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Register a new userTrading quantum states for temporal profiles: tomography by the overlap
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Quantum states and the modes of the optical field they occupy are intrinsically connected. Here, we show that one can trade the knowledge of a quantum state to gain information about the underlying mode structure and, vice versa, the knowledge about the modal shape allows one to perform a complete tomography of the quantum state. Our scheme can be executed experimentally using the interference between the signal and probe states on an unbalanced beam splitter with a single on/off-type detector. By changing the temporal overlap between the signal and the probe, the imperfect interference is turned into a powerful tool to extract the information about the signal mode structure. A single on/off detector is already sufficient to collect the necessary measurement data for the reconstruction of the diagonal part of the density matrix of an arbitrary multi-mode signal. Moreover, we experimentally demonstrate the feasibility of our scheme with just one control parameter -- the time-delay of a coherent probe field.
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We propose and experimentally demonstrate a quantum state tomography protocol that generalizes the Wallentowitz-Vogel-Banaszek-Wodkiewicz point-by-point Wigner function reconstruction. The full density operator of an arbitrary quantum state is efficiently reconstructed in the Fock basis, using semidefinite programming, after interference with a small set of calibrated coherent states. This new protocol is resource- and computationally efficient, is robust against noise, does not rely on approximate state displacements, and ensures the physicality of results.
We consider realistic measurement systems, where measurements are accompanied by decoherence processes. The aim of this work is the construction of methods and algorithms for precise quantum measurements with fidelity close to the fundamental limit. In the present work the notions of ideal and non-ideal quantum measurements are strictly formalized. It is shown that non-ideal quantum measurements could be represented as a mixture of ideal measurements. Based on root approach the quantum state reconstruction method is developed. Informational accuracy theory of non-ideal quantum measurements is proposed. The monitoring of the amount of information about the quantum state parameters is examined, including the analysis of the information degradation under the noise influence. The study of achievable fidelity in non-ideal quantum measurements is performed. The results of simulation of fidelity characteristics of a wide class of quantum protocols based on polyhedrons geometry with high level of symmetry are presented. The impact of different decoherence mechanisms, including qubit amplitude and phase relaxation, bit-flip and phase-flip, is considered.
In this paper, we study extended linear regression approaches for quantum state tomography based on regularization techniques. For unknown quantum states represented by density matrices, performing measurements under certain basis yields random outcomes, from which a classical linear regression model can be established. First of all, for complete or over-complete measurement bases, we show that the empirical data can be utilized for the construction of a weighted least squares estimate (LSE) for quantum tomography. Taking into consideration the trace-one condition, a constrained weighted LSE can be explicitly computed, being the optimal unbiased estimation among all linear estimators. Next, for general measurement bases, we show that $ell_2$-regularization with proper regularization gain provides even lower mean-square error under a cost in bias. The regularization parameter is tuned by two estimators in terms of a risk characterization. Finally, a concise and unified formula is established for the regularization parameter with complete measurement basis under an equivalent regression model, which proves that the proposed tuning estimators are asymptotically optimal as the number of samples grows to infinity under the risk metric. Additionally, numerical examples are provided to validate the established results.
The Second Law of Thermodynamics states that the entropy of a closed system is non-decreasing. Discussing the Second Law in the quantum world poses new challenges and provides new opportunities, involving fundamental quantum-information-theoretic questions and novel quantum-engineered devices. In quantum mechanics, systems with an evolution described by a so-called unital quantum channel evolve with a non-decreasing entropy. Here, we seek the opposite, a system described by a non-unital and, furthermore, energy-conserving channel that describes a system whose entropy decreases with time. We propose a setup involving a mesoscopic four-lead scatterer augmented by a micro-environment in the form of a spin that realizes this goal. Within this non-unital and energy-conserving quantum channel, the micro-environment acts with two non-commuting operations on the system in an autonomous way. We find, that the process corresponds to a partial exchange or swap between the system and environment quantum states, with the systems entropy decreasing if the environments state is more pure. This entropy-decreasing process is naturally expressed through the action of a quantum Maxwell demon and we propose a quantum-thermodynamic engine with four qubits that extracts work from a single heat reservoir when provided with a reservoir of pure qubits. The special feature of this engine, which derives from the energy-conservation in the non-unital quantum channel, is its separation into two cycles, a working cycle and an entropy cycle, allowing to run this engine with no local waste heat.
We report an experimental realization of adaptive Bayesian quantum state tomography for two-qubit states. Our implementation is based on the adaptive experimental design strategy proposed in [F.Huszar and N.M.T.Houlsby, Phys.Rev.A 85, 052120 (2012)] and provides an optimal measurement approach in terms of the information gain. We address the practical questions, which one faces in any experimental application: the influence of technical noise, and behavior of the tomographic algorithm for an easy to implement class of factorized measurements. In an experiment with polarization states of entangled photon pairs we observe a lower instrumental noise floor and superior reconstruction accuracy for nearly-pure states of the adaptive protocol compared to a non-adaptive. At the same time we show, that for the mixed states the restriction to factorized measurements results in no advantage for adaptive measurements, so general measurements have to be used.
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