Quantum Error Correction and Reversible Operations

This article gives a pedagogical account of Shor's nine-bit code for correcting arbitrary errors on single qubits and reviews work that determines when it is possible to maintain quantum coherence by reversing the deleterious effects of open-system quantum dynamics. The review provides an opportunity to introduce an efficient formalism for handling superoperators. Some bounds on entanglement fidelity, which might prove useful in analyses of approximate error correction, are presented and proved.     

Low Temperature Decoherence by Electron–Electron Interactions: Role of Quantum Fluctuations

We derive a general expression for the conductivity of a disordered conductor with electron–electron interactions (treated within the standard model) and evaluate the weak localization correction _wl employing no approximations beyond the accuracy of the definition of _wl . Our analysis applies to all orders in the interaction and extends our previous calculation by explicitly taking into account quantum fluctuations around the classical paths for interacting electrons (pre-exponent). We specifically address the most interesting low temperature limit and demonstrate that such fluctuations can only be important in the perturbative regime of short times while they are practically irrelevant for the Cooperon dynamics at longer times. We fully confirm our conclusion about the existence of interaction-induced decoherence of electrons at zero temperature for the problem in question. We also demonstrate irrelevance of a perturbative calculation by Aleiner et al. (AAV) [J. Low Temp. Phys. 126, 1377 (2002)] and refute AAV's critique of our earlier analysis.     

Experimental Evaluation of the Intrinsic Dissipation from Energy-Level Quantization in Josephson Devices

The main problem in realizing an experiment of macroscopic quantum coherence, namely, an experiment where the nonclassical behavior of a macroscopic system must be detected, is the fulfillment of many experimental constraints, in principle very difficult to achieve. One of the most critical parameters is the decoherence time of the system. The Rabi oscillations of a two-level system, in fact, are canceled if the quality factor associated with the oscillation is less than unity. In particular, it can be shown that the decoherence time for a SQUID system, once the temperature is given, depends only on the effective resistance. To evaluate the effective resistance of our system we have measured the energy-level quantization (ELQ) under stationary conditions at a temperature between 13 and 35 mK, for a Josephson junction and for an rf SQUID using the same type of junction. For both systems we can clearly see ELQ, because of the very low level of the intrinsic dissipation. From these measurements we can then set a lower limit for the effective system dissipation and then infer the decoherence time related to the overall setup of our experiment.     

Hyperfine Interactions and Electron Spin-Dynamics in a Quantum Dot

We study the dynamics of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei. The decoherence is caused by the spatial variation of the electron wave function within the dot, leading to a nonuniform hyperfine coupling A. We evaluate the spin correlation function and find that the decay is not exponential but rather power (inverse logarithm) law-like. For polarized nuclei we find an exact solution and show that the precession amplitude and the decay behavior can be tuned by the magnetic field. The decay time is given by N/A, where N is the number of nuclei inside the dot, and the amplitude of precession decays to a finite value. We show that there is a striking difference between the decoherence time for a single dot and the dephasing time for an ensemble of dots.     

Quantum decoherence with the Unruh single-particle state having right and left components

We investigate the effects of quantum decoherence generated by the Unruh effect in non-inertial frames under an amplitude damping channel and a phase damping channel, respectively, when the Unruh single particle has right and left components. We not only consider the influence of acceleration on entanglement, but also consider the influence of different rates between right and left components of the Unruh single-particle state on entanglement. We find that when the Unruh single-particle state has right and left components, i.e. |1?_U?=?q _L|0?_I|1?_II?+?q _R|1?_I|0?_II, |q _R|²?+?|q _L|²?=?1, with q _L?≠?0, there appears the sudden death of entanglement, which occurs earlier under both the amplitude damping channel and the phase damping channel with the increase of acceleration than that when the Unruh single-particle state only has a right component (q _R?=?1, q _L?=?0). We also find that the initial entanglement decreases with decrease of q _R from 1 to 1/2^1/2.     

Perspectives of an Experiment for Detecting Macroscopic Quantum Coherence

In the second half of 1993 we presented to INFN a proposal of an experiment for detecting macroscopic quantum coherence with a system of SQUIDs. It was based essentially on ideas presented first by Leggett and collaborators and developed in many articles in the 1980s. The experimental work started in the 1994 just after the approval of the INFN. As an introduction, the experimental method and the setup we choose in order to perform a set of measurements on a system of SQUIDs is described. Then the measuring procedures and their purposes are explained and discussed.As a future perspective, a possible test on the existence of the quantum gravity is discussed. According to a theoretical proposal by John Ellis and collaborators, the quantum gravitational friction could induce the transition from QM behavior of microscopic states to the classical behavior of macroscopic states, i.e., states containing an Avogadro number (M _pl/M _e ) of elementary particles, as may be obtained in a SQUID.     

Pre-selection of optical transitions in rare-earth ions in crystals perspective for quantum information processing

A systematic analysis of decoherence rates due to electron–phonon interactions for optical transitions of rare-earth dopant ions in crystals is presented in the frame of the point charge model. For this model, the large value of any one of the matrix elements of the unit tensor operator U ^{( k )} of rank k for transitions within the 4f-electronic configuration, viz. U2, U4 or U6, is enough to ensure the strong optical transition between different levels, while the Stark–Stark transitions within the multiplet can be characterized by the matrix element U2 alone, the influence of elements U4, U6 being of much smaller order of magnitude and neglected. The circumstance that exactly such Stark–Stark transitions within the multiplet define the efficiency of electron–phonon interaction and, consequently, the decoherence rate (except for the case of lowest, less than approximately 2–4?K, temperatures), enables selection of optical transitions which are strong enough and at the same time are characterized by relatively small decoherence rates. Correspondingly, these optical transitions, provided that they lie in an appropriate spectral range and the gap to the nearest neighboring energy level is large enough (>500?cm^?1) to prevent eventual fast phonon-assisted relaxation, should be considered as prospective for subsequent use in quantum informatics processing and communication. The list of such pre-selected transitions is given; the applicability area and limitations of our approach are discussed.     

