arXiv subjects
Publications and source records attributed to Graeme Smith.
We find a tight upper bound for the classical capacity of quantum thermal noise channels that is within $1/\ln 2$ bits of Holevo's lower bound. This lower bound is achievable using unentangled, classical signal states, namely displaced coherent states. Thus, we find that while quantum tricks might offer benefits, when it comes to classical communication they can only help a bit.
Almost all modern communication systems rely on electromagnetic fields as a means of information transmission, and finding the capacities of these systems is a problem of significant practical importance. The Additive White Gaussian Noise (AWGN) channel is often a good approximate description of such systems, and its capacity is given by a simple formula. However, when quantum effects are important, estimating the capacity becomes difficult: a lower bound is known, but a similar upper bound is missing. We present strong new upper bounds for the classical capacity of quantum additive noise channels, including quantum analogues of the AWGN channel. Our main technical tool is a quantum entropy power inequality that controls the entropy production as two quantum signals combine at a beam splitter. Its proof involves a new connection between entropy production rates and a quantum Fisher information, and uses a quantum diffusion that smooths arbitrary states towards gaussians.
The zero-error capacity of a channel is the rate at which it can send information perfectly, with zero probability of error, and has long been studied in classical information theory. We show that the zero-error capacity of quantum channels exhibits an extreme form of non-additivity, one which is not possible for classical channels, or even for the usual capacities of quantum channels. By combining probabilistic arguments with algebraic geometry, we prove that there exist channels E1 and E2 with no zero-error classical capacity whatsoever, C_0(E1) = C_0(E2) = 0, but whose joint zero-error quantum capacity is positive, Q_0(E1 x E2) >= 1. This striking effect is an extreme from of the superactivation phenomenon, as it implies that both the classical and quantum zero-error capacities of these channels can be superactivated simultaneously, whilst being a strictly stronger property of capacities. Superactivation of the quantum zero-error capacity was not previously known.
We provide an efficient method for computing the maximum likelihood mixed quantum state (with density matrix $ρ$) given a set of measurement outcome in a complete orthonormal operator basis subject to Gaussian noise. Our method works by first changing basis yielding a candidate density matrix $μ$ which may have nonphysical (negative) eigenvalues, and then finding the nearest physical state under the 2-norm. Our algorithm takes at worst $O(d^4)$ for the basis change plus $O(d^3)$ for finding $ρ$ 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 $O(d^3)$ 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.
We describe two quantum channels that individually cannot send any information, even classical, without some chance of decoding error. But together a single use of each channel can send quantum information perfectly reliably. This proves that the zero-error classical capacity exhibits superactivation, the extreme form of the superadditivity phenomenon in which entangled inputs allow communication over zero capacity channels. But our result is stronger still, as it even allows zero-error quantum communication when the two channels are combined. Thus our result shows a new remarkable way in which entanglement across two systems can be used to resist noise, in this case perfectly. We also show a new form of superactivation by entanglement shared between sender and receiver.
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 us to implement the associated forbidden transformation. Our approach includes both known quantum incapacity tests---positive partial transposition (PPT) and antidegradability (no cloning)---as special cases, putting them both on the same footing. We also find a physical principle explaining the nondistillability of PPT states: Any protocol for distilling entanglement from such a state would also give a protocol for implementing the forbidden time-reversal operation.
As with classical information, error-correcting codes enable reliable transmission of quantum information through noisy or lossy channels. In contrast to the classical theory, imperfect quantum channels exhibit a strong kind of synergy: there exist pairs of discrete memoryless quantum channels, 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.
A quantum communication channel can be put to many uses: it can transmit classical information, private classical information, or quantum information. It can be used alone, with shared entanglement, or together with other channels. For each of these settings there is a capacity that quantifies a channel's potential for communication. In this short review, I summarize what is known about the various capacities of a quantum channel, including a discussion of the relevant additivity questions. I also give some indication of potentially interesting directions for future research.
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 2 log d input qubits 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)log d. 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 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 > 7 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, easy encoding and decoding circuits are available.
We have obtained velocity dispersions from Keck high-resolution integrated spectroscopy of ten M31 globular clusters (GCs), including three candidate intermediate-age GCs. We show that these candidates have the same V-band mass-to-light (M/L_V) ratios as the other GCs, implying that they are likely to be old. We also find a trend of derived velocity dispersion with wavelength, but cannot distinguish between a systematic error and a physical effect. Our new measurements are combined with photometric and spectroscopic data from the literature in a reanalysis of all M31 GC M/L_V values. In a combined sample of 27 GCs, we show that the metal-rich GCs have *lower* M/L_V than the metal-poor GCs, in conflict with predictions from stellar population models. Fragmentary data for other galaxies support this observation. The M31 GC fundamental plane is extremely tight, and we follow up an earlier suggestion by Djorgovski to show that the fundamental plane can be used to estimate accurate distances (potentially 10% or better).
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.
Communication over a noisy quantum channel introduces errors in the transmission that must be corrected. A fundamental bound on quantum error correction is the quantum capacity, which quantifies the amount of quantum data that can be protected. We show theoretically that two quantum channels, each with a transmission capacity of zero, can have a nonzero capacity when used together. This unveils a rich structure in the theory of quantum communications, implying that the quantum capacity does not uniquely specify a channel's ability for transmitting quantum information.
We prove that a broad array of capacities of a quantum channel are continuous. That is, two channels that are close with respect to the diamond norm have correspondingly similar communication capabilities. We first show that the classical capacity, quantum capacity, and private classical capacity are continuous, with the variation on arguments epsilon apart bounded by a simple function of epsilon and the channel's output dimension. Our main tool is an upper bound of the variation of output entropies of many copies of two nearby channels given the same initial state; the bound is linear in the number of copies. Our second proof is concerned with the quantum capacities in the presence of free backward or two-way public classical communication. These capacities are proved continuous on the interior of the set of non-zero capacity channels by considering mutual simulation between similar channels.
We introduce the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we construct families of new single-error-correcting nonadditive quantum codes, in both binary and nonbinary cases, which not only outperform any stabilizer codes for finite block length, but also asymptotically achieve the quantum Hamming bound for large block length.
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).
Some early-type galaxies show a correlation between color and integrated magnitude among the brighter metal-poor globular clusters (GCs). This phenomenon, known as the blue tilt, implies a mass-metallicity relationship among these clusters. In this paper we show that self-enrichment in GCs can explain several aspects of the blue tilt, and discuss predictions of this scenario.