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Information theory establishes the ultimate limits on performance for noisy communication systems (1). Accurate models of physical communication devices must include quantum effects, but these typically make the theory intractable (2-5). As a result, communication capacities--the maximum possible rates of data transmission--are not known, even for transmission between two users connected by an electromagnetic waveguide with Gaussian noise (6). Here we present an exactly solvable model of communication with a fully quantum electromagnetic field. This gives explicit expressions for all point-to-point capacities of noisy quantum channels, with implications for quantum key distribution and fibre-optic communications. We also develop a theory of quantum communication networks by solving some rudimentary models including broadcast and multiple-access channels. We compare the predictions of our model with the orthodox Gaussian model and in all cases find agreement to within a few bits. At high signal-to-noise ratios, our simple model captures the relevant physics while remaining amenable to exact solution., A fundamental property of communication systems is the maximum rate of data transmission possible using the best communication schemes. This is called the 'capacity' of a channel. It is usually [...]

We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with superior parameters to any previously known. In particular, we find ((10, 18,3)) and ((10,20,3)) codes. We also show how to construct encoding circuits for all codes within our framework. Index Terms--Nonadditive codes, quantum error correction, stabilizer codes.

In this paper, we present an upper bound for the quantum channel capacity that is both additive and convex. Our bound can be interpreted as the capacity of a channel for high-fidelity quantum communication when assisted by a family of channels that have no capacity on their own. This family of assistance channels, which we call symmetric side channels, consists of all channels mapping symmetrically to their output and environment. The bound seems to be quite tight, and for degradable quantum channels, it coincides with the unassisted channel capacity. Using this symmetric side channel capacity, we find new upper bounds on the capacity of the depolarizing channel. We also briefly indicate an analogous notion for distilling entanglement using the same class of (one-way) channels, yielding one of the few entanglement measures that is monotonic under local operations with one-way classical communication (1-LOCC), but not under the more general class of local operations with classical communication (LOCC). Index Terms--Entanglement, quantum channel capacity, quantum communication.

We consider interactions as bidirectional channels. We investigate the capacities for interaction Hamiltonians and non-local unitary gates to generate entanglement and transmit classical information. We give analytic expressions for the entanglement generating capacity and entanglement-assisted one-way classical communication capacity of interactions, and show that these quantities are additive, so that the asymptotic capacities equal the corresponding 1-shot capacities. We give general bounds on other capacities, discuss some examples, and conclude with some open questions. Index Terms--Communication capacities, entanglement capacities, two-way quantum channels.

The entanglement-assisted classical capacity of a noisy quantum channel ([C.sub.E]) is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel, assuming that the sender and receiver have access to the resource of shared quantum entanglement, which may be used up by the communication protocol. We show that the capacity [C.sub.E] is given by an expression parallel to that for the capacity of a purely classical channel: i.e., the maximum, over channel inputs [rho], of the entropy of the channel input plus the entropy of the channel output minus their joint entropy, the latter being defined as the entropy of an entangled purification of [rho] after half of it has passed through the channel. We calculate entanglement-assisted capacities for two interesting quantum channels, the qubit amplitude damping channel and the bosonic channel with amplification/attenuation and Gaussian noise. We discuss how many independent parameters are required to completely characterize the asymptotic behavior of a general quantum channel, alone or in the presence of ancillary resources such as prior entanglement In the classical analog of entanglement-assisted communication--communication over a discrete memoryless channel (DMC) between parties who share prior random information--we show that one parameter is sufficient, i.e., that in the presence of prior shared random information, all DMCs of equal capacity can simulate one another with unit asymptotic efficiency. Index Terms--Channel capacity, entanglement, quantum information, Shannon theory.

We present new constructions of codes for asymmetric channels for both binary and nonbinary alphabets, based on methods of generalized code concatenation. For the binary asymmetric channel, our methods construct nonlinear single-error-correcting codes from ternary outer codes. We show that some of the Varshamov–Tenengol’ts–Constantin–Rao codes, a class of binary nonlinear codes for this channel, have a nice structure when viewed as ternary codes. In many cases, our ternary construction yields even better codes. For the nonbinary asymmetric channel, our methods construct linear codes for many lengths and distances which are superior to the linear codes of the same length capable of correcting the same number of symmetric errors. [ABSTRACT FROM AUTHOR]

