished from the results of based on hidden variables theories (see Bell's inequality). His results were confirmed by additional experiments, so that the quantum entanglement is now widely recognized as a physical phenomenon. He illustrated entanglement and EPR effect based on the comparison with Bertlmann socks.
According to Bohm is still an - not local - realistic interpretation with hidden variables (see De Broglie -Bohm theory). The Nobel Prize winner Anthony James Leggett could exacerbate the Bell's inequality for this case, and a research group led by Anton Zeilinger claimed in a publication in the journal Nature, to have an injury also shown the tighter inequality. This would show that even with a non-local mechanics a "realistic " interpretation of quantum mechanics is excluded. However, it is necessary to wait until this is confirmed by other scientists in this case.
Meanwhile, a group of the University of Geneva has an extremely high " lower limit " set by Nicolas Gisin of the speed of "spooky action at a distance ": The group was able to show experimentally that two entangled photons in various properties, including the polarization, with at least 10,000 times the speed of light to communicate.
Information transfer
If not literally, then the entanglement obeys but the spirit of the theory of relativity. Although two entangled systems can also interact across large spatial distance to each other, but it can not transmit information so that causality is not violated. There are two reasons for this:
- Quantum mechanical measurements are probabilistic, that is not strictly causal.
- The no -cloning theorem forbids the statistical verification of entangled quantum states.
Although information transfer is through entanglement alone is not possible, but probably with several entangled states together with a classical information channel ( quantum teleportation ). Despite the name, no information can be transmitted faster than light because of the classical information channel.
Of course, entangled systems
By femtosecond spectroscopy could be demonstrated that in photosystem light -harvesting complex of plants takes place reaching over the entire complex stable entanglement of photons, which makes it all possible efficient use of light energy without heat loss. Remarkable thing is, inter alia, the temperature stability of the phenomenon.
Generation of entangled systems
Entangled photons may be generated by parametric fluorescence ( parametric down conversion ) in nonlinear optical crystals. Here, a pair of entangled photons with lower energy generated ( one-half of the energy of Ursprungsphotons ) of a photon with a high energy in the crystal. The directions in which the two photons are emitted are correlated with each other and with the direction of the incident photon, so that you can use such entangled photons generated good for experiments (and other applications).
Certain types of atoms can be using a laser to stimulate such a way that they also emit a pair of entangled photons on their return to the unexcited ground state. However, they are blasted with equal probability in any spatial direction, so that they can not be used very efficiently.
For photons, the entanglement usually refers to the polarization of the photons. By measuring the polarization of a photon, thus the polarization of the other photon is fixed (eg, rotated by 90 ° ).
In atoms, the entanglement relates to their spin. If you excite a diatomic molecule with a spin of zero with a laser so high that it breaks up ( dissociates ), the two released atoms are entangled with respect to their spins. With an appropriate measurement of one of them the spin 1 / 2 will show the other -1 / 2 But it is not predictable which of the two atoms of the positive and which will have the negative. If you measure but the spin of the two atoms, thus the spin of the other is fixed.
Applications
- Quantum key exchange: Secure exchange of keys between two communication partners for encrypted transmission of information. The replacement is safe because it is not possible to listen to it without interference. The exchanging partners may, therefore, a "listening " key exchange notice.
- Quantum computers: In calculations using qubits on a quantum computer is used, the entanglement of qubits with each other in some algorithms. With quantum computers problems could be solved, although they are in principle solvable with conventional computers, but only with nichtrealisierbarem time.
Mathematical viewing
The following discussion requires knowledge of the Bra- Ket notation and the general mathematical formulation of quantum mechanics.
There are two systems and, with the Hilbert spaces and. The Hilbert space of the composite system is the Tensorproduktraum. The system is in a pure state and system in the pure state. Then the state of the composite system is also pure and given by:
Pure states which can be written in this form are called separable states, or product.
If we choose orthonormal bases and Hilbert spaces and then you can develop the states according to these bases and receives with complex coefficients and:
A condition of the form:
The separable states of are the ones that allow the coefficients of the representation, ie that can be factored as above. Is not a state is separable, it is called entangled him.
For example, two basis vectors of and two basis vectors are given by. Then the following condition, the so-called " singlet state ", crosses:
If the composite system is in this state, have neither a specific state, but their states are superposed and the systems are entangled in this sense.
As quantum mechanical measurements only eigenvalues of Hermitian operators can occur. Now let therefore " measurement operators" in each of the two subsystems and, which satisfy the following two eigenvalue equations:
By the tensor product with the identity operator can generate an operator on the Tensorproduktraum with the above measurement operators of the subsystems, the system is measured at the then listed in the subscript:
Suppose Alice watch system, Bob system. If Alice performs the measurement, two results may occur with equal probability:
In the first case each additional measurement by Bob will always result in the second case always. Thus, the system has been changed by the measurement performed by Alice, even if A and B are spatially separated. Here, the EPR paradox is due, and also the so-called quantum teleportation.
The result of Alice's measurement is random, it can not determine the state to which the system collapses, and therefore can not transmit information to Bob by the actions of their system. A possible loophole: If Bob can make multiple exact duplicates of the states that he receives, he could gather information on statistical way - the no- cloning theorem, but proves the impossibility of cloning of states. Therefore, it is - as mentioned above - the causality is not violated.
The degree of entanglement of a state is measured monotonous by the von Neumann entropy. The von Neumann entropy of a pure state is zero. However, the Von Neumann entropy of a maximally entangled state ( such as a Bell state ) is maximum.
Here it should be noted that in addition to the above discussed pure entangled states ( which the pure product states - without entanglement - the opposite side) are the entangled mixed states ( where the mixed product states - without entanglement - the opposite side).
Test for entanglement
For a pure entangled state of a system, which is composed of a subsystem 1 and subsystem 2, applies. If one forms the Partialspur one of the two systems (eg, system 1), we obtain the reduced density operator. Turning now to the square of the reduced density operator, and this is not equal, so the reduced density operator describes a mixture and thus describes an entangled state.
As an alternative to the above test, the Schmidt decomposition can be performed. If the Schmidt separation has more than one term, the state is entangled.