We would like to show you a description here but the site won’t allow blogger.com more data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKAAAAB4CAYAAAB1ovlvAAACs0lEQVR4Xu3XMWoqUQCG0RtN7wJck7VgEW1cR3aUTbgb7UUFmYfpUiTFK/xAzlQWAz/z3cMMvk3TNA2XAlGBNwCj8ma PhD thesis: Few-photon transport in strongly interacting light-matter systems: A scattering approach Tian Feng See Master's Thesis: Memory effects in quantum processes Philip Taranto *Free-to-read. Register for a free account to access these articles
(PDF) AARC Digital Library General Collection | Gina Dominique - blogger.com
Quantum key distribution QKD is a secure communication method which implements a renato renner phd thesis protocol involving components of quantum mechanics. It enables two parties to produce a shared random secret key known only to them, which can then be renato renner phd thesis to encrypt and decrypt messages. It is often incorrectly called quantum cryptographyas it is the best-known example of a quantum cryptographic task.
An important and unique property of quantum key distribution is renato renner phd thesis ability of the two communicating users to detect the presence of any third party trying to gain knowledge of the key.
This results from a fundamental aspect of quantum mechanics: the process of measuring a quantum system in general disturbs the system, renato renner phd thesis. A third renato renner phd thesis trying to eavesdrop on the key must in some way measure it, thus introducing detectable anomalies. By using quantum superpositions or quantum entanglement and transmitting information in quantum statesa communication system can be implemented that detects eavesdropping.
If the level of eavesdropping is below a certain threshold, renato renner phd thesis, a key can be produced that is guaranteed to be secure i, renato renner phd thesis. The security of encryption that uses quantum key distribution relies on the foundations of quantum mechanics, in contrast to traditional public key cryptographywhich relies on the computational difficulty of certain mathematical functionsrenato renner phd thesis, and cannot provide any mathematical proof as to the actual complexity of reversing the one-way functions used.
QKD has provable security based on information theoryand forward secrecy. The main drawback of quantum key distribution is that it usually relies on having an authenticated classical channel of communications. In modern cryptography, having an authenticated classical channel means that one has either already exchanged a symmetric key of sufficient length or public keys of sufficient security level.
Thus QKD does the work of a stream cipher at many times the cost. Noted security expert Bruce Schneier remarked that quantum key distribution is "as useless as it is expensive". Quantum key distribution is only used to produce and distribute a key, not to transmit any message data. This key can then be used with any chosen encryption algorithm to encrypt and decrypt a message, which can then be transmitted over a standard communication channel. The algorithm most commonly associated with QKD is the one-time padas it is provably secure when used with a secret, random key.
Quantum communication involves encoding information in quantum states, or qubitsas opposed to classical communication's use of bits. Usually, photons are used for these quantum states. Quantum key distribution exploits certain properties of these quantum states to ensure its security. There are several different approaches to quantum key distribution, renato renner phd thesis, but they can be divided into two main categories depending on which property they exploit.
These two approaches can each be further divided into three families of protocols: discrete variable, continuous variable and distributed phase reference coding, renato renner phd thesis. Discrete variable protocols were the first to be invented, and they remain the most widely implemented. The other two families are mainly concerned with overcoming practical limitations of experiments. The two protocols described below both use discrete variable coding.
This protocol, known as BB84 after its inventors and year of publication, was originally described using photon polarization states to transmit the information. The sender traditionally referred to as Alice and the receiver Bob are connected by a quantum communication channel which allows quantum states renato renner phd thesis be transmitted. In the case of photons this channel is generally either an optical fibre or simply free space. In addition they communicate via a public classical channel, for example using broadcast radio or the internet.
The protocol is designed with the assumption that an eavesdropper referred to as Eve can interfere in any way with the quantum channel, while the classical channel needs to be authenticated. The security of renato renner phd thesis protocol comes from encoding the information in non-orthogonal states, renato renner phd thesis. Quantum indeterminacy means that these states cannot in general be measured without disturbing the original state see No-cloning theorem.
