Qubit Channels Research Articles

Limits of Noisy Quantum Metrology with Restricted Quantum Controls.

The Heisenberg limit [(HL), with estimation error scales as 1/n] and the standard quantum limit (SQL, ∝1/sqrt[n]) are two fundamental limits in estimating an unknown parameter in n copies of quantum channels and are achievable with full quantum controls, e.g., quantum error correction (QEC). It is unknown though, whether these limits are still achievable in restricted quantum devices when QEC is unavailable, e.g., with only unitary controls or bounded system sizes. In this Letter, we discover various new limits for estimating qubit channels under restrictive controls. The HL is shown to be unachievable in various cases, indicating the necessity of QEC in achieving the HL. Furthermore, a necessary and sufficient condition to achieve the SQL is determined, where a single-qubit unitary control protocol is identified to achieve the SQL for certain types of noisy channels, and for other cases a constant floor on the estimation error is proven. A practical example of the unitary protocol is provided.

Identification of malfunctioning quantum devices

We consider the problem of correctly identifying a malfunctioning quantum device that forms part of a network of N such devices, which can be considered as the quantum analog of classical anomaly detection. In the case where the devices in question are sources assumed to prepare identical quantum pure states, with the faulty source producing a different anomalous pure state, we show that the optimal probability of successful identification requires a global quantum measurement. We also put forth several local measurement strategies—both adaptive and nonadaptive—that achieve the same optimal probability of success in the limit where the number of devices to be checked is large. In the case where the faulty device performs a known unitary operation, we show that the use of entangled probes provides an improvement that even allows perfect identification for values of the unitary parameter that surpass a certain threshold. Finally, if the faulty device implements a known qubit channel, we find that the optimal probability for detecting the position of rank-one and rank-two Pauli channels can be achieved by product state inputs and separable measurements for any size of network, whereas for rank-three and general amplitude damping channels, optimal identification requires entanglement with N qubit ancillas. Published by the American Physical Society 2024

Quantum Lego Expansion Pack: Enumerators from Tensor Networks

We provide the first tensor-network method for computing quantum weight enumerator polynomials in the most general form. If a quantum code has a known tensor-network construction of its encoding map, our method is far more efficient, and in some cases exponentially faster than the existing approach. As a corollary, it produces decoders and an algorithm that computes the code distance. For non-(Pauli)-stabilizer codes, this constitutes the current best algorithm for computing the code distance. For degenerate stabilizer codes, it can be substantially faster compared to the current methods. We also introduce novel weight enumerators and their applications. In particular, we show that these enumerators can be used to compute logical error rates exactly and thus construct (optimal) decoders for any independent and identically distributed single qubit or qudit error channels. The enumerators also provide a more efficient method for computing nonstabilizerness in quantum many-body states. As the power for these speedups rely on a quantum Lego decomposition of quantum codes, we further provide systematic methods for decomposing quantum codes and graph states into a modular construction for which our technique applies. As a proof of principle, we perform exact analyses of the deformed surface codes, the holographic pentagon code, and the two-dimensional Bacon-Shor code under (biased) Pauli noise and limited instances of coherent error at sizes that are inaccessible by brute force. Published by the American Physical Society 2024

Deterministic preparation of optical qubits with coherent feedback control

We propose a class of preparation schemes for orbital angular momentum and polarization qubits carried by single photons or classical states of light based on coherent feedback control by an ancillary degree of freedom of light. The preparation methods use linear optics and include the transcription of an arbitrary polarization state onto a two-level OAM system (swap) for arbitrary OAM values ±ℓ within a light beam, i.e., without a spatial interferometer. The preparations can be carried out with unit efficiency independent from the potentially unknown initial state of the system. The swap scheme also allows us to implement arbitrary unitary gates on OAM qubits (±ℓ) by reducing them to polarization gates. In addition, we show how to translate measurement-based qubit control channels into coherent feedback schemes for optical implementation.

