We consider noisy, non-local unitary operations or interactions, i.e. the corresponding evolutions are described by completely positive maps or master equations of Lindblad form. We show that by random local operations the completely positive maps can be depolarized to a standard form with a reduced number of parameters describing the noise process in such a way that the noiseless (unitary) part of the evolution is not altered. A further reduction of the parameters, in many cases even to a single one (i.e. global white noise), is possible by tailoring the decoherence process and increasing the amount of noise. We generalize these results to the dynamical case where the ideal unitary operation is given by some interaction Hamiltonian. The resulting standard forms may be used to compute lower bounds on channel capacities, to simplify quantum process tomography or to derive error thresholds for entanglement purification and quantum computation.
A simple model describing depolarization channels with zero-bandwidth environment is presented and exactly solved. The environment is modelled by Lorentzian, telegraphic and Gaussian zero-bandwidth noises. Such channels can go beyond the standard Markov dynamics and therefore can illustrate the influence of memory effects of the noisy communication channel on the transmitted information. To quantify the disturbance of quantum states the entanglement fidelity between arbitrary input and output states is investigated.
The depolarization channel is usually modelled as a quantum operation that destroys all input information, replacing it by a completely chaotic state. For qubits this has a quite intuitive interpretation as a shrinking of the Bloch sphere. We propose a way to deal with depolarizing dynamics (in the Markov approximation) for systems with arbitrary symmetries.
We prove that if any error channel has a Kraus decomposition that is simultaneously correctable and Hilbert-Schmidt (HS) complete, then the existence of Kraus sets with these properties guarantees the correctability of all quantum channels. As a proof of the existence of such Kraus sets, the $n$-level depolarization channel is shown to have a random-unitary (RU) decomposition that is both HS complete and correctable due its RU nature, thereby proving that all quantum channels are correctable. As an application, conditions for universal error-correction operations are presented.
The process by which open quantum systems thermalize with an environment is both of fundamental interest and relevant to noisy quantum devices. As a minimal model of this process, we consider a qudit chain evolving under local random unitaries and local depolarization channels. After mapping to a statistical mechanics model, the depolarization (noise) acts like a symmetry-breaking field, and we argue that it causes the system to thermalize within a timescale independent of system size. We show that various bipartite entanglement measures -- mutual information, operator entanglement, and entang…
Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core sub- routine in various computing tasks such as the Monte Carlo methods. One of those algorithms is based on the maximum likelihood estimate with parallelized quantum circuits. In this paper, we extend this method so that it incorporates the realistic noise effect, and then give an experimental demonstration on a superconducting IBM Quantum device. The maximum likelihood estimator is constructed based on the model assumi…
Noise structuring in fixed-depth Trotter simulation: stationary channels and observable-level depolarization
Dukhov Research Institute of Automatics (VNIIA)（杜霍夫自动学研究所）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences（俄罗斯科学院理论与应用电动力学研究所）
We consider properties of states of many qubits, which arise after sending certain entangled states via various noisy channels (white noise, coloured noise, local depolarization, dephasing and amplitude damping). Entanglement of these states is studied and their ability to violate certain classes of Bell inequalities. States which violate them allow for higher than classical efficiency of solving related distributed computational tasks with constrained communication. This is a direct property of such states -- not requiring their further modification via stochastic local operations and classic…
Quantum information processing tasks require exotic quantum states as a prerequisite. They are usually prepared with many different methods tailored to the specific resource state. Here we provide a versatile unified state preparation scheme based on a driven quantum network composed of randomly-coupled fermionic nodes. The output of such a system is then superposed with the help of linear mixing where weights and phases are trained in order to obtain desired output quantum states. We explicitly show that our method is robust and can be utilized to create almost perfect maximally entangled, NO…
In this paper, we show how to use low-fidelity operations to control the dynamics of quantum systems. Noisy operations usually drive a system to evolve into a mixed state and damage the coherence. Sometimes frequent noisy operations result in the coherent evolution of a subsystem, and the dynamics of the subsystem is controlled by tuning noisy operations. Based on this, we find that universal quantum computation can be carried out by low-fidelity (fidelity $<90\%$) operations.
