Scavenging quantum information: Multiple observations of quantum systems

Given an unknown state of a qudit that has already been measured optimally, can one still extract any information about the original unknown state? Clearly, after a maximally informative measurement, the state of the system `collapses' into a post-measurement state from which the {\em{same}} observer cannot obtain further information about the original state of the system. However, the system still encodes a significant amount of information about the original preparation for a second observer who is unaware of the actions of the first one. We study how a series of independent observers can obtain, or scavenge, information about the unknown state of a system (quantified by the fidelity) when they sequentially measure it. We give closed-form expressions for the estimation fidelity, when one or several qudits are available to carry information about the single-qudit state, and study the `classical' limit when an arbitrarily large number of observers can obtain (nearly) complete information on the system. In addition to the case where all observers perform most informative measurements we study the scenario where a finite number of observers estimate the state with equal fidelity,regardless of their position in the measurement sequence; and the scenario where all observers use identical measurement apparata (up to a mutually unknown orientation) chosen so that a particular observer's estimation fidelity is maximized.Comment: 17 pages, 1 figur

Direct versus measurement assisted bipartite entanglement in multi-qubit systems and their dynamical generation in spin systems

We consider multi-qubit systems and relate quantitatively the problems of generating cluster states with high value of concurrence of assistance, and that of generating states with maximal bipartite entanglement. We prove an upper bound for the concurrence of assistance. We consider dynamics of spin-1/2 systems that model qubits, with different couplings and possible presence of magnetic field to investigate the appearance of the discussed entanglement properties. We find that states with maximal bipartite entanglement can be generated by an XY Hamiltonian, and their generation can be controlled by the initial state of one of the spins. The same Hamiltonian is capable of creating states with high concurrence of assistance with suitably chosen initial state. We show that the production of graph states using the Ising Hamiltonian is controllable via a single-qubit rotation of one spin-1/2 subsystem in the initial multi-qubit state. We shown that the property of Ising dynamics to convert a product state basis into a special maximally entangled basis is temporally enhanced by the application of a suitable magnetic field. Similar basis transformations are found to be feasible in the case of isotropic XY couplings with magnetic field.Comment: (14 pages, 7 figures, RevTeX4

Recycling of quantum information: Multiple observations of quantum systems

Given a finite number of copies of an unknown qubit state that have already been measured optimally, can one still extract any information about the original unknown state? We give a positive answer to this question and quantify the information obtainable by a given observer as a function of the number of copies in the ensemble, and of the number of independent observers that, one after the other, have independently measured the same ensemble of qubits before him. The optimality of the protocol is proven and extensions to other states and encodings are also studied. According to the general lore, the state after a measurement has no information about the state before the measurement. Our results manifestly show that this statement has to be taken with a grain of salt, specially in situations where the quantum states encode confidential information.Comment: 4 page

Testing sequential quantum measurements: how can maximal knowledge be extracted?

The extraction of information from a quantum system unavoidably implies a modification of the measured system itself. It has been demonstrated recently that partial measurements can be carried out in order to extract only a portion of the information encoded in a quantum system, at the cost of inducing a limited amount of disturbance. Here we analyze experimentally the dynamics of sequential partial measurements carried out on a quantum system, focusing on the trade-off between the maximal information extractable and the disturbance. In particular we consider two different regimes of measurement, demonstrating that, by exploiting an adaptive strategy, an optimal trade-off between the two quantities can be found, as observed in a single measurement process. Such experimental result, achieved for two sequential measurements, can be extended to N measurement processes.Comment: 5 pages, 3 figure

Elusive Diagnosis of Superficial Peroneal Nerve Entrapment Case report

Isolated neuropathy of the superficial peroneal nerve (SPN) is a relatively rare type of peripheral neuropathy. It is linked to the mechanical entrapment of the SPN in predisposed locations of its anatomical pathway. Associated clinical findings are insufficient lifting of the latero-dorsal part of the foot, stepping on the lateral border of the foot, and commonly, a strong pain localized in the nerve dermatome.Case report. We describe a case of a 14-year-old female patient with right leg pain lasting 24 months. Repeated neurological examinations with negative findings on electromyography (EMG) were performed. The patient underwent a Steindler surgery for a suspected diagnosis of a heel spur, without any improvement. Despite complex pharmacotherapy, chronic pain developed. The patient was unable to walk, being bound to a wheelchair. Amputation of her lower limb under the knee was also considered. SPN entrapment was diagnosed at a physical examination at EuroPainClinics. Decompression of the SPN under local anaesthesia was performed at the clinic.Results. The symptoms improved immediately after the procedure, and following 2 months of rehabilitation, the patient was completely symptom-free. Her clinical state remains unchanged until this day.Conclusions. SPN entrapment is not a common diagnosis in the group of pain syndromes. Regarding the lower limb, it is imperative to include it on the list of differential diagnoses in cases of pain and functional disorders of the lateral muscle groups of the calf and leg. In the case of SPN entrapment, EMG findings may be negative

Effectiveness of granular matrix sensors in different irrigation treatments and installation depths

Continuous monitoring of soil moisture content plays a key role in irrigation scheduling and yield formation. This study was conducted to derive the technique and efficiency of application of granular matrix sensors (GMSs) in a sprinkler irrigation system of maize (Zea mays L.). Two irrigation (a2 = 60%- 100% of field capacity (FC), a3 = 80%-100% of FC) treatments were imposed during two growing seasons (2010, 2012) and compared with rainfed control plots (a1). GMSs are used as an indirect method for monitoring soil water status at two depths (b1 = 15 cm and b2 = 30 cm) in order to make a decision on when to irrigate. The sensors used in this study were calibrated using a mass-based gravimetric method. In both growing seasons, irrigation treatment and installation depths have a significant influence (P<0.01) on soil water content. Sensors have shown a satisfactory response to wetting and drying periods in irrigation scheduling at 30-cm depth. Yet, due to variability of weather conditions, a slow response to wetting and drying was recorded in periods with intensive rainfall events (2010) and drought conditions with frequent irrigation intervals (2012)