About 15 years ago, we (Heinz-Dietrich Doebner and I) proposed a special type of nonlinear modification of the usual Schrödinger time-evolution equation in quantum mechanics. Our equation was motivated by certain unitary representations of the group of diffeomorphisms of physical space, in the framework of either nonrelativistic local current algebra or quantum Borel kinematics. Subsequently, we developed this and related approaches to nonlinearity in quantum mechanics considerably further, to incorporate theories of measurement, groups of nonlinear gauge transformations, symmetry and invariance properties, unification of a large family of nonlinear perturbations, and possible physical contexts for quantum nonlinearity. Some of our results and highlights of some open questions are summarized.About 15 years ago, we (Heinz-Dietrich Doebner and I) proposed a special type of nonlinear modification of the usual Schrödinger time-evolution equation in quantum mechanics. Our equation was motivated by certain unitary representations of the group of diffeomorphisms of physical space, in the framework of either nonrelativistic local current algebra or quantum Borel kinematics. Subsequently, we developed this and related approaches to nonlinearity in quantum mechanics considerably further, to incorporate theories of measurement, groups of nonlinear gauge transformations, symmetry and invariance properties, unification of a large family of nonlinear perturbations, and possible physical contexts for quantum nonlinearity. Some of our results and highlights of some open questions are summarized.

Physics of Atomic NucleiMay 1, 20087 citations

Mutual Restriction between Concurrence and Intrinsic Concurrence for Arbitrary Two-Qubit States

A-Long Zhou, Dong Wang, Xiao‐Gang Fan +2 more

Concurrence is viewed as the most commonly approach for quantifying entanglement of two-qubit states, while intrinsic concurrence contains concurrence of four pure states consisting of a special pure state ensemble concerning an arbitrary two-qubit state. Thus, a natural question arises: Whether there is a specified relation between them. We firstly examine the relation between concurrence and intrinsic concurrence for the maximally nonlocal mixed state under a special unitary operation, which is not yet rigorously proved. In order to obtain a general result, we investigate the relation between concurrence and intrinsic concurrence using randomly generated two-qubit states, and derive an inequality relation between them. Finally, we take into account the relation between concurrence and intrinsic concurrence in open systems, and reveal the ratio of the two quantum resources, which is only correlated with the experiencing channels.Concurrence is viewed as the most commonly approach for quantifying entanglement of two-qubit states, while intrinsic concurrence contains concurrence of four pure states consisting of a special pure state ensemble concerning an arbitrary two-qubit state. Thus, a natural question arises: Whether there is a specified relation between them. We firstly examine the relation between concurrence and intrinsic concurrence for the maximally nonlocal mixed state under a special unitary operation, which is not yet rigorously proved. In order to obtain a general result, we investigate the relation between concurrence and intrinsic concurrence using randomly generated two-qubit states, and derive an inequality relation between them. Finally, we take into account the relation between concurrence and intrinsic concurrence in open systems, and reveal the ratio of the two quantum resources, which is only correlated with the experiencing channels.

Chinese Physics LettersNov 1, 20203 citations

A Relativity Paradox

Arthur Stanley Eddington

NatureDec 1, 19224 citations

Special relativity from quantum mechanics?

Sibel Başkal, Young S Kim, Marilyn E. Noz

Institute of Physics eBooksMay 1, 20210 citations

Resource Theory of Special Antiunitary Asymmetry

Kaifeng Bu, Heng Fan, Arun Kumar Pati +1 more

We propose the resource theory of a special antiunitary asymmetry in quantum theory. The notion of antiunitary asymmetry, in particular, ${\cal PT}$ -asymmetry is different from the usual resource theory for asymmetry about unitary representation of a symmetry group, as the ${\cal PT}$ operator is an antiunitary operator with ${\cal P}$ being any self-inverse unitary and ${\cal T}$ being the time-reversal operations. Here, we introduce the ${\cal PT}$ -symmetric states, ${\cal PT}$ -covariant operations and ${\cal PT}$ -asymmetry measures. For single qubit system, we find duality relations between the ${\cal PT}$ -asymmetry measures and the coherence. Moreover, for two-qubit states we prove the duality relations between the ${\cal PT}$ -asymmetry measures and entanglement measure such as the concurrence. This gives a resource theoretic interpretation to the concurrence which is lacking till today. Thus, the ${\cal PT}$ -asymmetry measure and entanglement can be viewed as two sides of an underlying resource. Finally, the ${\cal PT}$ -symmetric dynamics is discussed and some open questions are addressed.We propose the resource theory of a special antiunitary asymmetry in quantum theory. The notion of antiunitary asymmetry, in particular, ${\cal PT}$-asymmetry is different from the usual resource theory for asymmetry about unitary representation of a symmetry group, as the ${\cal PT}$ operator is an antiunitary operator with ${\cal P}$ being any self-inverse unitary and ${\cal T}$ being the time-reversal operations. Here, we introduce the ${\cal PT}$-symmetric states, ${\cal PT}$-covariant operations and ${\cal PT}$-asymmetry measures. For single qubit system, we find duality relations between the ${\cal PT}$-asymmetry measures and the coherence. Moreover, for two-qubit states we prove the duality relations between the ${\cal PT}$-asymmetry measures and entanglement measure such as the concurrence. This gives a resource theoretic interpretation to the concurrence which is lacking till today. Thus, the ${\cal PT}$-asymmetry measure and entanglement can be viewed as two sides of an underlying resource. Finally, the ${\cal PT}$-symmetric dynamics is discussed and some open questions are addressed.

arXiv:1610.09646Oct 30, 20164 citations

We propose the resource theory of a special antiunitary asymmetry in quantum theory. The notion of antiunitary asymmetry, in particular,

{\cal PT}

-asymmetry is different from the usual resource theory for asymmetry about unitary representation of a symmetry group, as the

{\cal PT}

operator is an antiunitary operator with

{\cal P}

being any self-inverse unitary and

{\cal T}

being the time-reversal operations. Here, we introduce the

{\cal PT}

-symmetric states,

{\cal PT}

-covariant operations and

{\cal PT}

-asymmetry measures. For single qubit system, we find duality relations between the

{\cal PT}

-asymmetry measures and the coherence. Moreover, for two-qubit states we prove the duality relations between the

{\cal PT}

-asymmetry measures and entanglement measure such as the concurrence. This gives a resource theoretic interpretation to the concurrence which is lacking till today. Thus, the

{\cal PT}

-asymmetry measure and entanglement can be viewed as two sides of an underlying resource. Finally, the

{\cal PT}

-symmetric dynamics is discussed and some open questions are addressed.