We investigate robustness of probabilistic storage and retrieval device optimized for phase gates to noise. We use noisy input composed of convex combination of unitary channel with either depolarizing or dephasing channel. We find out that the resistance to dephasing noise is higher than to depolarization. Interestingly, for the depolarisation the retrieval reduces the degree of noise. We also examine the possible realizations showing that their performance is different when the noise is present.
One of the challenges in quantum information is the demonstration of quantum coherence in the operations of experimental devices. While full quantum process tomography can do the job, it is both cumbersome and unintuitive. In this presentation, we show that a surprisingly detailed and intuitively accessible characterization of errors is possible by measuring the error statistics of only two complementary classical operations of a quantum gate.
We show how, in the presence of quantum noises generated by non-commuting Lindblad operators, a maximally entangled Bell state may suffer entanglement sudden death (ESD). Similarly, ESD may occur when a Bell state is under the action of a quantum operation generated by a Hamiltonian in the presence of a quantum noise, provided that the Hamiltonian does not commute with the corresponding Lindblad operator. Practically this means noisy quantum operations could cause ESD during the encoding process in quantum communication protocols like special dense coding ($\cal S$). Next, we show how in the p…
Entanglement distillation is a fundamental task in quantum information processing. It not only extracts entanglement out of corrupted systems but also leads to protecting systems of interest against intervention with environment. In this work, we consider a realistic scenario of entanglement distillation where noisy quantum operations are applied. In particular, the two-way distillation protocol that tolerates the highest error rate is considered. We show that among all types of noise there are only four equivalence classes according to the distillability condition. Since the four classes are …
We investigate the creation of squeezing via operations subject to noise and losses and ask for the optimal use of such devices when supplemented by noiseless passive operations. Both single and repeated uses of the device are optimized analytically and it is proven that in the latter case the squeezing converges exponentially fast to its asymptotic optimum, which we determine explicitly. For the case of multiple iterations we show that the optimum can be achieved with fixed intermediate passive operations. Finally, we relate the results to the generation of entanglement and derive the maximal…
Entangled states can help in quantum state discrimination by local operations and classical communication (LOCC). For example, a Bell state is necessary (and sufficient) to perfectly discriminate a set of either three or four Bell states by LOCC. In this paper, we consider the task of LOCC discrimination of the states of noisy Bell ensembles, where a given ensemble consists of the states obtained by mixing the Bell states with an arbitrary two-qubit state with nonzero probabilities. It is proved that a Bell state is required for optimal discrimination by LOCC, even though the ensembles do not …
A new purification scheme is proposed which applies to arbitrary dimensional bipartite quantum systems. It is based on the repeated application of a special class of nonlinear quantum maps and a single, local unitary operation. This special class of nonlinear quantum maps is generated in a natural way by a hermitian generalized XOR-gate. The proposed purification scheme offers two major advantages, namely it does not require local depolarization operations at each step of the purification procedure and it purifies more efficiently than other know purification schemes.