BB84 uses two pairs of states, renato renner phd thesis, with each pair conjugate to the other pair, and the two states within a pair orthogonal to each other. Pairs of renato renner phd thesis states are referred to as a basis. The usual polarization renato renner phd thesis pairs used are either the rectilinear basis of vertical 0° and horizontal 90°renato renner phd thesis, the diagonal basis of 45° and ° or the circular basis of left- and right-handedness.
Any two of these bases are conjugate to each other, and so any two can be used in the protocol. Below the rectilinear and diagonal bases are used. The first step in BB84 is quantum transmission.
Alice creates a random bit 0 or 1 and then randomly selects one of her two bases rectilinear or diagonal in this case to transmit it in. She then prepares a photon polarization state depending both on the bit value and basis, as shown in the adjacent table.
Alice then transmits a single photon in the state specified to Bob, using the quantum channel, renato renner phd thesis. This process is then repeated from the random bit stage, with Renato renner phd thesis recording the state, basis and time of each photon sent. According to quantum mechanics particularly quantum indeterminacyno possible measurement distinguishes between the 4 different polarization states, as they are not all orthogonal.
The only possible measurement is between any two orthogonal states an orthonormal basis. So, for example, measuring in the rectilinear basis gives a renato renner phd thesis of horizontal or vertical. If the photon was created as horizontal or renato renner phd thesis as a rectilinear eigenstate then this measures the correct state, but if it was created as 45° or ° diagonal eigenstates then the rectilinear measurement instead returns either horizontal or vertical at random.
Furthermore, after this measurement the photon is polarized in the state renato renner phd thesis was measured in horizontal or verticalwith all information about its initial polarization lost.
As Bob does not know the basis the photons were encoded in, all he can do is to select a basis at random to measure in, renato renner phd thesis rectilinear or diagonal, renato renner phd thesis. He does this for each photon he receives, recording the time, measurement basis used and measurement result, renato renner phd thesis. After Bob has measured all the photons, he communicates with Alice over the public classical channel.
Alice broadcasts the basis each photon was sent in, and Bob the basis each was measured in. They both discard photon measurements bits where Bob used a different basis, which is half on average, leaving half the bits as a shared key. To check for the presence of an eavesdropper, Alice and Bob now compare a predetermined subset of their remaining bit strings, renato renner phd thesis.
If a third party usually referred to as Eve, for "eavesdropper" has gained any information about the photons' polarization, this introduces errors in Bob's measurements. Other environmental conditions can cause errors in a similar fashion. Artur Ekert 's scheme [6] uses entangled pairs of photons. These can be created by Alice, by Bob, or by some source separate from both of them, including eavesdropper Eve. The photons are distributed so that Alice and Bob each end up with one photon from each pair.
The scheme relies on two properties of entanglement. The same is true if they both measure any other pair of complementary orthogonal polarizations. This necessitates that the two renato renner phd thesis parties have exact directionality synchronization. However, the particular results are completely random; it is impossible for Alice to predict if she and thus Bob will get vertical polarization or horizontal polarization. Second, any attempt at eavesdropping by Eve destroys these correlations in a way that Alice and Bob can detect.
Similarly to BB84the protocol involves a private measurement protocol before detecting the presence of Eve. They keep their series of basis choices private until measurements are completed. Two groups of photons are made: the first consists of photons measured using the same basis by Alice and Bob while the second contains all other photons, renato renner phd thesis. If this were not the case, then Alice and Bob can conclude Eve has introduced local realism to the system, violating Bell's Theorem.
If the protocol is successful, the first group can be used to generate keys since those photons are completely anti-aligned between Alice and Bob. The quantum key distribution protocols described above provide Alice and Bob with nearly identical shared keys, and also with an estimate of the discrepancy between the keys.
These differences can be caused by eavesdropping, but also by imperfections in the transmission line and detectors. As it is impossible to distinguish between these two types of errors, guaranteed security requires the assumption that all errors are due to eavesdropping.
