Efficient universal programmable quantum measurements

A universal programmable detector is a device that can be tuned to perform any desired measurement on a given quantum system, by changing the state of an ancilla. With a finite dimension d for the ancilla only approximate universal programmability is possible, with size d=f(epsilon(-1)) increasing the function of the "accuracy" epsilon(-1). In this Letter we show that, much better than the exponential size known in the literature, one can achieve polynomial size. An explicit example with linear size is also presented. Finally, we show that for covariant measurements exact programmability is feasible.     

Weak measurements as an instance of non-ideal measurements

We introduce weak measurements (WM) as a type of non-ideal measurement (NIM) coupling the system and the measuring device in a specific manner involving a weak interaction followed by post-selection. For the particular case of a WM measurement of spin, we solve the quantum dynamics for the coupled system-meter ensemble exactly for any type of non-ideal measurement. The standard WM regime is obtained as a limiting case; eccentric ??semi-weak?? values not only appear in other cases of NIM, but can also have a larger magnitude than the usual weak values. A couple of examples comparing the merits of the WM regime and of the exact treatment in situations of potential interest to quantum information applications are considered.     

Weak localization and universal conductance fluctuations in multi-layer graphene

We have performed magneto transport measurements on a multi-layer graphene device fabricated by conventional mechanical exfoliation. Suppression of weak localization (WL) as evidenced by the negative magnetoresistance (NMR) centered at zero field, and reproducible universal conductance fluctuations (UCFs) are observed. Interestingly, it is found that the phase coherence lengths calculated by fitting the observed NMR to conventional WL theory are longer than those determined from fitting the amplitudes of the UCFs to theory in the low temperature regime (T ≤ 8 K). In the high temperature regime (T > 8 K), the phase coherence lengths calculated by fitting the observed NMR to conventional WL theory are shorter than those determined from fitting the amplitudes of the UCFs to theory. Our new results therefore indicate a difference in the electron phase-breaking process between the two models of WL and UCFs in graphene. We speculate that the presence of the capping and bottom graphene layers, which leads the enhancement of disorder in-between, improves the localization condition for WL effect during carrier transportation in the low temperature regime. With increasing temperature, the localization condition for WL in multi-layer graphene becomes much weaker due to strong thermal damping. Therefore, the phase coherence lengths calculated by fitting the observed NMR to conventional WL theory are shorter than those determined from fitting the amplitudes of the UCFs to theory at high temperatures.     

Weak measurements with arbitrary probe states

The exact conditions on valid probe states for weak measurements are derived. It is demonstrated that weak measurements can be performed with any probe state with vanishing probability current density. This condition is found both for weak measurements of noncommuting observables and for c-number observables. In addition, the interaction between object and probe must be sufficiently weak. Strange weak values can be observed also with mixed probe states, but not for c-number observables.     

Weak measurements with a qubit meter

We derive schemes to measure the so-called weak values of quantum system observables by coupling of the system to a qubit meter system. We highlight, in particular, the meaning of the imaginary part of the weak values, and show how it can be measured directly on equal footing with the real part of the weak value. We present compact expressions for the weak value of single qubit observables and of product observables on qubit pairs. Experimental studies of the results are suggested with cold trapped ions.     

“Weak” measurements and supraluminal communication

A modified experiment with a correlated pair of particles in an entangled space is suggested. The experiment demonstrates that for weak and/or nondemolition measurements of one of the particles, information can be transmitted at a speed that is not limited by the speed of light.     

Weak disorder: anomalous transport and diffusion are normal yet again

We carry out a detailed study of the motion of particles driven by a constant external force over a landscape consisting of a periodic potential corrugated by a small amount of spatial disorder. We observe anomalous behavior in the form of subdiffusion and superdiffusion and even subtransport over very long time scales. Recent studies of transport over slightly random landscapes have focused only on parameters leading to normal behavior, and while enhanced diffusion has been identified when the external force approaches the critical value associated with the transition from locked to running solutions, the regime of anomalous behavior had not been recognized. We provide a qualitative explanation for the origin of these anomalies, and make connections with a continuous time random walk approach.     

