We report the creation of a wide range of quantum states with controllable degrees of entanglement and entropy using an optical two-qubit source based on spontaneous parametric down-conversion. The states are characterized using measures of entanglement and entropy determined from tomographically determined density matrices. The tangle-entropy plane is introduced as a graphical representation of these states, and the theoretic upper bound for the maximum amount of entanglement possible for a given entropy is presented. Such a combination of general quantum state creation and accurate characterization is an essential prerequisite for quantum device development.
We report the creation of a wide range of quantum states with controllable degrees of entanglement and entropy using an optical two-qubit source based on spontaneous parametric down-conversion. The states are characterized using measures of entanglement and entropy determined from tomographically determined density matrices. The tangle-entropy plane is introduced as a graphical representation of these states, and the theoretic upper bound for the maximum amount of entanglement possible for a given entropy is presented. Such a combination of general quantum state creation and accurate characterization is an essential prerequisite for quantum device development.
Using correlated photons from parametric down-conversion, we extend the boundaries of experimentally accessible two-qubit Hilbert space. Specifically, we have created and characterized maximally entangled mixed states that lie above the Werner boundary in the linear entropy-tangle plane. In addition, we demonstrate that such states can be efficiently concentrated, simultaneously increasing both the purity and the degree of entanglement. We investigate a previously unsuspected sensitivity imbalance in common state measures, i.e., the tangle, linear entropy, and fidelity.
Summary form only given. Entangled states of multi-particle systems are arguably the quintessential feature of quantum mechanics. In addition to their central role in discussions of non-local quantum correlations, they form the basis of quantum information, and enable such phenomena as quantum cryptography, quantum dense coding, teleportation, and quantum computation. Via the process of spontaneous parametric downconversion in a pair of nonlinear crystals, it is now possible to produce, with high efficiency, pairs of photons entangled in their polarisation degree of freedom. We can also control both the extent of entanglement and the purity of the state. Density matrices for states generated by this method, and measured using tomographic techniques, are shown.
In the case of mixed states ρAB of the composite system A ⊗ B, the previous relation generalizes to ρAB = ∑ k pkρ A k ⊗ρk , where pk are probabilities and ρk ’s (ρk ’s) are generic density matrix of the system A (B). The entanglement derives from “subtle” nonlocal correlations between the parts of a quantum system and combines three basic structural elements of quantum theory: the superposition principle, the quantum non-separability property and the exponential scaling of the state space with the number of partitions. This unique resource can be used to perform computational and cryptographic tasks otherwise impossible with classical systems. An entangled state shared by two or more separated parties is a valuable resource for fundamental quantum protocols, such as quantum teleportation [2], quantum computing [3] and quantum cryptography. By using entangled states we can deeply investigate the nonlocal properties of the quantum world. In fact, an entangled system exhibits correlations between two (or more) parties, which cannot be reproduced by a classical theory or, in general, by a Local Hidden Variables Theory (LHVT). Quantum optics represents an excellent experimental test bench for various novel concepts introduced within the framework of quantum information theory. Quantum states of photons, generally produced by a probabilistic process, namely spontaneous parametric down conversion (SPDC), may be easily and accurately manipulated using linear and nonlinear optical devices and measured by efficient single-photon detectors. Photonic qubits represent the typical carrier of quantum information and can be distributed over long distances, either in free-space or in low-loss optical fibers. Two-particle experiments correspond to operate with qubits belonging to a (2 × 2) Hilbert space. Many quantum information tasks and fundamental tests of quantum mechanics, such as the simulation of properties of quantum systems, the realization of quantum algorithms of increasing complexity and the investigation of the quantum world at a mesoscopic level, deal with a large number of qubits. In order to take full advantage of the possibilities offered by quantum mechanics, more qubits must be added to a quantum state. Two approaches may be followed to increase the number of qubits. The first one consists of increasing the number of entangled particles. In this way, multi-qubit entangled states are created by distributing the qubits between the particles so that each particle carries one qubit. A second strategy consists of encoding more than one qubit in each particle, by exploiting different degrees of freedom (DOFs) of the photon such as the polarization, the path, the emission time, the orbital angular momentum. This has been used to create two-photon fourand six-qubit states and up to five-photon ten-qubit graph states. The entanglement of two particles in different DOFs corresponds to socalled hyperentanglement. It is worth noting that multi-qubit hyperentanglement allows to achieve higher
Systems entangled in high dimensions have recently been proposed as important tools for various quantum information protocols, such as multibit quantum key distribution and loophole-free tests of nonlocality. It is therefore important to have precise knowledge of the nature of such entangled quantum states. We tomographically reconstruct the quantum state of the two photons produced by parametric downconversion that are entangled in a d-dimensional orbital angular momentum basis. We determine exactly the density matrix of the entangled two-qudit state with d ranging from 2 to 8. The recording of higher-dimensional states is limited only by the number of data points required and therefore the length of time needed to complete the measurements. We find all the measured states to have fidelities and linear entropies that satisfy the criteria required for a violation of the appropriate high-dimensional Bell inequality. Our results therefore precisely characterize the nature of the entanglement, thus establishing the suitability of such states for applications in quantum information science.
Recently quantum tomography has been proposed as a fundamental tool for prototyping a few qubit quantum device. It allows the complete reconstruction of the state produced from a given input into the device. From this reconstructed density matrix, relevant quantum information quantities such as the degree of entanglement and entropy can be calculated. Generally, orthogonal measurements have been discussed for this tomographic reconstruction. In this paper, we extend the tomographic reconstruction technique to two new regimes. First, we show how nonorthogonal measurements allow the reconstruction of the state of the system provided the measurements span the Hilbert space. We then detail how quantum-state tomography can be performed for multiqudits with a specific example illustrating how to achieve this in one- and two-qutrit systems.