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.
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 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.
We analyze Einsteins recoiling slit experiment and point out that the inevitable entanglement between the particle and the recoiling-slit was not part of Bohrs reply. We show that if this entanglement is taken into account, one can provided a simpler
answer to Einstein. We also derive the Englert-Greenberger-Yasin duality relation from this entanglement. In addition, we show that the Englert-Greenberger-Yasin duality relation can also be thought of as a consequence of the sum uncertainty relation for certain observables of the recoiling slit. Thus, the uncertainty relations and entanglement are both an integral part of the which-way detection process.
Karl Popper had proposed an experiment to test the standard interpretation of quantum mechanics. The proposal survived for many year in the midst of no clear consensus on what results it would yield. The experiment was realized by Kim and Shih in 199
9, and the apparently surprising result led to lot of debate. We review Poppers proposal and its realization in the light of current era when entanglement has been well studied, both theoretically and experimentally. We show that the ghost-diffraction experiment, carried out in a different context, conclusively resolves the controversy surrounding Poppers experiment.
Some recent works have introduced a quantum twist to the concept of complementarity, exemplified by a setup in which the which-way detector is in a superposition of being present and absent. It has been argued that such experiments allow measurement
of particle-like and wave-like behavior at the same time. Here we derive an inequality which puts a bound on the visibility of interference and the amount of which-way information that one can obtain, in the context of such modified experiments. As the wave-aspect can only be revealed by an ensemble of detections, we argue that in such experiments, a single detection can contribute only to one subensemble, corresponding to either wave-aspect or particle aspect. This way, each detected particle behaves either as particle or as wave, never both, and Bohrs complementarity is fully respected.
