User:Justin Milton/Quantum teleportation

Beginning of Quantum Teleportation
First proposed theoretically in 1993, quantum teleportation has since been demonstrated in many different guises. It has been carried out using two-level states of a single photon, a single atom and a trapped ion – among other quantum objects – and also using two photons. In 1997, two groups experimentally achieved quantum teleportation. The first group, led by Boschi, was based out of Italy. An experimental group led by Bouwmeester followed a few months later.

The results obtained from experiments done by Boschi's group concluded that classical channels alone could not replicate the teleportation of linearly polarized state and an elliptically polarized state. The Bell state measurement distinguished between the four Bell states, which can allow for a 100% success rate of teleportation, in an ideal representation.

Bouwmeester's group produced a pair of entangled photons by implementing the process of parametric down-conversion. In order to ensure that the two photons cannot be distinguished by their arrival times, the photons were generated using a pulsed pump beam. The photons were then sent through narrow-bandwidth filters to produce a coherence time that is much longer than the length of the pump pulse. They then used a two-photon interferometry for analyzing the entanglement so that the quantum property could be recognized when it is transferred from one photon to the other.

Photon 1 was polarized at 45° in the first experiment Bouwmeester conducted. Quantum teleportation is verified when both photons are detected in the $$|\Psi-\rangle_{12}$$ state, which has a probability of 25%. Two detectors, f1 and f2, are placed behind the beam splitter, and recording the coincidence will identify the $$|\Psi-\rangle_{12}$$ state. If there is a coincidence between detectors f1 and f2, then photon 3 is predicted to be polarized at a 45° angle. Photon 3 is passed through a polarizing beam splitter that selects +45° and -45° polarization. If quantum teleportation has happened, only detector d2, which is at the +45° output, will register a detection. Detector d1, located at the -45° output, will not detect a photon. If there is a coincidence between d2f1f2, with the 45° analysis, and a lack of a d1f1f2 coincidence, with -45° analysis, it is proof that the information from the polarized photon 1 has been teleported to photon 3 using quantum teleportation.

Quantum Teleportation Over 143 km

The quantum internet is predicted to become prominent in the coming generations because of its superior security and exponentially faster communication. Xiao-Song Ma's group developed an experiment using active feed-forward in real time and two free-space optical links, quantum and classical, between the Canary Islands of La Palma and Tenerife, a distance of over 143 kilometers. In order to achieve teleportation, a frequency-uncorrelated polarization-entangled photon pair source, ultra-low-noise single-photon detectors and entanglement assisted clock synchronization were implemented. The two locations were entangled to share the auxiliary state:

$$|\Psi-\rangle_{23}=\frac{1}{\surd2}((|H\rangle_2|V\rangle_3)-(|V\rangle_2|H\rangle_3))$$

La Palma and Tenerife can be compared to the quantum characters Alice and Bob. Alice and Bob share the entangled state above, with photon 2 being with Alice and photon 2 being with Bob. A third party, Charlie, provides photon 1 (the input photon) which will be teleported to Alice in the generalized polarization state:

$$|\phi\rangle_1=\alpha|H\rangle_1+\beta|V\rangle_1$$

where the complex numbers $$\alpha$$ and $$\beta$$ are unknown to Alice or Bob.

Alice will perform a Bell-state measurement (BSM) that randomly projects the two photons onto one of the four Bell states with each one having a probability of 25%. Photon 3 will be projected onto $$|\phi\rangle$$, the input state. Alice transmits the outcome of the BSM to Bob, via the classical channel, where Bob is able to apply the corresponding unitary operation to obtain photon 3 in the initial state of photon 1. Bob will not have to do anything if he detects the $$|\psi-\rangle_{12}$$ state. Bob will need to apply a $$\pi$$ phase shift to photon 3 between the horizontal and vertical component if the $$|\psi+\rangle_{12}$$ state is detected.

The results of Ma's group concluded that the average fidelity (overlap of the ideal teleported state with the measured density matrix) was 0.863 with a standard deviation of 0.038. The link attenuation during their experiments varied between 28.1 dB and 39.0 dB, which was a result of strong winds and rapid temperature changes. Despite the high loss in the quantum free-space channel, the average fidelity surpassed the classical limit of 2/3. Therefore, Ma's group successfully demonstrated quantum teleportation over a distance of 143 km.

Quantum teleportation across the Danube River
In 2004, a quantum teleportation experiment was conducted across the Danube River in Vienna, a total of 600 meters. An 800-meter-long optical fiber wire was installed in a public sewer system underneath the Danube River, and it was exposed to temperature changes and other environmental influences. Alice must perform a joint Bell state measurement (BSM) on photon b, the input photon, and photon c, her part of the entangled photon pair (photons c and d). Photon d, Bob's receiver photon, will contain all of the information on the input photon b, except for a phase rotation that depends on the state that Alice observed. This experiment implemented an active feed-forward system that sends Alice's measurement results via a classical microwave channel with a fast electro-optical modulator in order to exactly replicate Alice's input photon. The teleportation fidelity obtained from the linear polarization state at 45° varied between 0.84 and 0.90, which is well above the classical fidelity limit of 0.66.