Weak entanglement improves quantum communication using only product measurements

We show that weakly entangled states can improve communication over a qubit channel using only separate, interference-free, measurements of individual photons. We introduce a communication task corresponding to the cryptographic primitive known as secret sharing and show that all steerable two-qubit isotropic states provide a quantum advantage in the success rate using only product measurements. Furthermore, we show that such measurements can even reveal communication advantages from noisy partially entangled states that admit no quantum steering. We then go further and consider a stochastic variant of secret sharing based on more-sophisticated, yet standard, partial Bell-state analyzers, and show that this reveals advantages also for a range of unsteerable isotropic states. By preparing polarization qubits in unsteerable states, we experimentally demonstrate increased success rates of both secret-sharing tasks beyond the best entanglement-unassisted qubit protocol. Our results reveal the capability of simple and scalable measurements in entanglement-assisted quantum communication to overcome large amounts of noise. Published by the American Physical Society 2024

Dynamical Resource Theory of Informational Nonequilibrium Preservability.

Information is instrumental in our understanding of thermodynamics. Their interplay has been studied through completely degenerate Hamiltonians whereby the informational contributions to thermodynamic transformations can be isolated. In this setting, all states other than the maximally mixed state are considered to be in informational nonequilibrium. An important yet still open question is how to characterize the ability of quantum dynamics to preserve informational nonequilibrium. Here, the dynamical resource theory of informational nonequilibrium preservability is introduced to begin providing an answer to this question. A characterization of the allowed operations is given for qubit channels and the n-dimensional Weyl-covariant channels-a physically relevant subset of the general channels. An operational interpretation of a state discrimination game with Bell state measurements is given. Finally, an explicit link between a channel's classical capacity and its ability to preserve informational nonequilibrium is made.

Quantifying channel coherence via the norm distance

Quantifying the number of resources contained in a physical object has been one of the core topics in the resource theory of coherence. In this paper, we introduce the dynamical coherence measures based on a class of norms in the classical channel setting. It is proved that it satisfies faithfulness, decreases monotonically under the maximally incoherent superchannels, and is convex. Moreover, we show that it satisfies subadditivity under both the composition and tensor product of channels. Especially, the diamond measure as a special case is discussed in detail, it can reduce to trace norm of coherence, satisfies amortization inequality, and can be calculated efficiently using a semidefinite program. In addition, we introduce the creation-coherent diamond measure and find that neither the detection coherence nor the creation coherence of a channel exceeds the coherence of the channel, which does not exceed the purity of the channel. Second, we introduce the corresponding dephasing measure, which is a dynamical coherence measure under the dephasing-covariant incoherent superchannels. Meanwhile, we also introduce the dephasing diamond measure as a special case. Third, we use the dephasing diamond measure to accurately calculate the coherence values of some important noisy channels such as amplitude damping channel, phase damping channel, and depolarizing channel, respectively, and give the sufficient and necessary conditions for an unital qubit channel with a parameter probability vector to be a coherent channel. Finally, the operational interpretation of our diamond measure in the binary channel discrimination task is investigated.

The classification of rebit quantum channels

The classification of qubit channels is known since 2002. However, that of rebit channels has never been studied so far, maybe because of the scarcity of concrete rebit examples. In this paper we point out that the strategy used to classify qubit channels cannot be pursued in the rebit case and we propose an alternative which allows us to complete the rebit channel classification. This mathematical result has not only a purely abstract interest: as we shall briefly mention, it may have applications in the analysis of local properties and temporal evolution of real quantum systems and also in a recent color vision model based on quantum information.

On the eternal non-Markovianity of non-unital quantum channels

The eternally non-Markovian (ENM) Pauli channel is an example of a unital channel characterized by a negative decay rate for all time [Formula: see text]. Here, we consider the problem of constructing an analogous non-unital channel, and show in particular that a [Formula: see text]-dimensional generalized amplitude damping (GAD) channel cannot be ENM when the non-Markovianity originates solely from the non-unital part of the channel. We study specific ramifications of this result for qubit GAD. Specifically, we construct a quasi-ENM qubit GAD channel, characterized by a time [Formula: see text], such that the channel is non-Markovian (NM) only and for all time [Formula: see text]. We further point out that our negative result for the qudit GAD channel, namely, the impossibility of the eternal NM property, does not hold for a general qubit or higher-dimensional non-unital channel.

Experimental Communication Through Superposition of Quantum Channels

Information capacity enhancement through the coherent control of channels has attracted much attention of late, with work exploring the effect of coherent control of channel causal orders, channel superpositions, and information encoding. Coherently controlling channels necessitates a non-trivial expansion of the channel description, which for superposing qubit channels, is equivalent to expanding the channel to act on qutrits. Here we explore the nature of this capacity enhancement for the superposition of channels by comparing the maximum coherent information through depolarizing qubit channels and relevant superposed and qutrit channels. We show that the expanded qutrit channel description in itself is sufficient to explain the capacity enhancement without any use of superposition.

