Observability of relative phases of macroscopic quantum states

After a measurement, to observe the relative phases of macroscopically distinguishable states we have to ``undo'' a quantum measurement. We generalise an earlier model of Peres from two state to N-state quantum system undergoing measurement process and discuss the issue of observing relative phases of different branches. We derive an inequality which is satisfied by the relative phases of macroscopically distinguishable states and consequently any desired relative phases can not be observed in interference setups. The principle of macroscopic complementarity is invoked that might be at ease with the macroscopic world. We illustrate the idea of limit on phase observability in Stern-Gerlach measurements and the implications are discussed.Comment: Latex file, no figures, 12 pages, submitted to Phys. Lett.

Distinguishing two preparations for same pure state leads to signalling

Pure state of a physical system can be prepared in an infinite number of ways. Here, we prove that given a pure state of a quantum system it is impossible to distinguish two preparation procedures. Further, we show that if we can distinguish two preparation procedures for the same pure state then that can lead to signalling. This impossibility result is different than the no measurement without disturbance and the no-cloning. Extending this result for a pure bipartite entangled state entails that the impossibility of distinguishing two preparation procedures for a mixed state follows from the impossibility of distinguishing two preparations for a pure bipartite state.Comment: Two and half pages, Comments welcom

Fast quantum search algorithm and Bounds on it

We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps still further. We discuss the lower and upper bounds on the transition matrix elements when the unitary operator changes with time, thereby implying that quantum search process can not be too fast or too slow. This is a remarkable feature of quantum computation unlike classical one. Quantum mechanical uncertainty relation puts bounds on search process. Also we mention the problems of perturbation and other issues in time-dependent search operation.Comment: Latex file, Two column, 4 pages, no figure

Probabilistic exact cloning and probabilistic no-signalling

We show that non-local resources cannot be used for probabilistic signalling even if one can produce exact clones with the help of a probabilistic quantum cloning machine (PQCM). We show that PQCM cannot help to distinguish two statistical mixtures at a remote location. Thus quantum theory rules out the possibility of sending superluminal signals not only deterministically but also probabilistically. We give a bound on the success probability of producing multiple clones in an entangled system.Comment: Latex file, 6 pages, minor correction

Remote state preparation and measurement of single photon

Quantum information theory has revolutionized the way in which information is processed using quantum resources such as entangled states, local operations and classical communications. Two important protocols in quantum communications are quantum teleportation and remote state preparation. In quantum teleportation neither the sender nor the receiver know the identity of a state. In remote state preparation the sender knows the state which is to be remotely prepared without ever physically sending the object or the complete classical description of it. Using one unit of entanglement and one classical bit Alice can remotely prepare a photon (from special ensemble) of her choice at Bob's laboratory. In remote state measurement Alice asks Bob to simulate any single particle measurement statistics on an arbitrary photon. In this talk we will present these ideas and discuss the latest developments and future open problems.Comment: Latex file, 7 pages, Invited talk in Sixth International Conference on PHOTONICS-2002, held at TIFR, Mumbai, India from Dec-16-18, 200

Violation of Invariance of Entanglement Under Local PT Symmetric Unitary

Entanglement is one of the key feature of quantum world and any entanglement measure must satisfy some basic laws. Most important of them is the invariance of entanglement under local unitary operations. We show that this is no longer true with local ${\cal {PT}}$ symmetric unitary operations. If two parties share a maximally entangled state, then under local ${\cal {PT}}$ symmetric unitary evolution the entropy of entanglement for pure bipartite states does not remain invariant. Furthermore, we show that if one of the party has access to ${\cal {PT}}$-symmetric quantum world, then a maximally entangled state in usual quantum theory appears as a non-maximally entangled states for the other party. This we call as the "entanglement mismatch" effect which can lead to the violation of the no-signaling condition.Comment: 5 pages, Latex, No fi

Infinitesimal change is a Non-local Operation: Hidden power of Quantum Entanglement

We show that the global infinitesimal change in the multi-particle pure product state gives rise to an entangled state. This suggests that even if there is no interaction present between the subsystems, i.e., at each time instant the state is non-entangled, the tangent vector is typically entangled. Since the tangent space vectors tell the state-space vectors how to change this implies that quantum entanglement is necessary for motion or change in general. This is truly a `hidden power' of quantum entanglement. During quantum computation even though at each time instant the state is not entangled, quantum entanglement guides the process of computation. This observation applies to multi-particle pure, pseudo-pure and mixed states as well.Comment: Latex, 4 pages, No figures (Comments welcome

Measuring Electromagnetic Vector Potential via Weak Value

Electromagnetic vector potential has physical significance in quantum mechanics as revealed by the Aharonov-Bohm effect for charged particles. However, till date it is thought that we cannot measure the vector potential directly as this is not a gauge invariant quantity. Contrary to this belief, here we show that one can indeed measure the electromagnetic vector potential using the notion of weak value. We show that it is simply the difference between the weak value of the canonical momentum of a charged particle in the presence and absence of magnetic field. This suggests that the vector potential is not only a physical entity but can be measured directly in the experiment.Comment: Latex, 5 pages, Comments and suggestions welcom

Potent Value and Potent Operator with Pre- and Post-selected Quantum Systems

We introduce a novel concept which we call as potent value of system observable for pre- and post-selected quantum states. This describes, in general, how a quantum system affects the state of the apparatus during the time between two strong measurements corresponding to pre- and post-selections. The potent value can be realized for any interaction strength and for arbitrary coupling between the system and the apparatus observables. Most importantly, potent values generalize and unify the notion of the weak values and modular values of observables in quantum theory. Furthermore, we define a potent operator which describes the action of one system on the another and show that superposition of time-evolutions and time-translation machines are potent operators. These concepts may find useful applications in quantum information processing and can lead to technological benefits

Entropy decrease in Quantum Zeno Effect

If a measurement process is regarded as an irreversible process, then by Second law of thermodynamics the entropy should increase after any measurement process. By the same spirit a quantum system undergoing repeated measurement should show strong irreversibility leading to entropy production. On the contrary we show that in quantum Zeno effect setting the entropy of a quantum system decreases and goes to zero after a large number of measurements. We discuss the entropy change under continuous measurement model and show that entropy can decrease if we use a more accurate measuring apparatus.Comment: Latex file, 6 pages, no figure