Partial Measurements of Quantum Systems

Projective measurement is a commonly used assumption in quantum mechanics. However, advances in quantum measurement techniques allow for partial measurements, which accurately estimate state information while keeping the wavefunction intact. In this dissertation, we employ partial measurements to study two phenomena. First, we investigate an uncertainty relation -- in the style of Heisenberg's 1929 thought experiment -- which includes partial measurements in addition to projective measurements. We find that a weak partial measurement can decrease the uncertainty between two incompatible (non-commuting) observables. In the second study, we investigate the foundation of irreversible dynamics resulting from partial measurements. We do so by comparing the forward and time-reversed probabilities of measurement outcomes resulting from post-selected feedback protocols with both causal and reversed-causal order. We find that the statistics of partial measurements produce entropy in accordance with generalized second laws of thermodynamics. We perform these experiments using superconducting qubits. This dissertation also describes the fabrication process for these devices and details a novel fabrication technique that allows fast, single-step lithography of Josephson-junction superconducting circuits. The technique simplifies processing by utilizing a direct-write photolithography system, in contrast to traditional electron-beam lithography. Despite their large lithographic area, Josephson junctions made with this method have low critical currents and high coherence times.Projective measurement is a commonly used assumption in quantum mechanics. However, advances in quantum measurement techniques allow for partial measurements, which accurately estimate state information while keeping the wavefunction intact. In this dissertation, we employ partial measurements to study two phenomena. First, we investigate an uncertainty relation -- in the style of Heisenberg's 1929 thought experiment -- which includes partial measurements in addition to projective measurements. We find that a weak partial measurement can decrease the uncertainty between two incompatible (non-commuting) observables. In the second study, we investigate the foundation of irreversible dynamics resulting from partial measurements. We do so by comparing the forward and time-reversed probabilities of measurement outcomes resulting from post-selected feedback protocols with both causal and reversed-causal order. We find that the statistics of partial measurements produce entropy in accordance with generalized second laws of thermodynamics. We perform these experiments using superconducting qubits. This dissertation also describes the fabrication process for these devices and details a novel fabrication technique that allows fast, single-step lithography of Josephson-junction superconducting circuits. The technique simplifies processing by utilizing a direct-write photolithography system, in contrast to traditional electron-beam lithography. Despite their large lithographic area, Josephson junctions made with this method have low critical currents and high coherence times.

arXiv:2108.07828Aug 17, 20215 citations

Generalized partial measurements

Gheorghe Sorin Paraoanu

We introduce a type of measurements which generalize the so-called "partial measurements" performed in recent years with phase qubits. While in the case of partial measurements it has been demonstrated that one could undo the effect of the measurement only for non-switching events, we show here that generalized partial measurements can be reversed probabilistically for both switching and non-switching events. We calculate the associated Fisher information and discuss the estimation sensitivity for quantum tomography. Two ways of implementing this type of measurements with superconducting qubits are proposed.We introduce a type of measurements which generalize the so-called "partial measurements" performed in recent years with phase qubits. While in the case of partial measurements it has been demonstrated that one could undo the effect of the measurement only for non-switching events, we show here that generalized partial measurements can be reversed probabilistically for both switching and non-switching events. We calculate the associated Fisher information and discuss the estimation sensitivity for quantum tomography. Two ways of implementing this type of measurements with superconducting qubits are proposed.

arXiv:1105.4032Europhysics Letters (EPL)Mar 1, 201120 citations

Sub- $\mu\hbox{m}$ Josephson Junctions for Superconducting Quantum DevicesSub-$\mu\hbox{m}$ Josephson Junctions for Superconducting Quantum Devices

J. M. Meckbach, Michael Merker, Simon J. Buehler +7 more

For high-performance superconducting quantum devices based on Josephson junctions (JJs), decreasing lateral sizes is of great importance. Fabrication of sub-μm JJs is challenging, due to nonflat surfaces with step heights of up to several 100 nm generated during the fabrication process. We have refined a fabrication process with significantly decreased film thicknesses, resulting in almost flat surfaces at intermediate steps during the JJ definition. In combination with a mix-and-match process, combining electron-beam lithography and conventional photolithography, we can fabricate JJs with lateral dimensions down to 0.023 μm2. We propose this refined process as an alternative to the commonly used chemical-mechanical polishing procedure. Transport measurements of JJs, having critical-current densities ranging from 50 to 104A/cm2, are presented at 4.2 K. Our JJ process yields excellent quality parameters, Rsg/RNup to ~ 50, Vmfrom 15 to 80 mV and Vgapup to 2.81 mV, and also allows the fabrication of high-quality, sub-μm wide, long JJs (LJJs) for the study of Josephson vortex behavior. The developed technique can also be used for similar multilayer processes and is very promising for fabricating sub- μm JJs for quantum devices such as SQUIDs, qubits, and SIS mixers.For high-performance superconducting quantum devices based on Josephson junctions (JJs), decreasing lateral sizes is of great importance. Fabrication of sub-μm JJs is challenging, due to nonflat surfaces with step heights of up to several 100 nm generated during the fabrication process. We have refined a fabrication process with significantly decreased film thicknesses, resulting in almost flat surfaces at intermediate steps during the JJ definition. In combination with a mix-and-match process, combining electron-beam lithography and conventional photolithography, we can fabricate JJs with lateral dimensions down to 0.023 μm2. We propose this refined process as an alternative to the commonly used chemical-mechanical polishing procedure. Transport measurements of JJs, having critical-current densities ranging from 50 to 104A/cm2, are presented at 4.2 K. Our JJ process yields excellent quality parameters, Rsg/RNup to ~ 50, Vmfrom 15 to 80 mV and Vgapup to 2.81 mV, and also allows the fabrication of high-quality, sub-μm wide, long JJs (LJJs) for the study of Josephson vortex behavior. The developed technique can also be used for similar multilayer processes and is very promising for fabricating sub- μm JJs for quantum devices such as SQUIDs, qubits, and SIS mixers.

