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Two-photon states entangled in continuous variables such as wavevector or frequency represent a powerful resource for quantum information protocols in higher-dimensional Hilbert spaces. At the same time, there is a problem of addressing separately the corresponding Schmidt modes. We propose a method of engineering two-photon spectral amplitude in such a way that it contains several non-overlapping Schmidt modes, each of which can be filtered losslessly. The method is based on spontaneous parametric down-conversion (SPDC) pumped by radiation with a comb-like spectrum. There are many ways of producing such a spectrum; here we consider the simplest one, namely passing the pump beam through a Fabry-Perot interferometer. For the two-photon spectral amplitude (TPSA) to consist of non-overlapping Schmidt modes, the crystal dispersion dependence, the length of the crystal, the Fabry-Perot free spectral range and its finesse should satisfy certain conditions. We experimentally demonstrate the control of TPSA through these parameters. We also discuss a possibility to realize a similar situation using cavity-based SPDC.
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An analogous model system for high-dimensional quantum entanglement is proposed, based on the angular and radial degrees of freedom of the improved Laguerre Gaussian mode. Experimentally, we observed strong violations of the Bell-CGLMP inequality for maximally non-separable states of dimension 2 through 10. The results for violations in classical non-separable state are in very good agreement with quantum instance, which illustrates that our scheme can be a useful platform to simulate high-dimensional non-local entanglement. Additionally, we found that the Bell measurements provide sufficient criteria for identifying mode separability in a high-dimensional space. Similar to the two-dimensional spin-orbit non-separable state, the proposed high-dimensional angular-radial non-separable state may provide promising applications for classical and quantum information processing.
Hybrid entangled states, having entanglement between different degrees-of-freedom (DoF) of a particle pair, are of great interest for quantum information science and communication protocols. Among different DoFs, the hybrid entangled states encoded with polarization and orbital angular momentum (OAM) allow the generation of qubit-qudit entangled states, macroscopic entanglement with very high quanta of OAM and improvement in angular resolution in remote sensing. Till date, such hybrid entangled states are generated by using a high-fidelity polarization entangled state and subsequent imprinting of chosen amount of OAM using suitable mode converters such as spatial light modulator in complicated experimental schemes. Given that the entangled sources have feeble number of photons, loss of photons during imprinting of OAM using diffractive optical elements limits the use of such hybrid state for practical applications. Here we report, on a simple experimental scheme to generate hybrid entangled state in polarization and OAM through direct transfer of classical non-separable state of the pump beam in parametric down conversion process. As a proof of principle, using local non-separable pump state of OAM mode l=3, we have produced quantum hybrid entangled state with entanglement witness parameter of W-1.25 violating by 8 standard deviation. The generic scheme can be used to produce hybrid entangled state between two photons differing by any quantum number through proper choice of non-separable state of the pump beam.
Absolute separable states is a kind of separable state that remain separable under the action of any global unitary transformation. These states may or may not have quantum correlation and these correlations can be measured by quantum discord. We find that the absolute separable states are useful in quantum computation even if it contains infinitesimal quantum correlation in it. Thus to search for the class of two-qubit absolute separable states with zero discord, we have derived an upper bound for $Tr(varrho^{2})$, where $varrho$ denoting all zero discord states. In general, the upper bound depends on the state under consideration but if the state belong to some particular class of zero discord states then we found that the upper bound is state independent. Later, it is shown that among these particular classes of zero discord states, there exist sub-classes which are absolutely separable. Furthermore, we have derived necessary conditions for the separability of a given qubit-qudit states. Then we used the derived conditions to construct a ball for $2otimes d$ quantum system described by $Tr(rho^{2})leq Tr(X^{2})+2Tr(XZ)+Tr(Z^{2})$, where the $2otimes d$ quantum system is described by the density operator $rho$ which can be expressed by block matrices $X,Y$ and $Z$ with $X,Zgeq 0$. In particular, for qubit-qubit system, we show that the newly constructed ball contain larger class of absolute separable states compared to the ball described by $Tr(rho^{2})leq frac{1}{3}$. Lastly, we have derived the necessary condition in terms of purity for the absolute separability of a qubit-qudit system under investigation.
In this paper, based on a matrix norm, we first present a ball of separable unnormalized states around the identity matrix for the bipartite quantum system, which is larger than the separable ball in Frobenius norm. Then the proposed ball is used to get not only simple sufficient conditions for the separability of pseudopure states and the states with strong positive partial transposes, but also a separable ball centered at the identity matrix for the multipartite quantum system.
Entangled states are undoubtedly an integral part of various quantum information processing tasks. On the other hand, absolutely separable states which cannot be made entangled under any global unitary operations are useless from the resource theoretic perspective, and hence identifying non-absolutely separable states can be an important issue for designing quantum technologies. Here we report that nonlinear witness operators provide significant improvements in detecting non-absolutely separable states over their linear analogs, by invoking examples of states in various dimensions. We also address the problem of closing detection loophole and find critical efficiency of detectors above which no fake detection of non-absolutely separable (non-absolutely positive partial transposed) states is possible.
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