International Journal of Quantum Information

A quantum correlation ${{𝒬}}_w^x$ based on weak measurements for bipartite systems is introduced. It is shown that the product states do not contain this quantum correlation. Also, the necessary and sufficient condition for any two-qubit state becoming a product state is obtained. The quantum correlation ${{𝒬}}_w^x$ and other quantum correlation for two-qubit entangled pure state, Werner states and isotropic states are compared.

We propose a simple method for constructing positive operator-valued measures (POVMs) using any set of matrices which form an orthonormal basis for the space of complex matrices. Considering the orthonormal set of irreducible spherical tensors, we examine the properties of the construction on the $n+1$-dimensional subspace of the $2^n$-dimensional Hilbert space of $n$ qubits comprising the permutationally symmetric states. Using the notion of vectorization, the constructed POVMs are interpretable as projection operators in a higher-dimensional space. We then describe a method to physically realize the constructed POVMs for symmetric states using the Clebsch–Gordan decomposition of the tensor product of irreducible representations of the rotation group. We illustrate the proposed construction on a spin-1 system, and show that it is possible to generate entangled states from separable ones.

We consider a bipartite quantum system $S$ (including parties $A$ and $B$), interacting with an environment $E$ through a localized quantum dynamics ${{ℱ}}_{SE}$. We call a quantum dynamics ${{ℱ}}_{SE}$ localized if, e.g. the party $A$ is isolated from the environment and only $B$ interacts with the environment: ${{ℱ}}_{SE}=i{d}_A\otimes {{ℱ}}_{BE}$, where $i{d}_A$ is the identity map on the part $A$ and ${{ℱ}}_{BE}$ is a completely positive (CP) map on the both $B$ and $E$. We will show that the reduced dynamics of the system is also localized as ${{ℰ}}_S=i{d}_A\otimes {\overline{{ℰ}}}_B$, where ${\overline{{ℰ}}}_B$ is a CP map on $B$, if and only if the initial state of the system-environment is a Markov state. We then generalize this result to the two following cases: when both $A$ and $B$ interact with a same environment, and when each party interacts with its local environment.

Explicit separability of general two qubits density matrices is related to Lorentz transformations. We use the 4-dimensional form $R_{\mu ,\nu }(\mu ,\nu =0,1,2,3)$ of the Hilbert–Schmidt (HS) decomposition of the density matrix. For the generic case, in which Lorentz transformations diagonalize $R_{\mu ,\nu }$ into $s_0,s_1,s_2,s_3$, we give relations between the $s_{\mu }$ and the $R_{\mu ,\nu }$. In particular, we consider two cases: (a) Two qubits density matrices with one pair of linear terms in the HS decomposition. (b) Two qubits density matrices with two or three symmetric pairs of linear terms. Some of the theoretical results are demonstrated by numerical calculations. The four non-generic cases (which may be reduced to case (a) are analyzed and the non-generic property is related explicitly to Lorentz velocity $\beta =1$ which is not reachable physically.

In this work, we analyze two-flavor neutrino oscillations within the framework of quantum estimation theory (QET). We compute the quantum Fischer information (QFI) for the mixing angle $\theta$ and show that mass measurements are the ones that achieve optimal precision. We also study the Fischer information (FI) associated with flavor measurements and show that they are optimized at specific neutrino times-of-flight. Therefore, although the usual population measurement does not realize the precision limit set by the QFI, it can in principle be implemented with the best possible sensitivity to $\theta$. We investigate how these quantifiers relate to the single-particle, mode entanglement in neutrino oscillations. We demonstrate that this form of entanglement does not enhance either of them. In particular, our results show that in single-particle settings, entanglement is not directly connected with the enhancement of precision in metrological tasks.

We investigate the influence of one-body losses on the dynamics of squeezing and entanglement in two-mode Bose–Einstein condensates. We show that one-body losses play an important role in the dynamical process of generating squeezing and quantum entanglement. The stronger one-body losses induce smaller squeezing and lesser entanglement, but maintain in a longer time interval.

We investigate the dynamics of entanglement, quantum discord (QD) and state coherence in a bipartite and noninteracting spin-qutrits system under mixed classical noises. Specifically, the collective effects of static noise (SN) and random telegraphic noise (RTN) each being coupled with a marginal system, are analyzed. While the static noise models a non-Markovian environment, the dynamic noise can model both a Markovian or a non-Markovian environment, and both dynamics are studied. We show that quantum correlations and coherence may survive the noise degrading effects at sufficiently long time when the Markovian regime of the RTN is considered. Meanwhile, the opposite is found in the non-Markovian regime, wherein the nonmonotonic dynamics of quantum features avoid sudden death phenomena. However, the static noise is more fatal to the survival of quantum correlations and quantum state coherence as compared to the RTN.

A well-known feature of quantum mechanics is the secure exchange of secret bit strings which can then be used as keys to encrypt messages transmitted over any classical communication channel. It is demonstrated that this quantum key distribution allows a much more general and abstract access than commonly thought. The results include some generalizations of the Hilbert space version of quantum key distribution, but are based upon a general nonclassical extension of conditional probability. A special state-independent conditional probability is identified as origin of the superior security of quantum key distribution; this is a purely algebraic property of the quantum logic and represents the transition probability between the outcomes of two consecutive quantum measurements.