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Asymmetric broadcasting of entanglement and correlations

Aditya Jain, Indranil Chakrabarty, Sourav Chatterjee

Published Feb 7, 2017• 0 citations
OpenAlex

Abstract

In this work, we exhaustively investigate $1 \rightarrow 2$ local and non local broadcasting of entanglement and correlations (optimal and non-optimal) using asymmetric Pauli cloners, with the most general two qubit state as a resource. We exemplify the broadcasting of entanglement using Maximally Entangled Mixed States and demostrate the variation of broadcasting range with the amount of entanglement in resource state as well as the asymmetry in the cloner. We show that it is impossible to optimally broadcast quantum correlations that go beyond entanglement (Geometric Discord) with the help of these asymmetric Pauli cloning machines. We introduce the concept of asymmetry in correlations to quantify the degree of variation in the amount of correlation present in the output pairs obtained after broadcasting. We also study the problem of $1 \rightarrow 3$ broadcasting of entanglement using non-maximally entangled state (NME) as a resource. We adopt two different strategies : successive application of $1 \rightarrow 2$ optimal cloning machines and application of $1 \rightarrow 3$ optimal cloning machines. Interestingly, we show that $1 \rightarrow 3$ optimal cloner does a better job at broadcasting than the successive application of $1 \rightarrow 2$ cloners. Finally, we create an example to show that there are local unitaries, which when applied on non-maximally entangled state locally give us a better range of broadcasting, that surpasses the best possible range obtained using cloning machines. This result opens up a new direction in exploration of methods to perform broadcasting which may outperform standard broadcasting strategies implemented through cloning transformations.

Related papers

Asymmetric broadcasting of quantum correlations

Aditya Jain, Indranil Chakrabarty, Sourav Chatterjee

In this work, we exhaustively investigate $1\ensuremath{\rightarrow}2$ local and nonlocal broadcasting of entanglement as well as correlations beyond entanglement (geometric discord) using asymmetric Pauli cloners with the most general two-qubit state as the resource. We exemplify asymmetric broadcasting of entanglement using ``maximally entangled mixed states.'' We demonstrate the variation of broadcasting range with the amount of entanglement present in the resource state as well as with the asymmetry in the cloner. We show that it is impossible to optimally broadcast geometric discord with the help of these asymmetric Pauli cloning machines. We also study the problem of $1\ensuremath{\rightarrow}3$ broadcasting of entanglement using nonmaximally entangled state as the resource. For this task, we introduce a method we call successive broadcasting which involves application of $1\ensuremath{\rightarrow}2$ optimal cloning machines multiple times. We compare and contrast the performance of this method with the application of direct $1\ensuremath{\rightarrow}3$ optimal cloning machines. We show that $1\ensuremath{\rightarrow}3$ optimal cloner does a better job at broadcasting than the successive application of $1\ensuremath{\rightarrow}2$ cloners and the successive method can be beneficial in the absence of $1\ensuremath{\rightarrow}3$ cloners. We also bring out the fundamental difference between the tasks of cloning and broadcasting in the final part of the paper. We create examples to show that there exist local unitaries which can be employed to give a better range for broadcasting. Such unitary operations are not only economical, but also surpass the best possible range obtained using existing cloning machines enabling broadcasting of lesser entangled states. This result opens up a direction in exploration of methods to facilitate broadcasting which may outperform the standard strategies implemented through cloning transformations.

arXiv:1702.02123•Physical Review A•Feb 13, 2019•10 citations

Broadcasting of quantum correlations: Possibilities and impossibilities

Sourav Chatterjee, Sk Sazim, Indranil Chakrabarty

In this work, we extensively study the problem of broadcasting of quantum correlations (QCs). This includes broadcasting of quantum entanglement as well as correlations that go beyond the notion of entanglement (QCsbE). It is quite well known from the ``no-broadcasting theorem'' that perfect broadcasting of QCs is not possible. However, it does not rule out the possibility of partial broadcasting of QCs where we can get lesser correlated states from a given correlated state. In order to have a holistic view of broadcasting, we investigate this problem by starting with a most general representation of two qubit mixed states in terms of the Bloch vectors. As a cloning transformation we have used universal symmetric optimal Buzek-Hillery (BH) cloner both locally and nonlocally. Unlike entanglement, we find that it is impossible to broadcast QCsbE optimally. Lastly, we generalize these results for any symmetric or asymmetric cloning machines as well. This result brings out a fundamental difference between the correlations defined from the perspective of entanglement and the correlations measure which claims to go beyond entanglement.