There exist nonorthogonal quantum measurements that are perfectly repeatable

We show that, contrary to the widespread belief, in quantum mechanics repeatable measurements are not necessarily described by orthogonal projectors--the customary paradigm of observable. Nonorthogonal repeatability, however, occurs only for infinite dimensions. We also show that, when a nonorthogonal repeatable measurement is performed, the measured system retains some "memory" of the number of times that the measurement has been performed.     

How continuous quantum measurements in finite dimensions are actually discrete

We show that in finite dimensions a quantum measurement with a continuous set of outcomes can be always realized as a continuous random choice of measurements with a finite number of outcomes.     

Weak Measurement and Weak Information

Weak measurement devices resemble band pass filters: they strengthen average values in the state space or equivalently filter out some ‘frequencies’ from the conjugate Fourier transformed vector space. We thereby adjust a principle of classical communication theory for the use in quantum computation. We discuss some of the computational benefits and limitations of such an approach, including complexity analysis, some simple examples and a realistic not-so-weak approach.     

Taking tomographic measurements for photonic qubits 88 ns before they are created

We experimentally demonstrate that tomographic measurements can be performed for states of qubits before they are prepared.A variant of the quantum teleportation protocol is used as a channel between two instants in time,allowing measurements for polarization states of photons to be implemented 88 ns before they are created.Measurement data taken at the early time and later unscrambled according to the results of the protocol's Bell measurements,produces density matrices with an average fidelity of 0.90±0.01 against the ideal states of photons created at the later time.Process tomography of the time reverse quantum channel finds an average process fidelity of 0.84±0.02.While our proof-of-principle implementation necessitates some post-selection,the general protocol is deterministic and requires no post-selection to sift desired states and reject a larger ensemble.     

A universal ellipsometer

This paper describes the design of an instrument which can be used for studies of optical rotation, circular dichroism and conventional ellipsometry. The main features are that it is automatically recording and, unlike other instruments, allows the azimuth and ellipticity to be measured simultaneously on a twin channel recorder. The recorder has a common chart drive which is synchronised to a scanning monochromator that covers a wide wavelength range.     

Pseudo Weak Effect Algebras and Pseudo Weak D-posets

Pseudo weak effect algebras are base on an noncommutative, associative and cancellative partial addition, but in general not determined by it. Every pseudo BL-algebra gives rise to a pseudo weak effect algebra.     

Typical universal entanglers

A universal entangler is a very powerful fault-tolerant entangling device for generating quantum entanglements from any joint states. Our paper aims to address the construction of universal entanglers. We prove that universal entanglers may be obtained from random unitary gates according to the Harr measure. The success probability is close to 1 for large system spaces. This result represents the typical density of entanglement subspaces in large state spaces. It also partially solves an open problem of universal bipartite entanglers and is explained by some experiment simulations.     

Renormalization group operators for maps and universal scaling of universal scaling exponents

Renormalization group (RG) methods provide a unifying framework for understanding critical behaviour, such as transition to chaos in area-preserving maps and other dynamical systems, which have associated with them universal scaling exponents. Recently, de la Llave et al. (2007) [10] have formulated the Principle of Approximate Combination of Scaling Exponents (PACSE for short), which relates exponents for different criticalities via their combinatorial properties. The main objective of this paper is to show that certain integrable fixed points of RG operators for area-preserving maps do indeed follow the PACSE.     

Opacity and transport measurements reveal that dilute plasma models of sonoluminescence are not valid

A strong interaction between a nanosecond laser and a 70?μm radius sonoluminescing plasma is achieved. The overall response of the system results in a factor of 2 increase in temperature as determined by its spectrum. Images of the interaction reveal that light energy is absorbed and trapped in a region smaller than the sonoluminescence emitting region of the bubble for over 100?ns. We interpret this opacity and transport measurement as demonstrating that sonoluminescencing bubbles can be 1000 times more opaque than what follows from the Saha equation of statistical mechanics in the ideal plasma limit. To address this discrepancy, we suggest that the effects of strong Coulomb interactions are an essential component of a first principles theory of sonoluminescence.