We give an algorithm which produces a unique element of the Clifford group on n qubits (Cn) from an integer 0 ≤ i < |Cn| (the number of elements in thegroup). The algorithm involves O(n³) operations and provides, in addition to a canonical mapping from the integers to group elements g, a factorization of g into a sequence of at most 4n symplectic transvections. The algorithm can be used to efficiently select random elements of Cn which are often useful in quantum information theory and quantum computation. We also give an algorithm for the inverse map, indexing a group element in time O(n³). [ABSTRACT FROM AUTHOR]

Using unreliable or noisy components for reliable communication requires error correction. But which noise processes can support information transmission, and which are too destructive? For classical systems any channel whose output depends on its input has the capacity for communication, but the situation is substantially more complicated in the quantum setting. We find a generic test for incapacity based on any suitable forbidden transformation--a protocol for communication with a channel passing our test would also allow one to implement the associated forbidden transformation. Our approach includes both known quantum incapacity tests--positive partial transposition and antidegradability (no cloning)--as special cases, putting them both on the same footing. [ABSTRACT FROM AUTHOR]

We provide an efficient method for computing the maximum-likelihood mixed quantum state (with density matrix p) given a set of measurement outcomes in a complete orthonormal operator basis subject to Gaussian noise. Our method works by first changing basis yielding a candidate density matrix &mgr; which may have nonphysical (negative) eigenvalues, and then finding the nearest physical state under the 2-norm. Our algorithm takes at worst 0(d4) for the basis change plus 0(d3) for finding p where d is the dimension of the quantum state. In the special case where the measurement basis is strings of Pauli operators, the basis change takes only 0(d3) as well. The workhorse of the algorithm is a new linear-time method for finding the closest probability distribution (in Euclidean distance) to a set of real numbers summing to one. [ABSTRACT FROM AUTHOR]

We formulate a model for the steady state response of a nonlinear quantum oscillator structure, such as those used in a variety of superconducting qubit experiments, when excited by a steady, but not necessarily small, ac tone. We show that this model can be derived directly from a circuit description of some recent qubit experiments in which the state of the qubit is read out directly, without a superconducting quantum interference device (SQUID) magnetometer. The excitation profile has a rich structure depending on the detuning of the tone from the small-signal resonant frequency, on the degree of damping and on the excitation amplitude. We explore two regions in detail. Firstly, at high damping there is a trough in the excitation response as a function of detuning, near where the classical Duffing bifurcation occurs. This trough has been understood as a classical interference between two metastable responses with opposite phase. We use Wigner function studies to show that while this picture is roughly correct, there are also more quantum mechanical aspects to this feature. Secondly, at low damping we study the emergence of sharp, discrete spectral features from a continuum response. We show that these the structures, associated with discrete transitions between different excited-state eigenstates of the oscillator, provide an interesting example of a quantum Fano resonance. The trough in the Fano response evolves continuously from the 'classical' trough at high damping. [ABSTRACT FROM AUTHOR]

As with classical information, error-correcting codes enable reliable transmission of quantum information through noisy or lossy channels. In contrast to classical theory, imperfect quantum channels exhibit a strong kind of synergy: pairs of discrete memoryless quantum channels exist, each of zero quantum capacity, which acquire positive quantum capacity when used together. Here, we show that this 'superactivation' phenomenon also occurs in the more realistic setting of optical channels with attenuation and Gaussian noise. This paves the way for its experimental realization and application in real-world communications systems. [ABSTRACT FROM AUTHOR]

We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear error-correcting codes for classical asymmetric channels, with which we systematically construct quantum amplitude damping codes with parameters better than any prior construction known for any block length n\geq 8 except n=2^r-1. We generalize this construction to employ classical codes over GF(3) with which we numerically obtain better performing codes up to length 14. Because the resulting codes are of the codeword stabilized (CWS) type, conceptually simple (though potentially computationally expensive) encoding and decoding circuits are available. [ABSTRACT FROM AUTHOR]

The codeword stabilized (CWS) quantum code formalism presents a unifying approach to both additive and nonadditive quantum error-correcting codes [IEEE Trans. Inf. Theory 55, 433 (2009)]. This formalism reduces the problem of constructing such quantum codes to finding a binary classical code correcting an error pattern induced by a graph state. Finding such a classical code can be very difficult. Here, we consider an algorithm which maps the search for CWS codes to a problem of identifying maximum cliques in a graph. While solving this problem is in general very hard, we provide three structure theorems which reduce the search space, specifying certain admissible and optimal ((n,K,d)) additive codes. In particular, we find that the re does not exist any ((7,3,3)) CWS code though the linear programming bound does not rule it out. The complexity of the CWS-search algorithm is compared with the contrasting method introduced by Aggarwal and Calderbank [IEEE Trans. Inf. Theory 54, 1700 (2008)]. [ABSTRACT FROM AUTHOR]