arXiv:1411.4397•Physical Review A•Apr 7, 2016•15 citations

Broadcasting of quantum correlations in qubit-qudit systems

Rounak Mundra, Dhrumil Patel, Indranil Chakrabarty +2 more

Quantum mechanical properties like entanglement, discord, and coherence act as fundamental resources in various quantum information processing tasks. Consequently, the technique of generating more resources from a few, typically termed as broadcasting, serves as a promising candidate for the design of quantum networks. One way to broadcast resources could be using a cloning operation. In this article, broadcasting of quantum resources beyond $2\ensuremath{\bigotimes}2$ systems is investigated. In particular, in $2\ensuremath{\bigotimes}3$ dimensions, a class of states not useful for broadcasting of entanglement is characterized considering an optimal universal Heisenberg cloning machine. The broadcasting ranges for maximally entangled mixed states and two-parameter class of states are obtained to exemplify our protocol. A significant derivative of our protocol is that the cloning operation generates a qutrit ($3\ensuremath{\bigotimes}3$) entangled pair with positive partial transpose on one of the local sides, and an absolutely separable qubit ($2\ensuremath{\bigotimes}2$) pair on the other side of the input bipartite $2\ensuremath{\bigotimes}3$-dimensional resource state. Moving beyond entanglement, in $2\ensuremath{\bigotimes}d$ dimensions, the impossibility to optimally broadcast quantum discord and quantum coherence (${l}_{1}$ norm) is established. However, some significant illustrations are provided to highlight that nonoptimal broadcasting of discord and coherence is still possible.

arXiv:1807.11002•Physical Review A•Oct 18, 2019•7 citations

State Dependent and Independent cloner: Cloning and Broadcasting

Shukla, Manish Kumar, Indranil Chakrabarty, Sourav Chatterjee

In this work, we extensively study the problem of broadcasting of entanglement. In the first part of the work, we reconceptualize the idea of state dependent quantum cloning machine, and in that process we introduce different types of state dependent cloners like static and dynamic state dependent cloners. We derive the conditions under which we can make these cloners independent of the input state. In the broadcasting part, as our resource initial state, we start with general two qubit state and consider specific examples like, non maximally entangled state (NME), Werner like state (WS), and Bell diagonal state (BDS). We apply both state dependent/ state independent cloners, both locally and non-locally, in each of these cases. Incidentally, we find several instances where state dependent cloners outperform state independent cloners in broadcasting. This work gives us a holistic view on the broadcasting of entanglement in various two qubit states, when we have an almost exhaustive sets of cloning machines in our arsenal

arXiv:1511.05796•Nov 18, 2015•0 citations

Two-qubit quantum cloning machine and quantum correlation broadcasting

Azam Kheirollahi, Hamidreza Mohammadi, Seyed Javad Akhtarshenas

Due to the axioms of quantum mechanics, perfect cloning of an unknown quantum state is impossible. But since imperfect cloning is still possible, a question arises: ``Is there an optimal quantum cloning machine?'' Buzek and Hillery answered this question and constructed their famous B-H quantum cloning machine. The B-H machine clones the state of an arbitrary single qubit in an optimal manner and hence it is universal. Generalizing this machine for a two-qubit system is straightforward, but during this procedure, except for product states, this machine loses its universality and becomes a state-dependent cloning machine. In this paper, we propose some classes of optimal universal local quantum state cloners for a particular class of two-qubit systems, more precisely, for a class of states with known Schmidt basis. We then extend our machine to the case that the Schmidt basis of the input state is deviated from the local computational basis of the machine. We show that more local quantum coherence existing in the input state corresponds to less fidelity between the input and output states. Also we present two classes of a state-dependent local quantum copying machine. Furthermore, we investigate local broadcasting of two aspects of quantum correlations, i.e., quantum entanglement and quantum discord, defined, respectively, within the entanglement-separability paradigm and from an information-theoretic perspective. The results show that although quantum correlation is, in general, very fragile during the broadcasting procedure, quantum discord is broadcasted more robustly than quantum entanglement.