Fault-tolerant quantum computation with depolarization error often requires demanding error threshold and resource overhead. If the operations can maintain high noise bias -- dominated by dephasing error with small bit-flip error -- we can achieve hardware-efficient fault-tolerant quantum computation with a more favorable error threshold. Distinct from two-level physical systems, multi-level systems (such as harmonic oscillators) can achieve a desirable set of bias-preserving quantum operations while using continuous engineered dissipation or Hamiltonian protection to stabilize to the encoding…
Spin qubits are very valuable and scalable candidates in the area of quantum computation and simulation applications. In the last decades, they have been deeply investigated from a theoretical point of view and realized on the scale of few devices in the laboratories. In semiconductors, spin qubits can be built confining the spin of electrons in electrostatically defined quantum dots. Through this approach it is possible to create different implementations: single electron spin qubit, singlet-triplet spin qubit, or a three electrons architecture, e. g. the hybrid qubit. For each qubit type, we…
Routing plays an important role in programming noisy, intermediate-scale quantum (NISQ) devices, where limited connectivity in the register is overcome by swapping quantum information between locations. However, routing a quantum state using noisy gates introduces non-trivial noise dynamics, and deciding on an optimal route to minimize accumulated error requires estimates of the expected state fidelity. Here we validate a model for state-dependent routing dynamics in a NISQ processor based on correlated binary noise. We develop a composable, state-dependent noise model for CNOT and SWAP operat…
We study the nonlocal properties of two-qubit maximally-entangled and N-qubit Greenberger-Horne-Zeilinger states under local decoherence. We show that the (non)resilience of entanglement under local depolarization or dephasing is not necessarily equivalent to the (non)resilience of Bell-inequality violations. Apart from entanglement and Bell-inequality violations, we consider also nonlocality as quantified by the nonlocal content of correlations, and provide several examples of anomalous behaviors, both in the bipartite and multipartite cases. In addition, we study the practical implications o…
The reliability of logical operations is indispensable for the reliable operation of computational systems. Since the down-sizing of micro-fabrication generates non-negligible noise in these systems, a new approach for designing noise-immune gates is required. In this paper, we demonstrate that noise-immune gates can be designed by combining Bayesian inference theory with the idea of computation over a noisy signal. To reveal their practical advantages, the performance of these gates is evaluated in comparison with a stochastic resonance-based gate proposed previously. This approach for comput…
Sequential Quantum Secret Sharing schemes (QSS) do not use entangled states for secret sharing, rather they rely on sequential operations of the players on a single state which is circulated between the players. In order to check the viability of these schemes under imperfect operations and noise in the channels, we consider one such scheme in detail and show that under moderate conditions it is still possible to extract viable secure shared keys in this scheme. Although we specifically consider only one type of sequential scheme and three different noise models, our method is fairly general t…
We provide several applications of a previously introduced isomorphism between physical operations acting on two systems and entangled states [1]. We show: (i) how to implement (weakly) non-local two qubit unitary operations with a small amount of entanglement; (ii) that a known, noisy, non-local unitary operation as well as an unknown, noisy, local unitary operation can be purified; (iii) how to perform the tomography of arbitrary, unknown, non-local operations; (iv) that a set of local unitary operations as well as a set of non-local unitary operations can be stored and compressed; (v) how t…
Individual trapped atomic qubits represent one of the most promising technologies to scale quantum computers, owing to their negligible idle errors and the ability to implement a full set of reconfigurable gate operations via focused optical fields. However, the fidelity of quantum gate operations can be limited by weak confinement of the atoms transverse to the laser. We present measurements of this effect by performing individually-addressed entangling gates in chains of up to 25 trapped atomic ions that are weakly confined along the chain axis. We present a model that accurately describes t…
We establish the optimal quantum teleportation protocol for the realistic scenario when both input state and quantum channel are afflicted by noise. In taking these effects into account higher fidelities are achieved. The optimality of the proposed protocol prevails even when restricted to a reduced set of generically available operations.
We consider transmission of an (unknown) quantum state between two distant atoms via photons. Based on a quantum-optical realistic model, we define a noisy quantum channel which includes systematic errors as well as errors due to coupling to the environment. We present a protocol that allows one to accomplish ideal transmission by repeating the transfer operation as many times as needed.
Recently, Yang et al. (Quantum Inf Process 18, 74, 2019) proposed a two-party quantum key agreement protocol over a collective noisy channel. They claimed that their quantum key agreement protocol can ensure both of the participants have equal influence on the final shared key. However, this study shows that the participant who announces the permutation operation can manipulate the final shared key by himself/herself without being detected by the other. To avoid this loophole, an improvement is proposed here.
A quantum state transformation can be generally approximated by single- and two-qubit gates. This, however, does not hold with noisy intermediate-scale quantum technologies due to the errors appearing in the gate operations, where errors of two-qubit gates such as controlled-NOT and SWAP operations are dominated. In this work, we present a cost efficient single-copy certification for a realization of a two-qubit gate in the presence of depolarization noise, where it is aimed to identify if the realization is noise-free, or not. It is shown that entangled resources such as entangled states and …
We show that any unital qubit channel can be implemented by letting the input system interact unitarily with a $4$-dimensional environment in the maximally mixed state and then tracing out the environment. We also provide an example where the dimension of such an environment has to be at least $3$.