Provided the error rate between the keys is lower than a certain threshold These two steps are known as information reconciliation and privacy amplification respectively, renato renner phd thesis, and were first described in Information reconciliation is a form of error correction carried out between Alice and Bob's keys, in order to ensure both keys are identical.
It is conducted over the public channel and as such it is vital to minimise the information sent about each key, as this can be read by Eve. A common protocol used for information reconciliation is the cascade protocolproposed in If a difference in parity is found then a binary search is performed to find and correct the error.
If an error is found in a block from a previous round that had correct parity then another error must be contained in that block; this error is found and corrected as before.
This process is repeated recursively, which is the source of the cascade name. After all blocks have been compared, Alice and Bob both reorder their keys in the same random way, and a new round begins.
At the end of multiple rounds Alice and Bob have identical keys with high probability; however, Eve has additional information about the key from the parity information exchanged. However, from a coding theory point of view information reconciliation is essentially source coding with side information, renato renner phd thesis, in consequence any coding scheme that works for this problem can be used for information reconciliation.
Lately turbocodes, [10] LDPC codes [11] and polar codes [12] have been used for this purpose improving the efficiency of the cascade protocol. Privacy amplification is a method for reducing and effectively eliminating Eve's partial information about Alice and Bob's key. This partial information could have been gained both by eavesdropping on the quantum channel during key transmission thus introducing detectable errorsand on the public channel during information reconciliation where it is assumed Eve gains all possible parity information.
Privacy amplification uses Alice and Bob's key to produce a new, shorter key, in such a way that Eve has only negligible information about the new key.
This can be done using a universal hash functionchosen at random from a publicly known set of such functions, which takes as its input a binary string of length equal to the key and outputs a binary string of a chosen shorter length. The amount by which this new key is shortened is calculated, based on how much information Eve could have gained about the old key which is known due to the errors this would introducein order to reduce the probability of Eve having any knowledge of the new key to a very low value.
A European collaboration achieved free space QKD over km between two of the Canary Islands using entangled photons the Ekert scheme in[15] and using BB84 enhanced with decoy states [16] [17] [18] [19] [20] [21] in As of August [update] the longest distance for optical fiber km [23] was achieved by University of Geneva and Corning Renato renner phd thesis. In the same experiment, a secret key rate of In a team from Corning and various institutions in China achieved a distance of km, but at a bit rate too slow to be practical.
In Junephysicists led by Thomas Jennewein at the Institute for Quantum Computing and the University of Waterloo in Waterloo, renato renner phd thesis, Canada achieved the first demonstration of quantum key distribution from a ground transmitter to a moving aircraft.
They reported optical links with distances between 3—10 km and generated secure keys up to kilobytes in length. Also in Juneas part of the Quantum Experiments at Space Scale project, renato renner phd thesis, Chinese physicists led by Pan Jianwei at the University of Science and Technology of China measured entangled photons over a distance of km between two ground stations, laying the groundwork for future intercontinental quantum key distribution experiments.
The keys were combined and the result was used to transmit images and video between Beijing, China, and Vienna, Austria. In May a group led by Hong Guo at Peking University and Beijing University of Posts and Telecommunications reported field tests of a continuous-variable QKD system through commercial fiber networks in Xi'an and Guangzhou over distances of In DecemberIndian Defence Research and Development Organisation tested a QKD between two of its laboratories in Hyderabad facility.
The setup also demonstrated the validation of detection of a third party trying to gain knowledge of the communication.
A Sketch of My PhD Thesis by Pedro Papotto (Bruno Silva-Santos Lab)
, time: 3:19Share this Page - blogger.com
blogger.com is a platform for academics to share research papers data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKAAAAB4CAYAAAB1ovlvAAACs0lEQVR4Xu3XMWoqUQCG0RtN7wJck7VgEW1cR3aUTbgb7UUFmYfpUiTFK/xAzlQWAz/z3cMMvk3TNA2XAlGBNwCj8ma The GMDN is used by a large number of licensed members, including governments, healthcare providers and manufacturers, who are listed here
No comments:
Post a Comment