arXiv:1604.04995•Physical Review A•Nov 9, 2016•1 citation

Analysis of Quantum Correlations Obtained Using Local Optimal Universal Asymmetric Cloners

Cătălina Cîrneci, Iulia Ghiu

We apply the local optimal universal asymmetric cloning machine on an initially pure entangled state of two qubits. As output, we obtain two final states which present quantum correlations. We analyze three types of quantum correlations among the final states, namely, concurrence, quantum discord, and consonance. A detailed comparison between concurrence, quantum discord, and consonance is made, and we find that consonance is greater than quantum discord, which is in turn greater than concurrence.

Entropy•Dec 23, 2022•0 citations
In this work, we exhaustively investigate 1→21 \rightarrow 21→2 local and non local broadcasting of entanglement and correlations (optimal and non-optimal) using asymmetric Pauli cloners, with the most general two qubit state as a resource. We exemplify the broadcasting of entanglement using Maximally Entangled Mixed States and demostrate the variation of broadcasting range with the amount of entanglement in resource state as well as the asymmetry in the cloner. We show that it is impossible to optimally broadcast quantum correlations that go beyond entanglement (Geometric Discord) with the help of these asymmetric Pauli cloning machines. We introduce the concept of asymmetry in correlations to quantify the degree of variation in the amount of correlation present in the output pairs obtained after broadcasting. We also study the problem of 1→31 \rightarrow 31→3 broadcasting of entanglement using non-maximally entangled state (NME) as a resource. We adopt two different strategies : successive application of 1→21 \rightarrow 21→2 optimal cloning machines and application of 1→31 \rightarrow 31→3 optimal cloning machines. Interestingly, we show that 1→31 \rightarrow 31→3 optimal cloner does a better job at broadcasting than the successive application of 1→21 \rightarrow 21→2 cloners. Finally, we create an example to show that there are local unitaries, which when applied on non-maximally entangled state locally give us a better range of broadcasting, that surpasses the best possible range obtained using cloning machines. This result opens up a new direction in exploration of methods to perform broadcasting which may outperform standard broadcasting strategies implemented through cloning transformations.
In this work, we exhaustively investigate $1\ensuremath{\rightarrow}2$ local and nonlocal broadcasting of entanglement as well as correlations beyond entanglement (geometric discord) using asymmetric Pauli cloners with the most general two-qubit state as the resource. We exemplify asymmetric broadcasting of entanglement using ``maximally entangled mixed states.'' We demonstrate the variation of broadcasting range with the amount of entanglement present in the resource state as well as with the asymmetry in the cloner. We show that it is impossible to optimally broadcast geometric discord with the help of these asymmetric Pauli cloning machines. We also study the problem of $1\ensuremath{\rightarrow}3$ broadcasting of entanglement using nonmaximally entangled state as the resource. For this task, we introduce a method we call successive broadcasting which involves application of $1\ensuremath{\rightarrow}2$ optimal cloning machines multiple times. We compare and contrast the performance of this method with the application of direct $1\ensuremath{\rightarrow}3$ optimal cloning machines. We show that $1\ensuremath{\rightarrow}3$ optimal cloner does a better job at broadcasting than the successive application of $1\ensuremath{\rightarrow}2$ cloners and the successive method can be beneficial in the absence of $1\ensuremath{\rightarrow}3$ cloners. We also bring out the fundamental difference between the tasks of cloning and broadcasting in the final part of the paper. We create examples to show that there exist local unitaries which can be employed to give a better range for broadcasting. Such unitary operations are not only economical, but also surpass the best possible range obtained using existing cloning machines enabling broadcasting of lesser entangled states. This result opens up a direction in exploration of methods to facilitate broadcasting which may outperform the standard strategies implemented through cloning transformations.
In this work, we extensively study the problem of broadcasting of quantum correlations (QCs). This includes broadcasting of quantum entanglement as well as correlations that go beyond the notion of entanglement (QCsbE). It is quite well known from the ``no-broadcasting theorem'' that perfect broadcasting of QCs is not possible. However, it does not rule out the possibility of partial broadcasting of QCs where we can get lesser correlated states from a given correlated state. In order to have a holistic view of broadcasting, we investigate this problem by starting with a most general representation of two qubit mixed states in terms of the Bloch vectors. As a cloning transformation we have used universal symmetric optimal Buzek-Hillery (BH) cloner both locally and nonlocally. Unlike entanglement, we find that it is impossible to broadcast QCsbE optimally. Lastly, we generalize these results for any symmetric or asymmetric cloning machines as well. This result brings out a fundamental difference between the correlations defined from the perspective of entanglement and the correlations measure which claims to go beyond entanglement.