This paper describes the first quantum cryptography experiment, performed at the IBM Thomas J. Watson Research Center in the summer of 1989 by Charles H. Bennett and the author. The apparatus and some of the lesser-known details of the experiment are illustrated and discussed, and quantum cryptography is discussed in the light of some of the more recent research. Also included as an appendix is a short essay about Bennett written by Rolf Landauer. [ABSTRACT FROM AUTHOR]

Entanglement is a fundamental resource for quantum information processing. In its pure form, it allows quantum teleportation and sharing classical secrets. Realistic quantum states are noisy and their usefulness is only partially understood. Bound-entangled states are central to this question-they have no distillable entanglement, yet sometimes still have a private classical key. We present a construction of bound-entangled states with a private key based on classical probability distributions. From this emerge states possessing a new classical analogue of bound entanglement, distinct from the long-sought bound information. We also find states of smaller dimensions and higher key rates than previously known. Our construction has implications for classical cryptography: we show that existing protocols are insufficient for extracting private key from our distributions due to their "bound-entangled" nature. We propose a simple extension of existing protocols that can extract a key from them. [ABSTRACT FROM AUTHOR]

As quantum circuits increase in size, it is critical to establish scalable multiqubit fidelity metrics. Here we investigate, for the first time, three-qubit randomized benchmarking (RB) on a quantum device consisting of three fixed-frequency transmon qubits with pairwise microwave-activated interactions (cross-resonance). We measure a three-qubit error per Clifford of 0.106 for all-to-all gate connectivity and 0.207 for linear gate connectivity. Furthermore, by introducing mixed dimensionality simultaneous RB--simultaneous one- and two-qubit RB--we show that the three-qubit errors can be predicted from the one- and two-qubit errors. However, by introducing certain coherent errors to the gates, we can increase the three-qubit error to 0.302, an increase that is not predicted by a proportionate increase in the one- and two-qubit errors from simultaneous RB. This demonstrates the importance of multiqubit metrics, such as three-qubit RB, on evaluating overall device performance. [ABSTRACT FROM AUTHOR]

Privacy is a fundamental feature of quantum mechanics. A coherently transmitted quantum state is inherently private. Remarkably, coherent quantum communication is not a prerequisite for privacy: there are quantum channels that are too noisy to transmit any quantum information reliably that can nevertheless send private classical information. Here, we ask how much private classical information a channel can transmit if it has little quantum capacity. We present a class of channels Nd with input dimension d2, quantum capacity Q(Nd) ≤ 1, and private capacity P(Nd) = log d. These channels asymptotically saturate an interesting inequality P(N) ≤ (1/2)[log dA + Q(N)] for any channel N with input dimension dA and capture the essence of privacy stripped of the confounding influence of coherence. [ABSTRACT FROM AUTHOR]

We report a system where fixed interactions between noncomputational levels make bright the otherwise forbidden two-photon ∣00› → ∣11› transition. The system is formed by hand selection and assembly of two discrete component transmon-style superconducting qubits inside a rectangular microwave cavity. The application of a monochromatic drive tuned to this transition induces two-photon Rabilike oscillations between the ground and doubly excited states via the Bell basis. The system therefore allows all-microwave two-qubit universal control with the same techniques and hardware required for single qubit control. We report Ramsey-like and spin echo sequences with the generated Bell states, and measure a two-qubit gate fidelity of Fg = 90% (unconstrained) and 86% (maximum likelihood estimator). [ABSTRACT FROM AUTHOR]

The control and handling of errors arising from cross talk and unwanted interactions in multiqubit systems is an important issue in quantum information processing architectures. We introduce a bench- marking protocol that provides information about the amount of addressability present in the system and implement it on coupled superconducting qubits. The protocol consists of randomized benchmarking experiments run both individually and simultaneously on pairs of qubits. A relevant figure of merit for the addressability is then related to the differences in the measured average gate fidelities in the two experiments. We present results from two similar samples with differing cross talk and unwanted qubitqubit interactions. The results agree with predictions based on simple models of the classical cross talk and Stark shifts. [ABSTRACT FROM AUTHOR]

