Complementarity Relation for Coherence and Disturbance

Quantum measurements necessarily disturb the state of physical system. Once we perform a complete measurement, the system undergoes decoherence and loses its coherence. If there is no disturbance, the state retains all of its coherence. It is therefore natural to ask if there is trade-off between disturbance caused to a state and its coherence. We present a coherence disturbance complementarity relation using the relative entropy of coherence. For bipartite states we prove a complementarity relation between the quantum coherence, entanglement and disturbance. Similar relation also holds for quantum coherence, quantum discord and disturbance for a bipartite state. We illustrate the trade-off between the coherence and the disturbance for single qubit state for various quantum channels.Comment: 7 pages, 3 figure

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Quantum Coherence, Coherent Information and Information Gain in Quantum Measurement

A measurement is deemed successful, if one can maximize the information gain by the measurement apparatus. Here, we ask if quantum coherence of the system imposes a limitation on the information gain during quantum measurement. First, we argue that the information gain in a quantum measurement is nothing but the coherent information or the distinct quantum information that one can send from the system to apparatus. We prove that the maximum information gain from a pure state, using a mixed apparatus is upper bounded by the initial coherence of the system. Further, we illustrate the measurement scenario in the presence of environment. We argue that the information gain is upper bounded by the entropy exchange between the system and the apparatus. Also, to maximize the information gain, both the initial coherence of the apparatus, and the final entanglement between the system and apparatus should be maximum. Moreover, we find that for a fixed amount of coherence in the final apparatus state the more robust apparatus is, the more will be the information gain.Comment: 6 Pages, Comments are welcom

Efficiency of aluminum and iron electrodes in removal of colour, turbidity and total suspended solid from biologically treated municipal wastewater

The present investigation was undertaken to observe the effect of different combinations of aluminium and iron (Al-Al, Al-Fe, Fe-Fe and Fe-Al) electrodes on the removal of colour, turbidity (TD) and total suspended solids (TSS) of biologically treated municipal wastewater ( BTMW) using applied potential (V), operating time (OT) and initial pH. The maximum removal of colour (98.7 %) and TSS (96.89 %) was found with the use of Al-Al combination with optimum operating conditions (Voltage: 40 V; OT: 40 mins.; IED: 1.0 cm; EA: 160 cm2; initial pH: 7.5 and ST: 30 mins). It was interesting to note that TD of BTMW was completely removed at these optimal operating conditions. The economic evaluation of electrode combinations was observed to be in the order of Fe-Al (1.17 US /m3)> Al-Fe (1.11 US /m3)> Fe-Fe (1.08 US /m3) >Al-Al (1.01 US /m3) in terms of energy and electrode consumption. Thus, the BTMW can be effectively treated with the Al-Al electrode combination in comparison to other electrode combinations (Al-Fe , Fe-Fe and Fe-Al)

Efficiency of turbidity and BOD removal from secondarily treated sewage by electrochemical treatment

The present investigation observed the effect of operating time, current density, pH and supporting electrolyte on the removal efficiency of Turbidity (TD) and Biochemical oxygen demand (BOD) of secondarily treated sewage (STS) using electrochemical process. A glass chamber of 2 litre volume was used for the experiment with two electrode plates of aluminum, each having an area of 125 cm2 and 2 cm distance apart from each other. The treatment showed that the removal efficiency of TD and BOD increased to 87.41 and 81.38 % respectively with theincrease of current density (1.82 -7.52 mA/cm2), time (5 - 40 mins.) and different pH (4-8) of the STS. The most effective removal efficiency was observed around the pH 7. Further, 0.5 g/l NaCl as a supporting electrolyte for electrochemical treatment of STS was found to be more efficient for an increase to 95.56 % and 86.99 % for the removal of TD and BOD at 7.52 mA/cm2 current density in 40 mins. respectively. The electrode and energy consumption was found to vary from 2.52 x10-2 to 10.51 x10-2 kg Al/m3 and 2.76 kwh/m3 to 45.12 kWh/m3 depending on the operating conditions.The kinetic study results revealed that reaction rate (k) increased from 0.0174 to 0.03 min-1 for TD and 0.0169 to 0.024 min-1 for BOD with increase in current density from 1.82 to 7.52 mA/cm2

Influence of operating conditions on the electrolytic treatment for the removal of color, TSS, hardness and alkalinity using Al-Al electrode combination

The present investigation observed the effect of current density (CD), operating time (OT), inter electrode distance (IED), electrode area (EA), initial pH and settling time (ST) using Al-Al electrode combination on the removal of color, total suspended solids (TSS), hardness (HR) and alkalinity (ALK) from biologically treated municipal wastewater (BTMW) of Sewage Treatment Plant (STP), Jagjeetpur, Haridwar, India. The maximum removal of color (99.86%), TSS (98.7%), HR (78.9%) and ALK (43.69 %) from BTMW was found with the optimum operating conditions of CD (2.65 A/m2), OT (40 mins.), IED (0.5 cm), EA (160 cm2), initial pH (7.5) and ST (60 min.). However, the maximum removal of ALK was found with the optimum operating conditions of CD (1.68 A/m2), OT (40 mins.), IED (1.0 cm), EA (80 cm2), initial pH (7.5) and ST (90 min.) The electrolytic treatment ( ET) brought down the concentration of HR and ALK to the desirable limit of the BIS standards of drinking water. There was no need of pH adjustment of the BTMW during ET as the optimal removal efficiency was close to the pH of 7.5. Under optimal operating conditions, the operating cost was found to be 1.01 $/m3 in terms of the electrode consumption (23.71x 10-5 kg Al/m3) and energy consumption (101.76 Kwh/m3). The study revealed that BTMW can be effectively treated with the Al-Al electrode combination for color, TSS, HR and ALK removal

Removal of COD and BOD from biologically treated municipal wastewater by electrochemical treatment

The present investigation observed the effect of current density (CD), operating time (OT), inter electrode distance (IED), electrode area (EA), initial pH and settling time (ST) using Fe-Fe electrode combination on the removal of chemical oxygen demand (COD) and biochemical oxygen demand (BOD) from biologically treated municipal wastewater (BTMW) of Sewage Treatment Plant (STP). The maximum removal of COD (92.35%) from BTMW was found with the optimum operating conditions of CD (2.82 A/m2), OT (40 mins.), IED (0.5 cm), EA (160 cm2), initial pH (7.5) and ST (60 min.), while the maximum removal of BOD (84.88%) was found with the ST (30 min.) at the same operating conditions. There was no need of pH adjustment of the BTMW during ET as the optimal removal efficiency was close to the pH of 7.5. Under optimal operating conditions, the operating cost was found to be 54.29 Rs./m3 / 1.08 US$/m3 in terms of the electrode consumption (78.48 x 10-5 kg Al/m3 ) and energy consumption (108.48 Kwh/m3)