Quantum mechanical properties like entanglement, discord, and coherence act as fundamental resources in various quantum information processing tasks. Consequently, the technique of generating more resources from a few, typically termed as broadcasting, serves as a promising candidate for the design of quantum networks. One way to broadcast resources could be using a cloning operation. In this article, broadcasting of quantum resources beyond $2\ensuremath{\bigotimes}2$ systems is investigated. In particular, in $2\ensuremath{\bigotimes}3$ dimensions, a class of states not useful for broadcasting of entanglement is characterized considering an optimal universal Heisenberg cloning machine. The broadcasting ranges for maximally entangled mixed states and two-parameter class of states are obtained to exemplify our protocol. A significant derivative of our protocol is that the cloning operation generates a qutrit ($3\ensuremath{\bigotimes}3$) entangled pair with positive partial transpose on one of the local sides, and an absolutely separable qubit ($2\ensuremath{\bigotimes}2$) pair on the other side of the input bipartite $2\ensuremath{\bigotimes}3$-dimensional resource state. Moving beyond entanglement, in $2\ensuremath{\bigotimes}d$ dimensions, the impossibility to optimally broadcast quantum discord and quantum coherence (l1{l}_{1}l1​ norm) is established. However, some significant illustrations are provided to highlight that nonoptimal broadcasting of discord and coherence is still possible.
In this work, we extensively study the problem of broadcasting of entanglement. In the first part of the work, we reconceptualize the idea of state dependent quantum cloning machine, and in that process we introduce different types of state dependent cloners like static and dynamic state dependent cloners. We derive the conditions under which we can make these cloners independent of the input state. In the broadcasting part, as our resource initial state, we start with general two qubit state and consider specific examples like, non maximally entangled state (NME), Werner like state (WS), and Bell diagonal state (BDS). We apply both state dependent/ state independent cloners, both locally and non-locally, in each of these cases. Incidentally, we find several instances where state dependent cloners outperform state independent cloners in broadcasting. This work gives us a holistic view on the broadcasting of entanglement in various two qubit states, when we have an almost exhaustive sets of cloning machines in our arsenal
Due to the axioms of quantum mechanics, perfect cloning of an unknown quantum state is impossible. But since imperfect cloning is still possible, a question arises: ``Is there an optimal quantum cloning machine?'' Buzek and Hillery answered this question and constructed their famous B-H quantum cloning machine. The B-H machine clones the state of an arbitrary single qubit in an optimal manner and hence it is universal. Generalizing this machine for a two-qubit system is straightforward, but during this procedure, except for product states, this machine loses its universality and becomes a state-dependent cloning machine. In this paper, we propose some classes of optimal universal local quantum state cloners for a particular class of two-qubit systems, more precisely, for a class of states with known Schmidt basis. We then extend our machine to the case that the Schmidt basis of the input state is deviated from the local computational basis of the machine. We show that more local quantum coherence existing in the input state corresponds to less fidelity between the input and output states. Also we present two classes of a state-dependent local quantum copying machine. Furthermore, we investigate local broadcasting of two aspects of quantum correlations, i.e., quantum entanglement and quantum discord, defined, respectively, within the entanglement-separability paradigm and from an information-theoretic perspective. The results show that although quantum correlation is, in general, very fragile during the broadcasting procedure, quantum discord is broadcasted more robustly than quantum entanglement.
We apply the local optimal universal asymmetric cloning machine on an initially pure entangled state of two qubits. As output, we obtain two final states which present quantum correlations. We analyze three types of quantum correlations among the final states, namely, concurrence, quantum discord, and consonance. A detailed comparison between concurrence, quantum discord, and consonance is made, and we find that consonance is greater than quantum discord, which is in turn greater than concurrence.