arXiv subjects
Publications and source records attributed to B. S. Choudhury.
In this paper, a metric on $S_b$-metric space analogous to the Hausdorff metric has been introduced and some basic properties are obtained on multi-valued $S_b$-metric space. Further, the fundamental multi-valued contraction of Nadler(1962) has been extended to the $S_b$-metric space setting, and two results have been established. The entire study is supported by suitable examples.
In this work we describe a protocol by which one can secretly broadcast W-type state among three distant partners. This work is interesting in the sense that we introduce a new kind of local cloning operation to generate two W- type states between these partners from a W-type state initially shared by them.
We analyze a possibility of using the two qubit output state from Buzek-Hillery quantum copying machine (not necessarily universal quantum cloning machine) as a teleportation channel. We show that there is a range of values of the machine parameter $ξ$ for which the two qubit output state is entangled and violates Bell-CHSH inequality and for a different range it remains entangled but does not violate Bell-CHSH inequality. Further we observe that for certain values of the machine parameter the two-qubit mixed state can be used as a teleportation channel. The use of the output state from the Buzek-Hillery cloning machine as a teleportation channel provides an additional appeal to the cloning machine and motivation of our present work.
In this work we have introduced two party games with respective winning conditions. One cannot win these games deterministically in the classical world if they are not allowed to communicate at any stage of the game. Interestingly we find out that in quantum world, these winning conditions can be achieved if the players share an entangled state. We also introduced a game which is impossible to win if the players are not allowed to communicate in classical world (both probabilistically and deterministically), yet there exists a perfect quantum strategy by following which, one can attain the winning condition of the game.
In this work we investigate the problem of secretly broadcasting five qubit entangled state between three different partners We implement the protocol described in ref [16] on three particle W-state shared by three distant partners Alice,Bob and Charlie. The problem is interesting in the sense it is the first attempt to broadcast five qubit entangled state between three parties.
In this work, we introduce a special kind of quantum cloning machine called Hybrid quantum cloning machine. The introduced Hybrid quantum cloning machine or transformation is nothing but a combination of pre-existing quantum cloning transformations. In this sense it creates its own identity in the field of quantum cloners. Hybrid quantum cloning machine can be of two types: (i) State dependent and (ii) State independent or Universal. We study here the above two types of Hybrid quantum cloning machines. Later we will show that the state dependent hybrid quantum-cloning machine can be applied on only four input states. We will also find in this paper another asymmetric universal quantum cloning machine constructed from the combination of optimal universal B-H quantum cloning machine and universal anti-cloning machine. The fidelities of the two outputs are different and their values lie in the neighborhood of ${5/6} $
It is known that if one could clone an arbitrary quantum state one could send signal faster than the speed of light. However it remains interesting to see that if one can perfectly self replicate an arbitrary quantum state, does it violate the no signalling principle? Here we see that perfect self replication would also lead to superluminal signalling.
In this letter, we show the impossibility of the general operation introduced by Pati [3] using two different but consistent principles (i) no-signalling (ii) non increase of entanglement under LOCC.
In this work, we show that 'splitting of quantum information' [6] is an impossible task from three different but consistent principles of unitarity of Quantum Mechanics, no-signalling condition and non increase of entanglement under Local Operation and Classical Communication.
In this work we show that one cannot use non-local resources for probabilistic signalling even if one can delete a quantum state with the help of probabilistic quantum deletion machine. Here we find that probabilistic quantum deletion machine is not going to help us in identifying two statistical mixture at remote location. Also we derive the bound on deletion probability from no-signalling condition.
We know that we cannot split the information encoded in two non-orthogonal qubits into complementary parts deterministically. Here we show that each of the copies of the state randomly selected from a set of non orthogonal linearly independent states, splitting of quantum information can not be done even probabilistically. Here in this work we also show that under certain restricted conditions, we can probabilistically split the quantum information encoded in a qubit.
In this work,We investigate the problem of secretly broadcasting of three-qubit entangled state between two distant partners. The interesting feature of this problem is that starting from two particle entangled state shared between two distant partners we find that the action of local cloner on the qubits and the measurement on the machine state vector generates three-qubit entanglement between them. The broadcasting of entanglement is made secret by sending the measurement result secretly using cryptographic scheme based on orthogonal states. Further we show that this idea can be extended to generate three particle entangled state between three distant partners.
Suppose we are given an entangled pair and then one can ask how well we can produce two entangled pairs starting from a given entangled pair using only local operations. To give response of the above asked question, we study broadcasting of entanglement using state dependent quantum cloning machine as a local copier. We show that the length of the interval for probability-amplitude-squared for broadcasting of entanglement using state dependent cloner can be made larger than the length of the interval for probability-amplitude-squared for broadcasting entanglement using state independent cloner. Further we show that there exists local state dependent cloner which gives better quality copy (in terms of average fidelity) of an entangled pair than the local universal cloner.
In this work we study the quantum deletion machine with two transformers and show that the deletion machine with single transformer performs better than the deletion machine with more than two transformers. We also observe that the fidelity of deletion depends on the blank state used in the deleter and so for different blank state the fidelity is different. Further, we study the Pati-Braunsein deleter with transformer.