Profitable entanglement for channel discrimination

We investigate the usefulness of side entanglement in discriminating between two generic qubit channels, up to unitary pre- and post-processing, and determine exact conditions under which it does enhance (as well as conditions under which it does not) the success probability. This is done in a constructive way by first analysing the problem for channels that are extremal in the set of completely positive and trace-preserving qubit linear maps and then for channels that are inside such a set.

Geometry of phase-covariant qubit channels

We analyze the geometry on the space of non-unital phase-covariant qubit maps. Using the corresponding Choi-Jamiołkowski states, we derive the Hilbert-Schmidt line and volume elements using the channel eigenvalues together with the parameter that characterizes non-unitality. We find the shapes and analytically compute the volumes of phase-covariant channels, in particular entanglement breaking and obtainable with time-local generators.

A 1-GS/s 6–8-b Cryo-CMOS SAR ADC for Quantum Computing

This article presents a two-times interleaved, loop-unrolled SAR analog-to-digital converter (ADC) operational from 300 down to 4.2 K. The 6–8-bit resolution and the sampling speed up to 1 GS/s are targeted at digitizing the multi-channel frequency-multiplexed input in a spin-qubit reflectometry readout for quantum computing. To optimize the circuit for the altered device behavior at cryogenic temperatures, a modified common-mode switching scheme is adopted as well as a flexible calibration. The design is implemented in 40-nm CMOS technology and achieves 36.2-dB signal to noise and distortion ratio (SNDR) for Nyquist input at 4.2 K while maintaining a Walden figure of merit (FOMW) of 200 pJ/conv-step (for a 10.8-mW power consumption), including the clock receiver, and 15 pJ/conv-step (for a 0.8-mW power consumption) for just the core ADC. With these specifications, the ADC can support the simultaneous readout of 20 qubit channels with a power consumption of 0.5 mW/qubit, thus advancing toward the full integration of the cryogenic readout for future large-scale quantum processors.

Communication With Unreliable Entanglement Assistance

Entanglement resources can increase transmission rates substantially. Unfortunately, entanglement is a fragile resource that is quickly degraded by decoherence effects. In order to generate entanglement for optical communication, the transmitter and the receiver first prepare entangled spin-photon pairs locally, and then the photon at the transmitter is sent to the receiver through an optical fiber or free space. Without feedback, the transmitter does not know whether the entangled photon has reached the receiver. The present work introduces a new model of unreliable entanglement assistance, whereby the communication system operates whether entanglement assistance is present or not. While the sender is ignorant, the receiver knows whether the entanglement generation was successful. In the case of a failure, the receiver decodes less information. In this manner, the effective transmission rate is adapted according to the assistance status. Regularized formulas are derived for the classical and quantum capacity regions with unreliable entanglement assistance, characterizing the tradeoff between the unassisted rate and the excess rate that can be obtained from entanglement assistance. It is further established that time division between entanglement-assisted and unassisted coding strategies is optimal for the noiseless qubit channel, but can be strictly suboptimal for a noisy channel.

The Platypus of the Quantum Channel Zoo

Understanding quantum channels and the strange behavior of their capacities is a key objective of quantum information theory. Here we study a remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic quantum information-theoretic features. As the simplest example from this family, we focus on a qutrit-to-qutrit channel that is intuitively obtained by hybridizing together a simple degradable channel and a completely useless qubit channel. Such hybridizing makes this channel’s capacities behave in a variety of interesting ways. For instance, the private and classical capacity of this channel coincide and can be explicitly calculated, even though the channel does not belong to any class for which the underlying information quantities are known to be additive. Moreover, the quantum capacity of the channel can be computed explicitly, given a clear and compelling conjecture is true. This “spin alignment conjecture,” which may be of independent interest, is proved in certain special cases and additional numerical evidence for its validity is provided. Finally, we generalize the qutrit channel in two ways, and the resulting channels and their capacities display similarly rich behavior. In the companion paper [1], we further show that the qutrit channel demonstrates superadditivity when transmitting quantum information jointly with a variety of assisting channels, in a manner unknown before.