We report a superconducting artificial atom with a coherence time of T*2 = 92 μs and energy relaxation time T1 = 70μs. The system consists of a single Josephson junction transmon qubit on a sapphire substrate embedded in an otherwise empty copper waveguide cavity whose lowest eigenmode is dispersively coupled to the qubit transition. We attribute the factor of four increase in the coherence quality factor relative to previous reports to device modifications aimed at reducing qubit dephasing from residual cavity photons. This simple device holds promise as a robust and easily produced artificial quantum system whose intrinsic coherence properties are sufficient to allow tests of quantum error correction. [ABSTRACT FROM AUTHOR]

We use quantum process tomography to characterize a full universal set of all-microwave gates on two superconducting single-frequency single-junction transmon qubits. All extracted gate fidelities, including those for Clifford group generators, single-qubit IT/4 and 7r/8 rotations, and a two-qubit controlled-NOT, exceed 95% (98%), without (with) subtracting state preparation and measurement errors. Furthermore, we introduce a process map representation in the Pauli basis which is visually efficient and informative. This high-fidelity gate set serves as a critical building block towards scalable architectures of superconducting qubits for error correction schemes and pushes up on the known limits of quantum gate characterization. [ABSTRACT FROM AUTHOR]

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.

Privacy is a fundamental feature of quantum mechanics. A coherently transmitted quantum state is inherently private. Remarkably, coherent quantum communication is not a prerequisite for privacy: there are quantum channels that are too noisy to transmit any quantum information reliably that can nevertheless send private classical information. Here, we ask how much private classical information a channel can transmit if it has little quantum capacity. We present a class of channels N(d) with input dimension d(2), quantum capacity Q(N(d)) ≤ 1, and private capacity P(N(d)) = log d. These channels asymptotically saturate an interesting inequality P(N) ≤ (1/2)[log d(A) + Q(N)] for any channel N with input dimension d(A) and capture the essence of privacy stripped of the confounding influence of coherence.

We demonstrate an all-microwave two-qubit gate on superconducting qubits which are fixed in frequency at optimal bias points. The gate requires no additional subcircuitry and is tunable via the amplitude of microwave irradiation on one qubit at the transition frequency of the other. We use the gate to generate entangled states with a maximal extracted concurrence of 0.88, and quantum process tomography reveals a gate fidelity of 81%., (© 2011 American Physical Society)

We study the power of closed timelike curves (CTCs) and other nonlinear extensions of quantum mechanics for distinguishing nonorthogonal states and speeding up hard computations. If a CTC-assisted computer is presented with a labeled mixture of states to be distinguished--the most natural formulation--we show that the CTC is of no use. The apparent contradiction with recent claims that CTC-assisted computers can perfectly distinguish nonorthogonal states is resolved by noting that CTC-assisted evolution is nonlinear, so the output of such a computer on a mixture of inputs is not a convex combination of its output on the mixture's pure components. Similarly, it is not clear that CTC assistance or nonlinear evolution help solve hard problems if computation is defined as we recommend, as correctly evaluating a function on a labeled mixture of orthogonal inputs.

Quantum information theory establishes the ultimate limits on communication and cryptography in terms of channel capacities for various types of information. The private capacity is particularly important because it quantifies achievable rates of quantum key distribution. We study the power of quantum channels with limited private capacity, focusing on channels that dephase in random bases. These display extensive nonadditivity of private capacity: a channel with 2logd input qubits that has a private capacity less than 2, but when used together with a second channel with zero private capacity, the joint capacity jumps to (1/2)logd. In contrast to earlier work which found nonadditivity vanishing as a fraction of input size or conditional on unproven mathematical assumptions, this provides a natural setting manifesting nonadditivity of privacy of the strongest possible sort.

We consider two capacity quantities associated with bipartite unitary gates: the entangling and the disentangling power. Here, we prove that these capacities are different in general by constructing an explicit example of a qubit-qutrit unitary whose entangling power is maximal (2 ebits), but whose disentangling power is strictly less. A corollary is that there can be no unique ordering for unitary gates in terms of their ability to perform nonlocal tasks. Finally, we show that in large dimensions, almost all bipartite unitaries have entangling and disentangling capacities close to maximal.

