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Register a new userA Decomposition Form of the Werner State
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In this report, a scheme different from the PT and Wootters concurrence is developed to acquire a criterion to investigate the bipartite separability of the Werner state.
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The decompositions of separable Werner state, and also isotropic state, are well-known tough issues in quantum information theory, in this work we investigate them in the Bloch vector representation, exploring the symmetric informationally complete positive operator-valued measure (SIC-POVM) in the Hilbert space. We successfully get the decomposition for arbitrary $Ntimes N$ Werner state in terms of regular simplexes. Meanwhile, the decomposition of isotropic state is found to be related to the decomposition of Werner state via partial transposition. It is interesting to note that in the large $N$ limit, while the Werner states are either separable or non-steerably entangled, most of the isotropic states tend to be steerable.
We study the average quantum coherence over the pure state decompositions of a mixed quantum state. An upper bound of the average quantum coherence is provided and sufficient conditions for the saturation of the upper bound are shown. These sufficient conditions always hold for two and three dimensional systems. This provides a tool to estimate the average coherence experimentally by measuring only the diagonal elements, which remarkably requires less measurements compared with state tomography. We then describe the pure state decompositions of qubit state in Bloch sphere geometrically. For any given qubit state, the optimal pure state decomposition achieving the maximal average quantum coherence as well as three other pure state decompositions are shown in the Bloch sphere. The order relations among their average quantum coherence are invariant for any coherence measure. The results presented in this paper are universal and suitable for all coherence measures.
The verification of quantum entanglement under the influence of realistic noise and decoherence is crucial for the development of quantum technologies. Unfortunately, a full entanglement characterization is generally not possible with most entanglement criteria such as entanglement witnesses or the partial transposition criterion. In particular, so called bound entanglement cannot be certified via the partial transposition criterion. Here we present the full entanglement verification of dephased qubit and qutrit Werner states via entanglement quasiprobabilities. Remarkably, we are able to reveal bound entanglement for noisy-mixed states in the qutrit case. This example demonstrates the strength of the entanglement quasiprobabilities for verifying the full entanglement of quantum states suffering from noise.
We study nonclassical correlations beyond entanglement in a family of two-mode non-Gaussian states which represent the continuous-variable counterpart of two-qubit Werner states. We evaluate quantum discord and other quantumness measures obtaining exact analytical results in special instances, and upper and lower bounds in the general case. Non-Gaussian measurements such as photon counting are in general necessary to solve the optimization in the definition of quantum discord, whereas Gaussian measurements are strictly suboptimal for the considered states. The gap between Gaussian and optimal non-Gaussian conditional entropy is found to be proportional to a measure of non-Gaussianity in the regime of low squeezing, for a subclass of continuous-variable Werner states. We further study an example of a non-Gaussian state which is positive under partial transposition, and whose nonclassical correlations stay finite and small even for infinite squeezing. Our results pave the way to a systematic exploration of the interplay between nonclassicality and non-Gaussianity in continuous-variable systems, in order to gain a deeper understanding of -and to draw a bigger advantage from- these two important resources for quantum technology.
We realize Landau-Streater (LS) and Werner-Holevo (WH) quantum channels for qutrits on the IBM quantum computers. These channels correspond to interaction between the qutrit and its environment that result in the globally unitarily covariant qutrit transformation violating multiplicativity of the maximal $p$-norm. Our realization of LS and WH channels is based on embedding qutrit states into states of two qubits and using single-qubit and two-qubit CNOT gates to implement the specific interaction. We employ the standard quantum gates hence the developed algorithm suits any quantum computer. We run our algorithm on a 5-qubit and a 20-qubit computer as well as on a simulator. We quantify the quality of the implemented channels comparing their action on different input states with theoretical predictions. The overall efficiency is quantified by fidelity between the theoretical and experimental Choi states implemented on the 20-qubit computer.
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