Excitation-damping quantum channels

We study a class of quantum channels describing a quantum system, split into the direct sum of an excited and a ground sector, undergoing a one-way transfer of population from the former to the latter; this construction, which provides a generalization of the amplitude-damping qubit channel, can be regarded as a way to upgrade a trace non-increasing quantum operation, defined on the excited sector, to a possibly trace preserving operation on a larger Hilbert space. We provide necessary and sufficient conditions for the complete positivity of such channels, and we also show that complete positivity can be equivalent to simple positivity when the ground sector is one-dimensional. Finally, we examine the time-dependent scenario and characterize all CP-divisible channels and Markovian semigroups belonging to this class, thus providing a general recipe, beyond the Markovian scenario, to promote a given decay process to a legitimate quantum process on a larger space.

Generic Nonadditivity of Quantum Capacity in Simple Channels.

Determining capacities of quantum channels is a fundamental question in quantum information theory. Despite having rigorous coding theorems quantifying the flow of information across quantum channels, their capacities are poorly understood due to superadditivity effects. Studying these phenomena is important for deepening our understanding of quantum information, yet simple and clean examples of superadditive channels are scarce. Here we study a family of channels called platypus channels. Its simplest member, a qutrit channel, is shown to display superadditivity of coherent information when used jointly with a variety of qubit channels. Higher-dimensional family members display superadditivity of quantum capacity together with an erasure channel. Subject to the "spin-alignment conjecture" introduced in our companion paper [F. Leditzky, D. Leung, V. Siddhu, G. Smith, and J. A. Smolin, The platypus of the quantum channel zoo, IEEE Transactions on Information Theory (IEEE, 2023), 10.1109/TIT.2023.3245985], our results on superadditivity of quantum capacity extend to lower-dimensional channels as well as larger parameter ranges. In particular, superadditivity occurs between two weakly additive channels each with large capacity on their own, in stark contrast to previous results. Remarkably, a single, novel transmission strategy achieves superadditivity in all examples. Our results show that superadditivity is much more prevalent than previously thought. It can occur across a wide variety of channels, even when both participating channels have large quantum capacity.

On unital qubit channels

A canonical form for unital qubit channels under local unitary transforms is obtained. In particular, it is shown that the eigenvalues of the Choi matrix of a unital quantum channel form a complete set of invariants of the canonical form. It follows immediately that every unital qubit channel is the average of four unitary channels. More generally, a unital qubit channel can be expressed as the convex combination of unitary channels with convex coefficients $p_1, \dots, p_m$ as long as $2(p_1, \dots, p_m)$ is majorized by the vector of eigenvalues of the Choi matrix of the channel. A unital qubit channel in the canonical form will transform the Bloch sphere onto an ellipsoid. We look into the detailed structure of the natural linear maps sending the Bloch sphere onto a corresponding ellipsoid.

Adjusting phase-covariant qubit channel performance with non-unitality

We analyze quantum communication properties of phase-covariant channels depending on their degree of non-unitality. In particular, we derive analytical formulas for the minimal and maximal channel fidelity on pure states and maximal output purity. Next, we introduce a measure of non-unitality and show how to manipulate between unital and maximally non-unital maps by considering classical mixtures of quantum channels. Finally, we prove that maximal fidelity and maximal output purity increase with non-unitality and present several examples. Interestingly, non-unitality can also prolong quantum entanglement and lead to its rebirth.

The Communication Value of a Quantum Channel

There are various ways to quantify the communication capabilities of a quantum channel. In this work we introduce the communication value (cv) of quantum channel, which describes the optimal probability of guessing the channel input from its output. By connecting to prior work on zero-error channel simulation, we show that the cv and its entanglement-assisted variant also offer dual interpretations as the classical communication cost for perfectly simulating different aspects of a channel using non-signaling resources. Our study involves characterizing the communication value as a generalized conditional min-entropy over the cone of separable operators. Using this characterization, we evaluate the cv for all qubit channels and higher-dimensional channels with certain symmetries. We find that the any entanglement-breaking channel has multiplicative cv when used in parallel with any other channel; the same is shown to hold for Pauli channels and partially depolarizing channels. In contrast, the cv is found to be non-multiplicative for a subset of the well-known Werner-Holevo channels. A final component of this work investigates relaxations of the channel cv to other cones such as the set of operators having a positive partial transpose (PPT).