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arXiv:1310.8233 · Physica Scripta

Noise robustness in the detection of non-separable random unitary maps

Chiara Macchiavello, Matteo A. C. Rossi

Published Mar 1, 2013• 3 citations
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Abstract

We briefly review in this paper a recently proposed method to detect the properties of quantum noise processes and quantum channels. We illustrate in detail the method for detecting non-separable random unitary channels and consider, in particular, explicit examples of the CNOT and C-Z gates. We also analyse their robustness in the presence of noise for several quantum noise models.

DOI
10.1088/0031-8949/2013/t153/014044

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We briefly review in this paper a recently proposed method to detect the properties of quantum noise processes and quantum channels. We illustrate in detail the method for detecting non-separable random unitary channels and consider, in particular, explicit examples of the CNOT and C-Z gates. We also analyse their robustness in the presence of noise for several quantum noise models.
We present a method to detect properties of quantum channels, assuming that some a priori information about the form of the channel is available. The method is based on a correspondence with entanglement detection methods for multipartite density matrices based on witness operators. We first illustrate the method in the case of entanglement-breaking channels and nonseparable random unitary channels and show how it can be implemented experimentally by means of local measurements. We then study the detection of nonseparable maps and show that for pairs of systems of dimension higher than two the detection operators are not the same as in the random unitary case, highlighting a richer separability structure of quantum channels with respect to quantum states. Finally we consider the set of PPT maps, developing a technique to reveal NPT maps.
We demonstrate experimentally the possibility of efficiently detecting properties of quantum channels and quantum gates. The experimentally realized quantum channel detection method has been recently proposed theoretically, and allows us to characterize the properties of quantum channels with a much smaller experimental effort than quantum process tomography. Here, the optimal detection scheme is first achieved for nonentanglement breaking channels of the depolarizing form and is based on the generation and detection of polarized entangled photons. We then demonstrate channel detection for nonseparable maps by considering the CNOT gate and employing two-photon hyperentangled states.
In quantum information and computation, the generation of entanglement through unitary gates remains a significant and active area of research. However, there are states termed as absolutely separable, from which entanglement cannot be created through any non-local unitary action. Thus, from a resource-theoretic perspective, non-absolutely separable states are useful as they can be turned into entangled states using some appropriate unitary gates. In this work, we propose an efficient method to detect non-absolutely separable states. Our approach relies on evaluating moments that can bypass the need for full state tomography, thereby enhancing its practical applicability. We then present several examples in support of our detection scheme. We also address a closely related problem concerning states whose partial transpose remains positive under any arbitrary non-local unitary action. Furthermore, we examine the effectiveness of our moment-based approach in the detection of quantum channels that are not absolutely separating, which entails the detection of resource preserving channels. Finally, we demonstrate the operational significance of non-absolutely separable states by proving that every such state can provide an advantage in a quantum-channel discrimination task.
We define several quantitative measures of the robustness of a quantum gate against noise. Exact analytic expressions for the robustness against depolarizing noise are obtained for all bipartite unitary quantum gates, and it is found that the controlled-NOT gate is the most robust two-qubit quantum gate, in the sense that it is the quantum gate which can tolerate the most depolarizing noise and still generate entanglement. Our results enable us to place several analytic upper bounds on the value of the threshold for quantum computation, with the best bound in the most pessimistic error model being pth< 0.5.{p}_{\mathrm{th}}<~0.5.pth​< 0.5.
Benchmarking of noise that is induced during the implementation of quantum gates is the main concern for practical quantum computers. Several protocols have been proposed that empirically calculate various metrics that quantify the error rates of the quantum gates chosen from a preferred gate set. Unitarity randomized benchmarking (URB) protocol is a method to estimate the coherence of noise induced by the quantum gates which is measured by the metric \textit{unitarity}. In this paper, we for the first time, implement the URB protocol in a quantum simulator with all the parameters and noise model are used from a real quantum device. The direct implementation of the URB protocol in a quantum device is not possible using current technologies, as it requires the preparation of mixed states. To overcome this challenge, we propose a modification of the URB protocol, namely the m-URB protocol, that enables us to practically implement it on any quantum device. We validate our m-URB protocol using two single-qubit noise channels -- (a) depolarising channel and (b) bit-flip channel. We further alter the m-URB protocol, namely, native gate URB or Ng-URB protocol, to study the noise in the native gates into which the quantum circuits are compiled in a quantum computer. Using our Ng-URB protocol, we can also detect the presence of cross-talk errors which are correlated errors caused due to non-local and entangling gates such as CNOT gate. For illustration, we simulate the noise of the native gates taking the noise parameter from two real IBM-Q processors.
Entanglement is not only the most intriguing feature of quantum mechanics, but also a key resource in quantum information science. The entanglement content of random pure quantum states is almost maximal; such states find applications in various quantum information protocols. The preparation of a random state or, equivalently, the implementation of a random unitary operator, requires a number of elementary one- and two-qubit gates that is exponential in the number n_q of qubits, thus becoming rapidly unfeasible when increasing n_q. On the other hand, pseudo-random states approximating to the desired accuracy the entanglement properties of true random states may be generated efficiently, that is, polynomially in n_q. In particular, quantum chaotic maps are efficient generators of multipartite entanglement among the qubits, close to that expected for random states. This review discusses several aspects of the relationship between entanglement, randomness and chaos. In particular, I will focus on the following items: (i) the robustness of the entanglement generated by quantum chaotic maps when taking into account the unavoidable noise sources affecting a quantum computer; (ii) the detection of the entanglement of high-dimensional (mixtures of) random states, an issue also related to the question of the emergence of classicality in coarse grained quantum chaotic dynamics; (iii) the decoherence induced by the coupling of a system to a chaotic environment, that is, by the entanglement established between the system and the environment.