Pseudo-entangled

In this case, we will refer to pe as a pseudo-cat state. Generally, if p represents an entangled state, we say that Pe is pseudo-entangled. Now, if pi is a cat-state, the question is whether P( is entangled or not. We have to keep in mind that the density matrix of the whole spin system is Pe, and not p, but remember that NMR signals are proportional to pi, and not Pe. 

The problem of determining bounds of e for n qubits, is rather complicated. A general Peres criterium can be obtained for n qubits, but since its applicability is restricted to a small number of qubits, it cannot be used to analyze NMR entanglement and the scaling problem. An alternative and more general analysis was made by Braunstein and co-workers in 1999 [1]. They found that a n-qubit pseudo-entangled state will be separable for... 

Figure 6.3 (Quantum correlation feedback transfer demonstrated by Nelson and co-workers in 2000. The system of three spins starts at the equilibrium thermal state, with the deviation density matrix proportional to + /jf + A sequence of pulses creates a correlated (pseudo-entangled) between B and C ...

Entanglement transfer experiment in NMR quantum information processing - This paper of 2002 by Boulant and co-workers [18] describes an experiment of entanglement transfer by NMR. The aim is to transfer an entangled state of a pair of qubits to another pair of qubits, a process which was first demonstrated using photons in 1998, by Pan and collaborators. The authors used the four nuclei of crotonic acid as qubits. The process was followed by quantum state tomography and the efficacy of the experiment was quantified by a measured called attenuated correlation. A value of 0.65 for this measure at the end of the protocol, indicated that the pseudo-entangled state was indeed transferred from one pair of qubits to the other. 

Practical implementations of twirl operations - This paper, reported in 2005 by Anwar and co-workers [20], deals with a practical implementation of a proposal made by Bennett and co-workers in 1996 for the purification of entanglement from a mixed state. The typical situation would be that in which the qubits of an initially pure entangled state rjr ) = ( 01) - 110 V2 are sent through a noisy channel. The twirl operation is a step for the purification. This operation converts an arbitrary mixed state of two qubits into a pseudo-entangled state ... 

Such considerations appear to be very relevant to the deformation of polymethylmethacrylate (PMMA) in the glassy state. At first sight, the development of P200 with draw ratio appears to follow the pseudo-affine deformation scheme rather than the rubber network model. It is, however, not possible to reconcile this conclusion with the temperature dependence of the behaviour where the development of orientation reduces in absolute magnitude with increasing temperature of deformation. It was proposed by Raha and Bowden 25) that an alternative deformation scheme, which fits the data well, is to assume that the deformation is akin to a rubber network, where the number of cross-links systematically reduces as the draw ratio is increased. It is assumed that the reduction in the number of cross-links per unit volume N i.e. molecular entanglements is proportional to the degree of deformation. 

Unfortunately, the method is based on a fairly large nunber of assumptions. If we want to relate GN to the pseudo-equilibrium rubber plateau modulus, G , and to the effect of chain entangling in ordinary networks produced by cross-linking in the unstrained state, the following assumptions are required ... 

Figure 3. Modulus contributions from chemical cross-links (Cx, filled triangles) and from chain entangling (Gx, unfilled symbols) plotted against the extension ratio during cross-linking, A0, for 1,2-polybutadiene. Key O, GN, equibiaxial extension , G.v, pure shear A, Gx, simple extension Gx°, pseudo-equilibrium rubber plateau modulus for a polybutadiene with a similar microstructure. See Ref. 10.

The two-network method has been carefully examined. All the previous two-network results were obtained in simple extension for which the Gaussian composite network theory was found to be inadequate. Results obtained on composite networks of 1,2-polybutadiene for three different types of strain, namely equibiaxial extension, pure shear, and simple extension, are discussed in the present paper. The Gaussian composite network elastic free energy relation is found to be adequate in equibiaxial extension and possibly pure shear. Extrapolation to zero strain gives the same result for all three types of strain The contribution from chain entangling at elastic equilibrium is found to be approximately equal to the pseudo-equilibrium rubber plateau modulus and about three times larger than the contribution from chemical cross-links. 

The maximum tensile strength of the pseudo-IPNs appeared at about the 80 20 ratio of PU/VMCC for both pseudo-IPNs with and without opposite charge groups. Presumably the maximum entangle-ment between the VMCC chains and the PU network also occurred at this composition ( Figure 1). ... 

Entanglements that are not trapped have transistory existence (and will be referred to as "temporary" entanglements). Since the dynamic moduli of these systems depend on the frequency, temperature and shear history of the system, we shall refer to such system as a gel-like or pseudo-gel in contrast to a true gel. A schematic diagram of the pseudo-gel structure is shown in Figure 1. 

The viscoelastic response of the UHMWPE pseudo-gels depends also on the solution concentration. As shown in Figure 10, the G increased with concentration at frequency 50 sec"l over the temperature range from -20 C to 100 C. This is probably due to the higher entanglement density and/or higher crystallinity in the higher concentration solution. 

A pseudo solid-like behavior of the T2 relaxation is also observed in i) high Mn fractionated linear polydimethylsiloxanes (PDMS), ii) crosslinked PDMS networks, with a single FID and the line shape follows the Weibull function (p = 1.5)88> and iii) in uncrosslinked c/.s-polyisoprenes with Mn > 30000, when the presence of entanglements produces a transient network structure. Irradiation crosslinking of polyisoprenes having smaller Mn leads to a similar effect91 . The non-Lorentzian free-induction decay can be a consequence of a) anisotropic molecular motion or b) residual dipolar interactions in the viscoelastic state. 

Chain entanglements are the cause of rubber-elastic properties in the liquid. Below the "critical" molecular mass (Mc) there are no indications of a rubbery plateau. The length of the latter is strongly dependent on the length of the molecular chains, i.e. on the molar mass of the polymer. From the shear modulus of the pseudo rubber plateau the molecular weight between entanglements may be calculated ... 

At h h polymer concentrations, polymer molecules entangle, producing pseudo-plastic rheological behavior. This occurs at a polymer concentration, cf = comparable to that in the polymer... 

Certain dynamic mechanical measurements are thought to reflect the pseudo-network formed by the entanglements and yield a quantity Z f presumably equal to Z (7, 18). For example, the pseudo network creep compliance observed as a plateau in the creep compliance response is believed to be related to Z through the expression (7)... 

We shall ask whether Grover s quantum algorithm for solving this problem on an entanglement-free pseudo-pure state based machine can offer any speedup over classical performance. The key feature of Grover s algorithm for a pure-state implementation is that at step k the quantum computer is in state... 

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