We study the power of quantum channels with little or no capacity for private communication. Because privacy is a necessary condition for quantum communication, one might expect that such channels would be of little use for transmitting quantum states. Nevertheless, we find strong evidence that there are pairs of such channels that, when used together, can transmit far more quantum information than the sum of their individual private capacities. Because quantum transmissions are necessarily private, this would imply a large violation of additivity for the private capacity. Specifically, we present channels which display either (1) a large joint quantum capacity but very small individual private capacities or (2) a severe violation of additivity for the Holevo information.

A central goal in information theory and cryptography is finding simple characterizations of optimal communication rates under various restrictions and security requirements. Ideally, the optimal key rate for a quantum key distribution (QKD) protocol would be given by a single-letter formula involving optimization over a single use of an effective channel. We explore the possibility of such a formula for the simplest and most widely used QKD protocol, Bennnett-Brassard-84 with one-way classical postprocessing. We show that a conjectured single-letter formula is false, uncovering a deep ignorance about good private codes and exposing unfortunate complications in the theory of QKD. These complications are not without benefit-with added complexity comes better key rates than previously thought possible. The threshold for secure key generation improves from a bit error rate of 0.124 to 0.129.

Most known quantum codes are additive, meaning the code can be described as the simultaneous eigenspace of an Abelian subgroup of the Pauli group. While in some scenarios such codes are strictly suboptimal, very little is understood about how to construct nonadditive codes with good performance. Here we present a family of distance 2 nonadditive quantum codes for all odd block lengths n, that has a particularly simple form. Our codes detect single qubit errors (or correct single qubit erasures) while encoding a higher dimensional space than is possible with an additive code or, for n> or =11, any previous codes. We exhibit the encoding circuits and automorphism group for our codes as well.

A striking feature of quantum error correcting codes is that they can sometimes be used to correct more errors than they can uniquely identify. Such degenerate codes have long been known, but have remained poorly understood. We provide a heuristic for designing degenerate quantum codes for high noise rates, which is applied to generate codes that can be used to communicate over almost any Pauli channel at rates that are impossible for a nondegenerate code. The gap between nondegenerate and degenerate code performance is quite large, in contrast to the tiny magnitude of the only previous demonstration of this effect. We also identify a channel for which none of our codes outperform the best nondegenerate code and show that it is nevertheless quite unlike any channel for which nondegenerate codes are known to be optimal.

Given a bipartite quantum state (in arbitrary dimension) and a decomposition of it as a superposition of two others, we find bounds on the entanglement of the superposition state in terms of the entanglement of the states being superposed. In the case that the two states being superposed are biorthogonal, the answer is simple, and, for example, the entanglement of the superposition cannot be more than one ebit more than the average of the entanglement of the two states being superposed. However, for more general states, the situation is very different.

We exhibit quantum channels whose classical and quantum capacities, when assisted by classical feedback, exceed their unassisted classical Holevo capacity. These channels are designed to be noisy in a way that can be corrected with the help of the output and a reference system entangled with part of the input. A similar construction yields quantum channels whose classical capacity, when assisted by two-way classical communication independent of the source, exceeds their classical capacity assisted by feedback alone. We give a hierarchy of capacity inequalities and open questions.

We show that a central presumption in the debate over black-hole information loss is incorrect. Ensuring that information not escape during evaporation does not require that it all remain trapped until the final stage of the process. Using the recent quantum information-theoretic result of locking, we show that the amount of information that must remain can be very small, even as the amount already radiated is negligible. Information need not be additive: A small system can lock a large amount of information, making it inaccessible. Only if the set of initial states is restricted can information leak.

We show that there exist bipartite quantum states which contain a large locked classical correlation that is unlocked by a disproportionately small amount of classical communication. In particular, there are (2n+1)-qubit states for which a one-bit message doubles the optimal classical mutual information between measurement results on the subsystems, from n/2 bits to n bits. This phenomenon is impossible classically. However, states exhibiting this behavior need not be entangled. We study the range of states exhibiting this phenomenon and bound its magnitude.

We show that, in a multiparty setting, two nondistillable (bound-entangled) states tensored together can make a distillable state. This is an example of true superadditivity of distillable entanglement. We also show that unlockable bound-entangled states cannot be asymptotically unentangled, providing the first proof that some states are truly bound-entangled in the sense of being both nondistillable and nonseparable asymptotically.