Using Conditional Measurements to Combat Decoherence

With the help of some remarkable examples, it is shown that conditional measurements performed on two-level atoms just after they have interacted with a resonant cavity field mode are able to recover the coherence of number-state superpositions, which is lost due to dissipation.     

Probing Single-Electron Spin Decoherence in Quantum Dots using Charged Excitons

We propose to use optical detection of magnetic resonance (ODMR) to measure the decoherence time T₂ of a single-electron spin in a semiconductor quantum dot. The electron is in one of the spin 1/2 states and a circularly polarized laser can only create an optical excitation for one of the electron spin states due to Pauli blocking. An applied electron spin resonance (ESR) field leads to Rabi spin flips and thus to a modulation of the photoluminescence or, alternatively, of the photocurrent. This allows one to measure the ESR linewidth and the coherent Rabi oscillations, from which the electron spin decoherence can be determined. We study different possible schemes for such an ODMR setup, including cw or pulsed laser excitation. An erratum to this article is available at .     

Estimation of nonclassical properties of multiphoton coherent states from optical tomograms

We have examined both single and entangled two-mode multiphoton coherent states and shown how the ‘Janus-faced’ properties between two partner states are mirrored in appropriate tomograms. Entropic squeezing, quadrature squeezing and higher-order squeezing properties for a wide range of nonclassical states are estimated directly from tomograms. We have demonstrated how squeezing properties of two-mode entangled states produced at the output port of a quantum beamsplitter are sensitive to the relative phase between the reflected and transmitted fields. This feature allows for the possibility of tuning the relative phase to enhance squeezing properties of the state. Finally, we have examined the manner in which decoherence affects squeezing and the changes in the optical tomogram of the state due to interaction with the environment.     

Constraints on Non-Newtonian Gravity From the Experiment on Neutron Quantum States in the Earth’s Gravitational Field

An upper limit to non-Newtonian attractive forces is obtained from the measurement of quantum states of neutrons in the Earth’s gravitational field. This limit improves the existing constraints in the nanometer range.     

The GMMBS Method for Time-temperature Superposition of Viscoelastic Materials

Using the time-temperature superposition principle,the dynamic properties of viscoelastic materials can be shifted to obtain a master curve.A shifting method based on the Generalized Maxwell Model(GMMBS) ,is proposed for the time-temperature superposition process of thermo-rheological simple,linear viscoelastic materials.Experimental data points under different temperatures are all considered as a whole and expressed with one unified representation by the GMMBS,which utilizes the feature that the Generalized Maxwell Model can describe a large class of viscoelastic materials with needed accuracy.Compared with traditional overlapping window based shifting methods,the proposed constitutive model based method needn’t judge the size or existence of the overlapping window first,and computes shift factors with useful information contained in all experimental data points.The effectiveness of the proposed method is verified by simulated data,generated from published test results,with various experimental noise levels,densities of data points and sizes of overlapping windows.It has been shown that the GMMBS is robust and accurate.     

The Strong Impact of the Weak Superconductivity

The Josephson effect offers an unparalleled tool to shed light on aspects of the underlying physics of phenomena which go also far beyond the field of superconductivity. Some considerations on a few examples of the highlights concerning both exciting achievements and challenging perspectives of this fascinating topic are briefly outlined sharing the attention on both possible applications and intriguing implications.     

Physical properties of a trapped two-level ion decaying by thermal and squeezed vacuum reservoirs

In this paper, we first study the interaction between a trapped two-level ion with a field reservoir in a general form. Then, we use thermal and squeezed vacuum reservoirs to continue our investigation. We try to find the equation of motion for the whole system density operator by applying the Weisskopf theory. Next, we evaluate the explicit form of the density matrix elements analytically. In the obtained density matrix elements, we arrive at some physical parameters of the trapped ion system as well as the applied field reservoirs by which one can control the transition probabilities between the trapped ionic states. We also introduce some hermitian operators for the trapped ion system and calculate the expectation values of their time evolution by considering the mentioned two reservoirs. In the continuation, we design a system for measuring the hermitian trapped ion’s operators theoretically. Finally, we find a way to transport the information of the trapped ion system by our proposed quantum processor.     

The Non-Linear Viscoelastic Response of Polycarbonate in Torsion: An Investigation of Time-Temperature and Time-Strain Superposition

Data are presented from torsional stress relaxationexperiments on a commercial polycarbonate. Tests were performedon samples over a range of torsional strains from 0.0025 to 0.08and at temperatures from 30 to 110°C at a fixed aging time of64,800 s (18 h). Following the scaling approach of Penn andKearsley [Trans. Soc. Rheol. 20 (1976)] we were able todetermine the stress relaxation response at shear strains to0.07. Then the individual data sets at each strain andtemperature could be described using a stretched exponential formrelaxation function. Over the range of temperatures studied thedata at each strain were superimposed using conventional time-temperature superposition. For strains up to the yield strainthe data at each temperature could also be superimposed to form amaster curve following the principle of time-strainsuperposition. Interestingly, the master curves found from time-strain superposition at each temperature did not have the sameform. Similarly, the master curves found from time-temperaturesuperposition at each strain did not have the same form.     

量子化学方法在色谱分析中的应用

运用量子化学的方法定量描述了在气相色谱中,各种醇类与不同固定相之间的相互作用.进而预 测了各种醇在气相色谱不同固定相中的保留值.