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arXiv:0906.3468 · Contemporary Physics

Uncollapsing the wavefunction by undoing quantum measurements

Andrew N. Jordan, Alexander N. Korotkov

Published Dec 17, 2009• 44 citations
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Abstract

We review and expand on recent advances in theory and experiments concerning the problem of wavefunction uncollapse: given an unknown state that has been disturbed by a generalised measurement, restore the state to its initial configuration. We describe how this is probabilistically possible with a subsequent measurement that involves erasing the information extracted about the state in the first measurement. The general theory of abstract measurements is discussed, focusing on quantum information aspects of the problem, in addition to investigating a variety of specific physical situations and explicit measurement strategies. Several systems are considered in detail: the quantum double dot charge qubit measured by a quantum point contact (with and without Hamiltonian dynamics), the superconducting phase qubit monitored by a SQUID detector, and an arbitrary number of entangled charge qubits. Furthermore, uncollapse strategies for the quantum dot electron spin qubit, and the optical polarisation qubit are also reviewed. For each of these systems the physics of the continuous measurement process, the strategy required to ideally uncollapse the wavefunction, as well as the statistical features associated with the measurement are discussed. We also summarise the recent experimental realisation of two of these systems, the phase qubit and the polarisation qubit.

DOI
10.1080/00107510903385292

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•Jan 1, 2019•0 citations
We review and expand on recent advances in theory and experiments concerning the problem of wavefunction uncollapse: given an unknown state that has been disturbed by a generalised measurement, restore the state to its initial configuration. We describe how this is probabilistically possible with a subsequent measurement that involves erasing the information extracted about the state in the first measurement. The general theory of abstract measurements is discussed, focusing on quantum information aspects of the problem, in addition to investigating a variety of specific physical situations and explicit measurement strategies. Several systems are considered in detail: the quantum double dot charge qubit measured by a quantum point contact (with and without Hamiltonian dynamics), the superconducting phase qubit monitored by a SQUID detector, and an arbitrary number of entangled charge qubits. Furthermore, uncollapse strategies for the quantum dot electron spin qubit, and the optical polarisation qubit are also reviewed. For each of these systems the physics of the continuous measurement process, the strategy required to ideally uncollapse the wavefunction, as well as the statistical features associated with the measurement are discussed. We also summarise the recent experimental realisation of two of these systems, the phase qubit and the polarisation qubit.
We propose an experiment which demonstrates the undoing of a weak continuous measurement of a solid-state qubit, so that any unknown initial state is fully restored. The undoing procedure has only a finite probability of success because of the nonunitary nature of quantum measurement, though it is accompanied by a clear experimental indication of whether or not the undoing has been successful. The probability of success decreases with increasing strength of the measurement, reaching zero for a traditional projective measurement. Measurement undoing ("quantum undemolition") may be interpreted as a kind of quantum eraser, in which the information obtained from the first measurement is erased by the second measurement, which is an essential part of the undoing procedure. The experiment can be realized using quantum dot (charge) or superconducting (phase) qubits.
We demonstrate in a superconducting qubit the conditional recovery (uncollapsing) of a quantum state after a partial-collapse measurement. A weak measurement extracts information and results in a nonunitary transformation of the qubit state. However, by adding a rotation and a second partial measurement with the same strength, we erase the extracted information, canceling the effect of both measurements. The fidelity of the state recovery is measured using quantum process tomography and found to be above 70% for partial-collapse strength less than 0.6.
In this article, we report the recent progress on decoherence dynamics of electrons in quantum dot quantum computing systems using the exact master equation we derived recently based on the Feynman–Vernon influence functional approach. The exact master equation is valid for general nanostructure systems coupled to multi-reservoirs with arbitrary spectral densities, temperatures and biases. We take the double quantum dot charge qubit system as a specific example, and discuss in details the decoherence dynamics of the charge qubit under coherence controls. The decoherence dynamics risen from the entanglement between the system and the environment is mainly non-Markovian. We further discuss the decoherence of the double-dot charge qubit induced by quantum point contact (QPC) measurement where the master equation is re-derived using the Keldysh non-equilibrium Green function technique due to the non-linear coupling between the charge qubit and the QPC. The non-Markovian decoherence dynamics in the measurement processes is extensively discussed as well.
Quantum information processing in semiconductor quantum dots using single and multi-spin qubitsThe idea of a quantum computer, a device capable of processing information using quantum bits (qubit) instead of classical bits that outperforms classical computer in terms of computation speed, is still science ction. However, recent advances in quantum information processing showed that this ction may come true faster than anticipated. A promising platform for the physical realization of a qubit are spin qubits where the information is encoded in the quantum mechanical spin of an electron con ned in a semiconductor quantum dot. There are a variety of di erent implementations how the logical qubit is physically encoded, the use of a single electron spin or the use of the spins of multi electrons. This thesis focuses on the implementation of the spin- 1/2 qubit using the spin of a single electron in a single quantum dot, the exchangeonly (EO) qubit using three electron spins distributed in three quantum dots, and the novel quadrupolar exchange-only (QUEX) qubit using four electron spins distributed in three quantum dots. In this thesis we investigate several theoretical aspects of the physical implementation of the aforementioned qubit encodings. Since all three qubit encodings are allelectric controlled these implementations su er decoherence, the loss of information, from electric uctuations of the environment commonly called charge noise. Typically, the use of more quantum dots increases the decoherence due to charge noise while it decreases the decoherence due to magnetic noise. The rst main aspect investigated in this thesis is the protection of the quantum information encoded in the di erent qubit implementations against charge noise. Special attention is paid to the multi-electron spin implementations where high-symmetry points of operation are discovered which are less sensitive to the charge noise. Protection against charge noise is even better by increasing the number of electrons while keeping the number of quantum dots making the QUEX qubit superior to the EO qubit. So far the main direction in this thesis is the reduction of the qubit sensitivity to electric uctuations. However, coherent electromagnetic elds in form of microwaves v can be used to interconnect qubits. In this thesis also a high-performance coupling between two spin-1/2 is investigated. The use of a resonator, subsequently, allows for a coupling of qubits over macroscopic distances as well as to extract valuable information about the physical system. Because of the larger susceptibility of multi-spin qubits to the electric eld of the resonator, this thesis focuses on the coupling between an EO or a QUEX qubit and a microwave resonator. Points of operations are discovered for both qubit implementations which o er a strong coupling towards a microwave resonator while maintaining their protection against charge noise. Subsequently, a series of measurements are proposed to extract information about the microscopic structure of the quantum dots. Finally, a promising high-performance protocol for coupling two qubits remotely via the resonator is investigated in detail.