We report a bulk optics experiment demonstrating the possibility of restoring the entanglement distribution through noisy quantum channels by inserting a suitable unitary operation (filter) in the middle of the transmission process. We focus on two relevant classes of single-qubit channels consisting in repeated applications of rotated phase damping or rotated amplitude damping maps, both modeling the combined Hamiltonian and dissipative dynamics of the polarization state of single photons. Our results show that interposing a unitary filter between two noisy channels can significantly improve …
Quantum network coding is an effective solution for alleviating bottlenecks in quantum networks. We introduce a measurement-based quantum network coding scheme for quantum repeater networks (MQNC), and analyze its behavior based on results acquired from Monte-Carlo simulation that includes various error sources over a butterfly network. By exploiting measurement-based quantum computing, operation on qubits for completing network coding proceeds in parallel. We show that such an approach offers advantages over other schemes in terms of the quantum circuit depth, and therefore improves the commu…
Local pure states represent a fundamental resource in quantum information theory. In this work we obtain one-shot achievable bounds on the rates for local purity distillation, in the single-party and in the two-party cases. In both situations, local noisy operations are freely available, while in the two-party case also one-way classical communication can be used. In addition, in both situations local pure ancillas can be borrowed, as long as they are discounted from the final net rate of distillation. The one-shot rates that we obtain, written in terms of mutual information-like quantities, a…
Quantum tomography makes it possible to obtain comprehensive information about certain logical elements of a quantum computer. In this regard, it is a promising tool for debugging quantum computers. The practical application of tomography, however, is still limited by systematic measurement errors. Their main source are errors in the quantum state preparation and measurement procedures. In this work, we investigate the possibility of suppressing these errors in the case of ion-based qudits. First, we will show that one can construct a quantum measurement protocol that contains no more than a s…
Sender and receiver can control noisy channels by means of the resources they own, that is local operations, potentially correlated using classical communication, and entangled pairs shared between them. Using the Choi-Jamiolkowski isomorphism, we express the control of a noisy channel in terms of control of (non-normalized) states, and show how the available resources enter the analysis. Our formalism provides a general scheme for the protection of quantum state transmission when a single use of the physical channel is considered. Moreover, it paves the way to the application of control theor…
Several noisy intermediate-scale quantum computations can be regarded as logarithmic-depth quantum circuits on a sparse quantum computing chip, where two-qubit gates can be directly applied on only some pairs of qubits. In this paper, we propose a method to efficiently verify such noisy intermediate-scale quantum computation. To this end, we first characterize small-scale quantum operations with respect to the diamond norm. Then by using these characterized quantum operations, we estimate the fidelity $\langleψ_t|\hatρ_{\rm out}|ψ_t\rangle$ between an actual $n$-qubit output state $\hatρ_{\rm …
Two separated observers, by applying local operations to a supply of not-too-impure entangled states ({\em e.g.} singlets shared through a noisy channel), can prepare a smaller number of entangled pairs of arbitrarily high purity ({\em e.g.} near-perfect singlets). These can then be used to faithfully teleport unknown quantum states from one observer to the other, thereby achieving faithful transfrom one observer to the other, thereby achieving faithful transmission of quantum information through a noisy channel. We give upper and lower bounds on the yield $D(M)$ of pure singlets ($\ket{Ψ^-}$)…
In this contribution, we introduce a technique to freeze the parameters which describe the accelerated states between two users to be used in the context of quantum cryptography and quantum teleportation. It is assumed that, the two users share different dimension sizes of particles, where we consider a qubit-qutrit system. This technique depends on local operations, where it is allowed that each particle interacts locally with a noisy phase channel. We show that, the possibility of freezing the information of quantum channel between the users depends on the initial state setting parameters, t…