Deterministic quantum teleportation with atoms
Three qubits are required for this process: the source qubit from the sender, the ancillary qubit, and the receiver's target qubit, which is maximally entangled with the ancillary qubit. For this experiment, ions were used as the qubits. Ions 2 and 3 are prepared in the Bell state $$|\psi+\rangle_{23}=\frac{1}{\sqrt{2}}(|0\rangle_2|1\rangle_3+|1\rangle_2|0\rangle_3)$$. The state of ion 1 is prepared arbitrarily. The quantum states of ions 1 and 2 are measured by illuminating them with light at a specific wavelength. The obtained fidelities for this experiment ranged between 73% and 76%. This is larger than the maximum possible average fidelity of 66.7% that can be obtained using completely classical resources.

Ground-to-satellite quantum teleportation
The quantum state being teleported in this experiment is $$|\chi\rangle_1=\alpha|H\rangle_1+\beta|V\rangle_1$$, where $$\alpha$$ and $$\beta$$ are unknown complex numbers, $$|H\rangle$$ represents the horizontal polarization state, and $$|V\rangle$$ represents the vertical polarization state. The qubit prepared in this state is generated in a laboratory in Ngari, Tibet. The goal was to teleport the quantum information of the qubit to the Micius satellite that was launched on August 16, 2016 at an altitude of around 500 km. When a Bell state measurement is conducted on photons 1 and 2 and the resulting state is $$|\phi+\rangle_{12}=\frac{1}{\sqrt{2}}(|H\rangle_1|H\rangle_2+|V\rangle_1|V\rangle_2))$$, photon 3 carries this desired state. If the Bell state detected is $$|\phi-\rangle_{12}=\frac{1}{\sqrt{2}}(|H\rangle_1|H\rangle_2-|V\rangle_1|V\rangle_2)$$, then a phase shift of $$\pi$$ is applied to the state to get the desired quantum state. The distance between the ground station and the satellite changes from as little as 500 km to as large as 1,400 km. Because of the changing distance, the channel loss of the uplink varies between 41 dB and 52 dB. The average fidelity obtained from this experiment was 0.80 with a standard deviation of 0.01. Therefore, this experiment successfully established a ground-to-satellite uplink over a distance of 500-1,400 km using quantum teleportation. This is an essential step towards creating a global-scale quantum internet.

Valich
Quantum teleportation is a demonstration of what Albert Einstein famously called "spooky action at a distance"—also known as quantum entanglement. In entanglement—one of the basic of concepts of quantum physics—the properties of one particle affect the properties of another, even when the particles are separated by a large distance. Quantum teleportation involves two distant, entangled particles in which the state of a third particle instantly "teleports" its state to the two entangled particles. Quantum teleportation is an important means for transmitting information in quantum computing. While a typical computer consists of billions of transistors, called bits, quantum computers encode information in quantum bits, or qubits. A bit has a single binary value, which can be either "0" or "1," but qubits can be both "0" and "1" at the same time. The ability for individual qubits to simultaneously occupy multiple states underlies the great potential power of quantum. computers.

Quantum teleportation is an important means for transmitting information in quantum computing. The ability for individual qubits to simultaneously occupy multiple states underlies the great potential power of quantum computers.

Minksy
In quantum physics, teleportation is not just possible, it’s been achieved, with scientists now making steps towards bringing teleportation to the masses. But unlike physical teleportation, the quantum version doesn’t involve any matter changing location in space. Instead, information is mysteriously and instantaneously teleported from one quantum particle or quantum system to another. In a way, entangled particles behave as if they are aware of how the other particle is behaving. Quantum particles, at any point, are in a quantum state of probabilities, where properties like position, momentum, and spin of the particle are not precisely determined until there is some measurement. For entangled particles, the quantum state of each depends on the quantum state of the other; if one particle is measured and changes state, for example, the other particle’s state will change accordingly

The development of technologies which can process information based on the laws of quantum physics are predicted to have profound impacts on modern society. However, these technologies all rely on "quantum information," which is typically encoded in single quantum particles that are extremely difficult to control and measure.

How to teleport a quantum object?
When two quantum objects are entangled, they are connected so that if one is disturbed, the other will also immediately change, no matter how far apart they are from each other. Simply observing one of these particles will change its quantum state, therefore also changing the state of the other entangled particle, no matter the distance between them. Theoretically, even if they are light-years apart, if you observe one, it will immediately change the other, without any time delay

Teleportation may seem impossible to many, but in certain situations, it can be achieved. The main process to make this possible is through quantum entanglement, which occurs when a pair or group of particles are tangled up together in a way that the quantum state of each particle cannot be described independently, and they act as a single quantum object, described by a single wave function.