Deletion of imperfect cloned copies (original) (raw)

Probabilistic cloning and deleting of quantum states

Physical Review A, 2002

We construct a probabilistic cloning and deleting machine which, taking several copies of an input quantum state, can output a linear superposition of multiple cloning and deleting states. Since the machine can perform cloning and deleting in a single unitary evolution, the probabilistic cloning and other cloning machines proposed in the previous literature can be thought of as special cases of our machine. A sufficient and necessary condition for successful cloning and deleting is presented, and it requires that the copies of an arbitrarily presumed number of the input states are linearly independent. This simply generalizes some results for cloning. We also derive an upper bound for the success probability of the cloning and deleting machine.

Extremal asymmetric universal cloning machines

2010

The trade-offs among various output fidelities of asymmetric universal cloning machines are investigated. First we find out all the attainable optimal output fidelities for the 1 to 3 asymmetric universal cloning machine and it turns out that there are two kinds of extremal machines which have to cooperate in order to achieve some of the optimal output fidelities. Second we construct a family of extremal cloning machines that includes the universal symmetric cloning machine as well as an asymmetric 1 to 1+N cloning machine for qudits with two different output fidelities such that the optimal trade-off between the measurement disturbance and state estimation is attained in the limit of infinite N.

Improving the fidelity of deletion

Physical Review A, 2006

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.

Distort one qubit from copying and deleting

Quantum Information Processing, 2012

Immeasurability of a quantum state has important consequence in practical implementation of quantum computers. Our purpose is to analyze the efficiency of the entangled output of Pati-Braunstein deleting machine or Wootters-Zurek quantum copying machine as a quantum channel. Interestingly we find that for special values of the input parameter the state does not violate the Bell's inequality. Moreover, we analyze the performances of the entangled output of Pati-Braunstein deleting after the Wootters-Zurek copying machine.

Quantum deletion: Beyond the no-deletion principle

Physical Review A, 2005

Suppose we are given two identical copies of an unknown quantum state and we wish to delete one copy from among the given two copies. The quantum no-deletion principle restricts us from perfectly deleting a copy but it does not prohibit us from deleting a copy approximately. Here we construct two types of a " universal quantum deletion machine" which approximately deletes a copy such that the fidelity of deletion does not depend on the input state. The two types of universal quantum deletion machines are (1) a conventional deletion machine described by one unitary operator and (2) a modified deletion machine described by two unitary operators. Here it is shown that modified deletion machine deletes a qubit with fidelity 4 3 , which is the maximum limit for deleting an unknown quantum state. In addition to this we also show that the modified deletion machine retains the qubit in the first mode with average fidelity 0.77 (approx.) which is slightly greater than the fidelity of measurement for two given identical state, showing how precisely one can determine its state [13]. We also show that the deletion machine itself is input state independent i.e. the information is not hidden in the deleting machine, and hence we can delete the information completely from the deletion machine.

Performance of quantum cloning and deleting machines over coherence

Quantum Information Processing, 2017

Coherence, being at the heart of interference phenomena, is found to be an useful resource in quantum information theory. Here we want to understand quantum coherence under the combination of two fundamentally dual processes, viz., cloning and deleting. We found the role of quantum cloning and deletion machines with the consumption and generation of quantum coherence. We establish cloning as a cohering process and deletion as a decohering process. Fidelity of the process will be shown to have connection with coherence generation and consumption of the processes.

Quantum Cloning and Deletion in Quantum Information Theory

emotional supports, entertainments, academic discussions and care they provided. This research has been supported and funded by Council of Scientific and Industrial Research, government of India, under project F.No.8/3(38)/2003-EMR-1, New Delhi. I would like to thank them for their confidence in me. Lastly, and most importantly, I feel a deep sense of gratitude to my Father and Mother who formed part of my vision and taught me the good things that really matter in life. They bore me, raised me, supported me, taught me and loved me. To them I dedicate this thesis.

Theoretical Study of the No-Cloning Theorem

We review the no-cloning theorem that relies on the properties of the quantum theory. Usually, the no-cloning theorem implies that two quantum states are identical or orthogonal if we allow a cloning to be on the two quantum states. Here, we rely on the maximum value of the square of an expected value. We may result in the fact that the two quantum states under consideration could not be orthogonal if we consider the maximum value of the square of the expected value. The no-cloning theorem may imply that the two quantum states under consideration may be identical if we consider the maximum value of the square of the expected value. The nocloning theorem itself has this character.

No-Cloning and No-Deleting Theorems through the Existence of Incomparable States Under LOCC

Quantum Information Processing, 2007

No-Cloning and No-Deleting theorems are verified with the constraint on local state transformations via the existence of incomparable states. Assuming the existence of exact cloning or deleting operation defined on a minimum number of two arbitrary states, an incomparable pair of states of the joint system between two parties can be made to compare under deterministic LOCC. We have restricted our proof with the assumption that the machine states of the cloning or deleting operations do not keep any information about the input states. We use the same setting to establish the no-cloning and no-deleting theorems via incomparability that supports the reciprocity of the two operations in their operational senses. The work associates the impossibility of operations with the evolution of an entangled system by LOCC.

Common Origin of No-Cloning and No-Deleting Principles Conservation of Information

Foundations of Physics, 2005

We discuss the role of the notion of information in the description of physical reality. We consider theories for which dynamics is linear with respect to stochastic mixing. We point out that the nocloning and no-deleting principles emerge in any such theory, if law of conservation of information is valid, and two copies contain more information than one copy. We then describe the quantum case from this point of view. This paper is dedicated to Asher Peres on the occasion of his seventieth birthday.