arXiv:1210.1012IEEE Transactions on Applied SuperconductivityDec 4, 201211 citations

Demonstration of irreversibility and dissipation relation of thermodynamics with a superconducting qubit

Xueyi Guo, Yi Peng, Changnan Peng +6 more

We investigate experimentally the relation between thermodynamical irreversibility and dissipation on a superconducting Xmon qubit. This relation also implies the second law and the Landauer principle on dissipation in the irreversible computations. In our experiment, the qubit is initialized to states according to Gibbs distribution. Work injection and extraction processes are conducted through two kinds of unitary driving protocols, for both a forward process and its corresponding mirror reverses. Relative entropy and relative Re'nyi entropy are employed to measure the asymmetry between paired forward and backward work injection or extraction processes. We show experimentally that relative entropy and relative Re'nyi entropy measured irreversibility are related to the average of work dissipation and average of exponentiated work dissipation respectively. Our work provides solid experimental support for the theory of quantum thermodynamics.We investigate experimentally the relation between thermodynamical irreversibility and dissipation on a superconducting Xmon qubit. This relation also implies the second law and the Landauer principle on dissipation in the irreversible computations. In our experiment, the qubit is initialized to states according to Gibbs distribution. Work injection and extraction processes are conducted through two kinds of unitary driving protocols, for both a forward process and its corresponding mirror reverses. Relative entropy and relative Re'nyi entropy are employed to measure the asymmetry between paired forward and backward work injection or extraction processes. We show experimentally that relative entropy and relative Re'nyi entropy measured irreversibility are related to the average of work dissipation and average of exponentiated work dissipation respectively. Our work provides solid experimental support for the theory of quantum thermodynamics.

arXiv:1710.10234Oct 27, 20172 citations

Partial entanglement, complementary, and simultaneous measurement of discrete observables

Alexei S. Trifonov, Jonas Söderholm, Gunnar G. Bjork

Different quantum information schemes, such as eavesdropping in quantum cryptography, dictate the necessity of extracting information about pair conjugate observables from a single copy of a quantum system. Mathematically, quantum measurements are usually described by an uncertainty relation. The difference between the simultaneous measurement uncertainty relation form those known from the textbooks on quantum mechanics is the additional uncertainty associated with the measurement procedure itself in contrast to the state preparation uncertainties described by the Schroedinger-Robertson type uncertainty relations. We present here an overview of our approach based on the state estimation theory and maximum likelihood strategy. We make a theoretical analysis and an experimental verification of minimum-uncertainty product of the two-states quantum system simultaneous measurement based on partially entangled photon pairs.Different quantum information schemes, such as eavesdropping in quantum cryptography, dictate the necessity of extracting information about pair conjugate observables from a single copy of a quantum system. Mathematically, quantum measurements are usually described by an uncertainty relation. The difference between the simultaneous measurement uncertainty relation form those known from the textbooks on quantum mechanics is the additional uncertainty associated with the measurement procedure itself in contrast to the state preparation uncertainties described by the Schroedinger-Robertson type uncertainty relations. We present here an overview of our approach based on the state estimation theory and maximum likelihood strategy. We make a theoretical analysis and an experimental verification of minimum-uncertainty product of the two-states quantum system simultaneous measurement based on partially entangled photon pairs.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEApr 3, 20021 citation

Notes on implementing generalized measurements with superconducting qubits

Justin Dressel, Todd A. Brun, Alexander N. Korotkov

We describe a method to perform any generalized purity-preserving measurement of a qubit with techniques tailored to superconducting systems. We start with considering two methods for realizing a two-outcome partial projection: using a thresholded continuous measurement in the circuit QED setup and using an indirect ancilla qubit measurement. Then we decompose an arbitrary puritypreserving two-outcome measurement into single qubit unitary rotations and a partial projection. Finally, we systematically reduce any multiple-outcome measurement to a sequence of two-outcome measurements and unitary operations.We describe a method to perform any generalized purity-preserving measurement of a qubit with techniques tailored to superconducting systems. We start with considering two methods for realizing a two-outcome partial projection: using a thresholded continuous measurement in the circuit QED setup and using an indirect ancilla qubit measurement. Then we decompose an arbitrary puritypreserving two-outcome measurement into single qubit unitary rotations and a partial projection. Finally, we systematically reduce any multiple-outcome measurement to a sequence of two-outcome measurements and unitary operations.

Dec 4, 20130 citations

Sub-

\mu\hbox{m}

Josephson Junctions for Superconducting Quantum Devices