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Register a new userRobust and Efficient High-dimensional Quantum State Tomography
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The exponential growth in Hilbert space with increasing size of a quantum system means that accurately characterising the system becomes significantly harder with system dimension d. We show that self-guided tomography is a practical, efficient, and robust technique of measuring higher-dimensional quantum states. The achieved fidelities are over 99.9% for qutrits (d=3) and ququints (d=5), and 99.1% for quvigints (d=20), the highest values ever realised for qudits. We demonstrate robustness against experimental sources of noise, both statistical and environmental. The technique is applicable to any higher-dimensional system, from a collection of qubits through to individual qudits, and any physical realisation, be it photonic, superconducting, ionic, or spin.
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The accuracy of estimating $d$-dimensional quantum states is limited by the Gill-Massar bound. It can be saturated in the qubit ($d=2$) scenario using adaptive standard quantum tomography. In higher dimensions, however, this is not the case and the accuracy achievable with adaptive quantum tomography quickly deteriorates with increasing $d$. Moreover, it is not known whether or not the Gill-Massar bound can be reached for an arbitrary $d$. To overcome this limitation, we introduce an adaptive tomographic method that is characterized by a precision that is better than half that of the Gill-Massar bound for any finite dimension. This provides a new achievable accuracy limit for quantum state estimation. We demonstrate the high-accuracy of our method by estimating the state of 10-dimensional quantum systems. With the advent of new technologies capable of high-dimensional quantum information processing, our results become critically relevant as state reconstruction is an essential tool for certifying the proper operation of quantum devices.
Standard Bayesian credible-region theory for constructing an error region on the unique estimator of an unknown state in general quantum-state tomography to calculate its size and credibility relies on heavy Monte~Carlo sampling of the state space followed by sample rejection. This conventional method typically gives negligible yield for very small error regions originating from large datasets. We propose an operational reformulated theory to compute both size and credibility from region-average quantities that in principle convey information about behavior of these two properties as the credible-region changes. We next suggest the accelerated hit-and-run Monte~Carlo sampling, customized to the construction of Bayesian error-regions, to efficiently compute region-average quantities, and provide its complexity estimates for quantum states. Finally by understanding size as the region-average distance between two states in the region (measured for instance with either the Hilbert-Schmidt, trace-class or Bures distance), we derive approximation formulas to analytically estimate both distance-induced size and credibility under the pseudo-Bloch parametrization without resorting to any Monte~Carlo computation.
The characterization of quantum processes, e.g. communication channels, is an essential ingredient for establishing quantum information systems. For quantum key distribution protocols, the amount of overall noise in the channel determines the rate at which secret bits are distributed between authorized partners. In particular, tomographic protocols allow for the full reconstruction, and thus characterization, of the channel. Here, we perform quantum process tomography of high-dimensional quantum communication channels with dimensions ranging from 2 to 5. We can thus explicitly demonstrate the effect of an eavesdropper performing an optimal cloning attack or an intercept-resend attack during a quantum cryptographic protocol. Moreover, our study shows that quantum process tomography enables a more detailed understanding of the channel conditions compared to a coarse-grained measure, such as quantum bit error rates. This full characterization technique allows us to optimize the performance of quantum key distribution under asymmetric experimental conditions, which is particularly useful when considering high-dimensional encoding schemes.
Several methods, known as Quantum Process Tomography, are available to characterize the evolution of quantum systems, a task of crucial importance. However, their complexity dramatically increases with the size of the system. Here we present the theory describing a new type of method for quantum process tomography. We describe an algorithm that can be used to selectively estimate any parameter characterizing a quantum process. Unlike any of its predecessors this new quantum tomographer combines two main virtues: it requires investing a number of physical resources scaling polynomially with the number of qubits and at the same time it does not require any ancillary resources. We present the results of the first photonic implementation of this quantum device, characterizing quantum processes affecting two qubits encoded in heralded single photons. Even for this small system our method displays clear advantages over the other existing ones.
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.
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