CS265-HW 5: Surekha Shinde
QUANTUM MECHANICS AND CRYPTOGRAPHY
In his paper Dr. David Blockus has explained that how the concepts of quantum computing and quantum
mechanics can be applied to cryptography. He has also covered the various steps in abstraction of measurement,
spin angular momentum, orthonarmal bases, quantum mechanical key distribution and general problems in it.
Quantum Cryptography is a method that exploits the EPR (Einstein-Podolsky-Rosen) paradox to
distribute a one-time-pad to two locations. It is secure against undetectable eavesdropping, but although an active
attack could be detected, it could still lead to the attacker reading a message. Classical Physics discusses about
various scalar (t –time) and vector quantities (x-position) and tensor-vector I, which is quantity in matrix form and
constitutes more than single dimension component. Moment of inertia is a tendency of object to prevent it from
spinning. There are various ways of representing physical quantities, two of which being Cartesian and spherical
representation. Observable are abstracted in quantum mechanics and more abstraction needs more capabilities.
For example: Hermitian operator in Hilbert space. So the problem in quantum mechanics: 1.Find operators to specify system.
2.Find possible expectation values of operators
Angular momentum experiment demonstrates that classical tops are rigid bodies, which obey simple
equations of motion based upon conservation of angular momentum. Angular momentum:-[Lx,Ly]=LxLyLyLx=0,then Lx and Ly are said to commute. We cannot find energy and time simultaneously as they do not
commute. For ex.[E,t]=Et-te= 0=-ih .Here E and t is a pair which do not commute. Then E t>=1/2 h. E= <<E^2><E^2>>. E T is called time-bandwidth limit. Multiple plane-polarizing filters can be used to study the polarization
of a laser beam by different types of polarizing filter i.e. horizontal, vertical and planes skewed at certain angles.
The polarizing filter experiments demonstrates that in a process measurement, we can alert the state of process
and we won’t know that we are changing it and that we are just selecting one of several possibilities and not doing
actual measurement.
The figure below demonstrates how the quantum key distribution can be done using a quantum channel:Classical Channel
Alice
Bob
Quantum Channel
Eve
In classical channel case, we can send data either in clear form or encrypted. It is susceptible to
eavesdropping and susceptible to modification whereas while using a quantum channel key distribution is done
and the key used is generally a symmetric key. In this case eavesdropping changes quantum mechanical stage.
No repeaters or switches must be used in quantum channel.
Key distribution:-It is essential that Alice and Bob should peak same bases so as to receive right data at
Bob’s side. Here Eve may come online and peak random bases and can damage the data. If an attacker sends
particles with a known spin out, then if it happens both sides are measuring for horizontal polarization when he
sent the particles out with a fixed vertical polarization, for example, the two parties may have mismatched digits in
their one-time-pads, thus encountering a garble and therefore detecting tampering. An attempt to find the
polarization of one of the particles, and replace it with one of the same polarization, will also fail if the wrong
direction is chosen in the same way.
Conclusion: - Quantum cryptography has unique features for sending coded data at practical transmission rates
and detecting eavesdroppers. The entanglement process can generate a completely random sequence of 0s and
1s distributed exclusively to two users at remote locations. Any eavesdropper's attempt to intercept this sequence
will alter the message in a detectable way, enabling the users to discard the appropriate parts of the data. This
random sequence of digits, or "key," can then be plugged into a code scheme known as a "one-time pad cipher,”
which converts the message into a completely random sequence of letters.