Nonclassical correlation in NMR quadrupolar systems

The existence of quantum correlation (as revealed by quantum discord), other than entanglement and its role in quantum-information processing (QIP), is a current subject for discussion. In particular, it has been suggested that this nonclassical correlation may provide computational speedup for some quantum algorithms. In this regard, bulk nuclear magnetic resonance (NMR) has been successfully used as a test bench for many QIP implementations, although it has also been continuously criticized for not presenting entanglement in most of the systems used so far. In this paper, we report a theoretical and experimental study on the dynamics of quantum and classical correlations in an NMR quadrupolar system. We present a method for computing the correlations from experimental NMR deviation-density matrices and show that, given the action of the nuclear-spin environment, the relaxation produces a monotonic time decay in the correlations. Although the experimental realizations were performed in a specific quadrupolar system, the main results presented here can be applied to whichever system uses a deviation-density matrix formalism.Comment: Published versio

Experimental Implementation of Logical Bell State Encoding

Liquid phase NMR is a general purpose test-bed for developing methods of coherent control relevant to quantum information processing. Here we extend these studies to the coherent control of logical qubits and in particular to the unitary gates necessary to create entanglement between logical qubits. We report an experimental implementation of a conditional logical gate between two logical qubits that are each in decoherence free subspaces that protect the quantum information from fully correlated dephasing.Comment: 9 Pages, 5 Figure

Bounds on the entanglability of thermal states in liquid-state nuclear magnetic resonance

The role of mixed state entanglement in liquid-state nuclear magnetic resonance (NMR) quantum computation is not yet well-understood. In particular, despite the success of quantum information processing with NMR, recent work has shown that quantum states used in most of those experiments were not entangled. This is because these states, derived by unitary transforms from the thermal equilibrium state, were too close to the maximally mixed state. We are thus motivated to determine whether a given NMR state is entanglable - that is, does there exist a unitary transform that entangles the state? The boundary between entanglable and nonentanglable thermal states is a function of the spin system size $N$ and its temperature $T$. We provide new bounds on the location of this boundary using analytical and numerical methods; our tightest bound scales as $N \sim T$, giving a lower bound requiring at least $N \sim 22,000$ proton spins to realize an entanglable thermal state at typical laboratory NMR magnetic fields. These bounds are tighter than known bounds on the entanglability of effective pure states.Comment: REVTeX4, 15 pages, 4 figures (one large figure: 414 K

Experimental implementation of a NMR entanglement witness

Entanglement witnesses (EW) allow the detection of entanglement in a quantum system, from the measurement of some few observables. They do not require the complete determination of the quantum state, which is regarded as a main advantage. On this paper it is experimentally analyzed an entanglement witness recently proposed in the context of Nuclear Magnetic Resonance (NMR) experiments to test it in some Bell-diagonal states. We also propose some optimal entanglement witness for Bell-diagonal states. The efficiency of the two types of EW's are compared to a measure of entanglement with tomographic cost, the generalized robustness of entanglement. It is used a GRAPE algorithm to produce an entangled state which is out of the detection region of the EW for Bell-diagonal states. Upon relaxation, the results show that there is a region in which both EW fails, whereas the generalized robustness still shows entanglement, but with the entanglement witness proposed here with a better performance

Quantum information processing by NMR using a 5-qubit system formed by dipolar coupled spins in an oriented molecule

Quantum Information processing by NMR with small number of qubits is well established. Scaling to higher number of qubits is hindered by two major requirements (i) mutual coupling among qubits and (ii) qubit addressability. It has been demonstrated that mutual coupling can be increased by using residual dipolar couplings among spins by orienting the spin system in a liquid crystalline matrix. In such a case, the heteronuclear spins are weakly coupled but the homonuclear spins become strongly coupled. In such circumstances, the strongly coupled spins can no longer be treated as qubits. However, it has been demonstrated elsewhere, that the $2^N$ energy levels of a strongly coupled N spin-1/2 system can be treated as an N-qubit system. For this purpose the various transitions have to be identified to well defined energy levels. This paper consists of two parts. In the first part, the energy level diagram of a heteronuclear 5-spin system is obtained by using a newly developed heteronuclear z-cosy (HET-Z-COSY) experiment. In the second part, implementation of logic gates, preparation of pseudopure states, creation of entanglement and entanglement transfer is demonstrated, validating the use of such systems for quantum information processing.Comment: 23 pages, 8 figure

Complete quantum teleportation using nuclear magnetic resonance

Quantum mechanics provides spectacular new information processing abilities (Bennett 1995, Preskill 1998). One of the most unexpected is a procedure called quantum teleportation (Bennett et al 1993) that allows the quantum state of a system to be transported from one location to another, without moving through the intervening space. Partial implementations of teleportation (Bouwmeester et al 1997, Boschi et al 1998) over macroscopic distances have been achieved using optical systems, but omit the final stage of the teleportation procedure. Here we report an experimental implementation of the full quantum teleportation operation over inter-atomic distances using liquid state nuclear magnetic resonance (NMR). The inclusion of the final stage enables for the first time a teleportation implementation which may be used as a subroutine in larger quantum computations, or for quantum communication. Our experiment also demonstrates the use of quantum process tomography, a procedure to completely characterize the dynamics of a quantum system. Finally, we demonstrate a controlled exploitation of decoherence as a tool to assist in the performance of an experiment.Comment: 15 pages, 2 figures. Minor differences between this and the published versio

Experimental realization of the Yang-Baxter Equation via NMR interferometry

The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory. Recently, the interest on the equation has increased due to its connection to quantum information processing. It has been shown that the Yang-Baxter equation is closely related to quantum entanglement and quantum computation. Therefore, owing to the broad relevance of this equation, besides theoretical studies, it also became significant to pursue its experimental implementation. Here, we show an experimental realization of the Yang-Baxter equation and verify its validity through a Nuclear Magnetic Resonance (NMR) interferometric setup. Our experiment was performed on a liquid state Iodotrifluoroethylene sample which contains molecules with three qubits. We use Controlled-transfer gates that allow us to build a pseudo-pure state from which we are able to apply a quantum information protocol that implements the Yang-Baxter equation.Comment: 10 pages and 6 figure