handofg0d Posted:

Quantum communication involves encoding information in quantum states, or qubits, as opposed to clbumical communications use of bits. Usually, photons are used for these quantum states. Quantum cryptography exploits certain properties of these quantum states to ensure its security. There are several different approaches to quantum key distribution, but they can be divided into two main categories depending on which property they exploit.

Prepare and measure protocols

In contrast to clbumical physics, the act of measurement is an integral part of quantum mechanics. In general, measuring an unknown quantum state will change that state in some way. This is known as quantum indeterminacy, and underlies results such as the Heisenberg uncertainty principle, information-disturbance theorem and no cloning theorem. This can be exploited in order to detect any eavesdropping on communication (which necessarily involves measurement) and, more importantly, to calculate the amount of information that has been intercepted.

Entanglement based protocols

The quantum states of two (or more) separate objects can become linked together in such a way that they must be described by a combined quantum state, not as individual objects. This is known as entanglement and means that, for example, performing a measurement on one object will affect the other. If an entangled pair of objects is shared between two parties, anyone intercepting either object will alter the overall system, allowing the presence of the third party (and the amount of information they have gained) to be determined.

These two approaches can each be further divided into three families of protocols; discrete variable, continuous variable and distributed phase reference coding. 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.

handofg0d Posted:

BB84 protocol: Charles H. Bennett and Gilles Brbumard (1984)

This protocol, known as BB84 after its inventors and year of publication, was originally described using photon polarization states to transmit the information. However, any two pairs of conjugate states can be used for the protocol, and many optical fibre based implementations described as BB84 use phase encoded states. The sender (traditionally referred to as Alice) and the receiver (Bob) are connected by a quantum communication channel which allows quantum states to 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 clbumical channel, for example using broadcast radio or the internet. Neither of these channels need to be secure; the protocol is designed with the bumumption that an eavesdropper (referred to as Eve) can interfere in any way with both.

The security of the protocol comes from encoding the information in non-orthogonal states. 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, with each pair conjugate to the other pair, and the two states within a pair orthogonal to each other. Pairs of orthogonal states are referred to as a basis. The usual polarization state pairs used are either the rectilinear basis of vertical (0°) and horizontal (90°), the diagonal basis of 45° and 135° 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.

Basis 0 1

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 table to the left. So for example a 0 is encoded in the rectilinear basis (+) as a vertical polarization state, and a 1 is encoded in the diagonal basis (x) as a 135° state. Alice then transmits a single photon in the state specified to Bob, using the quantum channel. This process is then repeated from the random bit stage, with Alice recording the state, basis and time of each photon sent.

Quantum mechanics (particularly quantum indeterminacy) says there is no possible measurement that will distinguish between the 4 different polarization states, as they are not all orthogonal. The only measurement possible is between any two orthogonal states (a basis), so for example measuring in the rectilinear basis will give a result of horizontal or vertical. If the photon was created as horizontal or vertical (as a rectilinear eigenstate) then this will measure the correct state, but if it was created as 45° or 135° (diagonal eigenstates) then the rectilinear measurement will instead return either horizontal or vertical at random. Furthermore, after this measurement the photon will be polarized in the state it was measured in (horizontal or vertical), with all information about its initial polarization lost.

As Bob does not know the basis the photons were encoded in, all he can do is select a basis at random to measure in, either rectilinear or diagonal. He does this for each photon he receives, recording the time, measurement basis used and measurement result. After Bob has measured all the photons, he communicates with Alice over the public clbumical 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 will be half on average, leaving half the bits as a shared key.

Alice’s random bit 0 1 1 0 1 0 0 1

Alice’s random sending basis

Photon polarization Alice sends

Bob’s random measuring basis

Photon polarization Bob measures

PUBLIC DISCUSSION OF BASIS

Shared secret key 0 1 0 1

To check for the presence of eavesdropping Alice and Bob now compare a certain subset of their remaining bit strings. If a third party (usually referred to as Eve, for ‘eavesdropper’Log in to see images!

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Somebody Posted:

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handofg0d Posted:

Log in to see images!

quangntenemy edited this message on 08/04/2009 11:04AM

spacekadt Posted:

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The highest bit rate system currently demonstrated exchanges secure keys at 1 Mbit/s (over 20 km of optical fibre) and 10 kbit/s (over 100 km of fibre), achieved by a collaboration between the University of Cambridge and Toshiba using the BB84 protocol with decoy pulses[5].

As of March 2007[update] the longest distance over which quantum key distribution has been demonstrated using optic fibre is 148.7 km, achieved by Los Alamos/NIST using the BB84 protocol[6]. Significantly, this distance is long enough for almost all the spans found in today’s fibre networks. The distance record for free space QKD is 144 km between two of the Canary Islands, achieved by a European collaboration using entangled photons (the Ekert scheme) in 2006[7], and using BB84 enhanced with decoy states[8] in 2007 [9]. The experiments suggest transmission to satellites is possible, due to the lower atmospheric density at higher altitudes. For example although the minimum distance from the International Space Station to the ESA Space Debris Telescope is about 400 km, the atmospheric thickness is about an order of magnitude less than in the European experiment, thus yielding less attenuation compared to this experiment.

The DARPA Quantum Network[10], a 10-node quantum cryptography network, has been running since 2004 in Mbumachusetts, USA. It is being developed by BBN Technologies, Harvard University, Boston University and QinetiQ.

There are currently four companies offering commercial quantum cryptography systems; id Quantique (Geneva), MagiQ Technologies (New York), SmartQuantum (France) and Quintessence Labs (Australia). Several other companies also have active research programmes, including Toshiba, HP, IBM, Mitsubishi, NEC and NTT (See External links for direct research links).

Quantum encryption technology provided by the Swiss company Id Quantique was used in the Swiss canton (state) of Geneva to transmit ballot results to the capitol in the national election occurring on Oct. 21, 2007.[10]

In 2004, the world’s first bank transfer using quantum cryptography was carried in Vienna, Austria. An important cheque, which needed absolute security, was transmitted from the Mayor of the city to an Austrian bank.[11]

The world’s first computer network protected by quantum cryptography was implemented in October 2008, at a scientific conference in Vienna. The network used 200 km of standard fibre optic cable to interconnect six locations across Vienna and the town of St Poelten located 69 km to the west. The event was witnessed by Gilles Brbumard and Anton Zeilinger. [11]

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