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

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

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

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