It is shown that the nature of quantum states that emerge from decoherence is such that one can {em measure} the expectation value of any observable of the system in a single measurement. This can be done even when such pointer states are a priori un
known. The possibility of measuring the expectation value of any observable, without any prior knowledge of the state, points to the objective existence of such states.
We show that single-slit two-photon ghost diffraction can be explained very simply by using a wave-packet evolution of a generalised EPR state. Diffraction of a wave travelling in the x-direction can be described in terms of the spreading in time of
the transverse (z-direction) wave-packet, within the Fresnel approximation. The slit is assumed to truncate the transverse part of the wavefunction of the photon to within the width of the slit. The analysis reproduces all features of the two-photon single-slit ghost diffraction.
Making measurements on single quantum systems is considered difficult, almost impossible if the state is a-priori unknown. Protective measurements suggest a possibility to measure single quantum systems and gain some new information in the process. P
rotective measurement is described, both in the original and generalized form. The degree to which the system and the apparatus remain entangled in a protective measurement, is assessed. A possible experimental test of protective measurements is discussed.
The complementary wave and particle character of quantum objects (or quantons) was pointed out by Niels Bohr. This wave-particle duality, in the context of the two-slit experiment, is now described not just as two extreme cases of wave and particle c
haracteristics, but in terms of quantitative measures of these natures. These measures of wave and particle aspects are known to follow a duality relation. A very simple and intuitive derivation of a closely related duality relation is presented, which should be understandable to the introductory student.
We propose and analyze a modified ghost-interference experiment, and show that revealing the particle-nature of a particle passing through a double-slit hides the wave-nature of a spatially separated particle which it is entangled with. We derive a n
onlocal duality relation, ${mathcal D}_1^2 + {mathcal V}_2^2 le 1$, which connects the path distinguishability of one particle to the interference visibility of the other. It extends Bohrs principle of complementarity to a nonlocal scenario. We also propose a ghost quantum eraser in which, erasing the which-path information of one particle brings back the interference fringes of the other.
The ghost interference observed for entangled photons is theoretically analyzed using wave-packet dynamics. It is shown that ghost interference is a combined effect of virtual double-slit creation due to entanglement, and quantum erasure of which-pat
h information for the interfering photon. For the case where the two photons are of different color, it is shown that fringe width of the interfering photon depends not only on its own wavelength, but also on the wavelength of the other photon which it is entangled with.
The issue of interference and which-way information is addressed in the context of 3-slit interference experiments. A new path distinguishability ${mathcal D_Q}$ is introduced, based on Unambiguous Quantum State Discrimination (UQSD). An inequality c
onnecting the interference visibility and path distinguishability, ${mathcal V} + {2{mathcal D_Q}over 3- {mathcal D_Q}} le 1$, is derived which puts a bound on how much fringe visibility and which-way information can be simultaneously obtained. It is argued that this bound is tight. For 2-slit interference, we derive a new duality relation which reduces to Englerts duality relation and Greenberger-Yasins duality relation, in different limits.
Recently demonstrated ghost interference using correlated photons of different frequencies, has been theoretically analyzed. The calculation predicts an interesting nonlocal effect: the fringe width of the ghost interference depends not only on the w
ave-length of the photon involved, but also on the wavelength of the other photon with which it is entangled. This feature, arising because of different frequencies of the entangled photons, was hidden in the original ghost interference experiment. This prediction can be experimentally tested in a slightly modified version of the experiment.
We propose a new Quantum Key Distribution method in which Alice sends pairs of qubits to Bob, each in one of four possible states. Bob uses one qubit to generate a secure key and the other to generate an auxiliary key. For each pair he randomly decid
es which qubit to use for which key. The auxiliary key has to be added to Bobs secure key in order to match Alices secure key. This scheme provides an additional layer of security over the standard BB84 protocol.
A new scheme of Quantum Key Distribution is proposed using three entangled particles in a GHZ state. Alice holds a 3-particle source and sends two particles to Bob, keeping one with herself. Bob uses one particle to generate a secure key, and the oth
er to generate a master-key. This scheme should prove to be harder to break in non-ideal situations as compared to the standard protocols BB84 and Eckert. The scheme uses the concept of Quantum Disentanglement Eraser. Extension to multi-partite scheme has also been investigated.
