Optimal Entanglement Enhancement for mixed states

The resource theory of superposition is a generalization of coherence theory. A rigorous framework for quantifying superposition of linear independent states has been given by previous studies. In this paper, the optimal superposition enhancement of a mixed state is studied. Based on the $l_{1}$ measure of superposition the optimal superposition enhancement value of a mixed state can be obtained under the stochastic diagonal superposition-free operations(or incomplete diagonal superposition-free operations). In addition, the optimal probability corresponding to the optimal superposition enhancement value of a mixed state is also discussed. The results show that although the superposition-free operations can decrease the superposition of a state, the superposition enhancement of a state is possible, a single mixed state can be probabilistically transformed into another state with higher superposition than before by superposition-free operations. These studies will give us a better understanding of the superposition manipulation and the resource theory of superposition.The resource theory of superposition is a generalization of coherence theory. A rigorous framework for quantifying superposition of linear independent states has been given by previous studies. In this paper, the optimal superposition enhancement of a mixed state is studied. Based on the $l_{1}$ measure of superposition the optimal superposition enhancement value of a mixed state can be obtained under the stochastic diagonal superposition-free operations(or incomplete diagonal superposition-free operations). In addition, the optimal probability corresponding to the optimal superposition enhancement value of a mixed state is also discussed. The results show that although the superposition-free operations can decrease the superposition of a state, the superposition enhancement of a state is possible, a single mixed state can be probabilistically transformed into another state with higher superposition than before by superposition-free operations. These studies will give us a better understanding of the superposition manipulation and the resource theory of superposition.

Results in PhysicsJan 1, 20221 citation

Robust entanglement measure for mixed quantum states

Dharmaraj Ramachandran, Aditya Dubey, Subrahmanyam S. G. Mantha +1 more

arXiv:2412.08304Quantum Information ProcessingJul 31, 20252 citations

Entanglement estimation in non-optimal qubit states

Stefano Scali, Roberto Franzosi

arXiv:1811.05598Annals of PhysicsOct 26, 20195 citations

Optimal enhancement of the fidelity of two qubits.

Frank Verstraete, Henri Verschelde

We consider a single copy of a mixed state of two qubits and prove tight lower and upper bounds for its fidelity in terms of its concurrence or negativity. Next we derive the optimal filtering operations and the optimal trace-preserving local operations assisted by classical communication (LOCC) such as to maximize the fidelity of a given copy of a mixed state of two qubits. The optimal LOCC operations turn out to be very simple and implementable by 1-LOCC protocols, and always yield a fidelity larger then 1/2 if the original state was entangled.We consider a single copy of a mixed state of two qubits and prove tight lower and upper bounds for its fidelity in terms of its concurrence or negativity. Next we derive the optimal filtering operations and the optimal trace-preserving local operations assisted by classical communication (LOCC) such as to maximize the fidelity of a given copy of a mixed state of two qubits. The optimal LOCC operations turn out to be very simple and implementable by 1-LOCC protocols, and always yield a fidelity larger then 1/2 if the original state was entangled.

Physical Review AJan 1, 20026 citations

Optimal Local Filtering Operation for Enhancing Quantum Entanglement

Nina Sukhodoeva, Zhaofeng Su

Jan 1, 20230 citations

Optimal Entanglement Enhancement for Mixed States

Adrian Kent, Noah Linden, Serge Massar

We consider the actions of protocols involving local quantum operations and classical communication (LQCC) on a single system consisting of two separated qubits. We give a complete description of the orbits of the space of states under LQCC and characterize the representatives with maximal entanglement of formation. We thus obtain a LQCC entanglement concentration protocol for a single given state (pure or mixed) of two qubits which is optimal in the sense that the protocol produces, with nonzero probability, a state of maximal possible entanglement of formation. This defines a new entanglement measure, the maximum extractable entanglement.We consider the actions of protocols involving local quantum operations and classical communication (LQCC) on a single system consisting of two separated qubits. We give a complete description of the orbits of the space of states under LQCC and characterize the representatives with maximal entanglement of formation. We thus obtain a LQCC entanglement concentration protocol for a single given state (pure or mixed) of two qubits which is optimal in the sense that the protocol produces, with nonzero probability, a state of maximal possible entanglement of formation. This defines a new entanglement measure, the maximum extractable entanglement.

arXiv:quant-ph/9902022Physical Review LettersSep 27, 199970 citations

l_{1}

measure of superposition the optimal superposition enhancement value of a mixed state can be obtained under the stochastic diagonal superposition-free operations(or incomplete diagonal superposition-free operations). In addition, the optimal probability corresponding to the optimal superposition enhancement value of a mixed state is also discussed. The results show that although the superposition-free operations can decrease the superposition of a state, the superposition enhancement of a state is possible, a single mixed state can be probabilistically transformed into another state with higher superposition than before by superposition-free operations. These studies will give us a better understanding of the superposition manipulation and the resource theory of superposition.