arXiv subjects

Martin Plesch

Publications and source records attributed to Martin Plesch.

44 records · Page 3Linked to original sources

arXiv2009

Scrutinizing single-qubit quantum channels: Theory and experiment with trapped ions

We report experimental implementation of various types of qubit channels using an individual trapped ion. We analyzed experimental data and we performed tomographic reconstruction of quantum channels based on these data. Specifically, we studied phase damping channels, where the damping acts either in the xy-plane of the Bloch sphere or in an arbitrary plane that includes the origin of the Bloch sphere. We also experimentally realized and consequently analyzed quantum channels that in addition to phase damping affect also a polarization rotation. We used three reconstruction schemes for estimation of quantum channels from experimental data: (1) a linear inverse method, (2) a maximum likelihood estimation, and (3) a constrained maximum likelihood estimation. We took into account realistic experimental conditions where imperfect test-state preparations and biased measurements are incorporated into the estimation schemes. As a result we found that imperfections present in the process of preparation of test states and as well as in measurements of the considered ion trap system do not limit the control of the implementation of the desired channel. Even imperfect preparation of test state and subsequent measurements still provide sufficient resources for the complete quantum-channel tomography.

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arXiv2006

Towards optimization of quantum circuits

Any unitary operation in quantum information processing can be implemented via a sequence of simpler steps - quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, seeking for a short sequence of gates - efficient quantum circuit for a given operation, is an important task. We contribute to this issue by proposing optimization of the well-known universal procedure proposed by Barenco et.al [1]. We also created a computer program which realizes both Barenco's decomposition and the proposed optimization. Furthermore, our optimization can be applied to any quantum circuit containing generalized Toffoli gates, including basic quantum gate circuits.

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arXiv2005

Process reconstruction: From unphysical to physical maps via maximum likelihood

We show that the method of maximum likelihood (MML) provides us with an efficient scheme for reconstruction of quantum channels from incomplete measurement data. By construction this scheme always results in estimations of channels that are completely positive. Using this property we use the MML for a derivation of physical approximations of un-physical operations. In particular, we analyze the optimal approximation of the universal NOT gate as well as a physical approximation of a quantum nonlinear polarization rotation.

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arXiv2004

Process reconstruction from incomplete and/or inconsistent data

We analyze how an action of a qubit channel (map) can be estimated from the measured data that are incomplete or even inconsistent. That is, we consider situations when measurement statistics is insufficient to determine consistent probability distributions. As a consequence either the estimation (reconstruction) of the channel completely fails or it results in an unphysical channel (i.e., the corresponding map is not completely positive). We present a regularization procedure that allows us to derive physically reasonable estimates (approximations) of quantum channels. We illustrate our procedure on specific examples and we show that the procedure can be also used for a derivation of optimal approximations of operations that are forbidden by the laws of quantum mechanics (e.g., the universal NOT gate).

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arXiv2004

Reconstruction of superoperators from incomplete measurements

We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[rho_j ] that originate from a set of four linearly independent test states j (j = 1, 2, 3, 4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator rho = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel.

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arXiv2003

Controlling bi-partite entanglement in multi-qubit systems

Bi-partite entanglement in multi-qubit systems cannot be shared freely. The rules of quantum mechanics impose bounds on how multi-qubit systems can be correlated. In this paper we utilize a concept of entangled graphs with weighted edges in order to analyze pure quantum states of multi-qubit systems. Here qubits are represented by vertexes of the graph while the presence of bi-partite entanglement is represented by an edge between corresponding vertexes. The weight of each edge is defined to be the entanglement between the two qubits connected by the edge, as measured by the concurrence. We prove that each entangled graph with entanglement bounded by a specific value of the concurrence can be represented by a pure multi-qubit state. In addition we present a logic network with O(N2) elementary gates that can be used for preparation of the weighted entangled graphs of N qubits.

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arXiv2003

Entangled graphs II: Classical correlations in multi-qubit entangled systems

Bipartite correlations in multi-qubit systems cannot be shared freely. The presence of entanglement or classical correlation on certain pairs of qubits may imply correlations on other pairs. We present a method of characterization of bi-partite correlations in multi-qubit systems using a concept of entangled graphs that has been introduced in our earlier work [M.Plesch and V.Buzek, Phys. Rev. A 67, 012322 (2003)]. In entangled graphs each qubit is represented by a vertex while the entanglement and classical correlations are represented by two types of edges. We prove by construction that any entangled graph with classical correlations can be represented by a mixed state of N qubits. However, not all entangled graphs with classical correlations can be represented by a pure state.

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arXiv2002

Entangled graphs: Bipartite entanglement in multi-qubit systems

Quantum entanglement in multipartite systems cannot be shared freely. In order to illuminate basic rules of entanglement sharing between qubits we introduce a concept of an entangled structure (graph) such that each qubit of a multipartite system is associated with a point (vertex) while a bi-partite entanglement between two specific qubits is represented by a connection (edge) between these points. We prove that any such entangled structure can be associated with a pure state of a multi-qubit system. Moreover, we show that a pure state corresponding to a given entangled structure is a superposition of vectors from a subspace of the $2^N$-dimensional Hilbert space, whose dimension grows linearly with the number of entangled pairs.

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