arXiv subjects

Andreas Winter

Publications and source records attributed to Andreas Winter.

At least 73 records · Page 4Linked to original sources

arXiv2021

Extendibility limits the performance of quantum processors

Resource theories in quantum information science are helpful for the study and quantification of the performance of information-processing tasks that involve quantum systems. These resource theories also find applications in other areas of study; e.g., the resource theories of entanglement and coherence have found use and implications in the study of quantum thermodynamics and memory effects in quantum dynamics. In this paper, we introduce the resource theory of unextendibility, which is associated to the inability of extending quantum entanglement in a given quantum state to multiple parties. The free states in this resource theory are the k-extendible states, and the free channels are k-extendible channels, which preserve the class of k-extendible states. We make use of this resource theory to derive non-asymptotic, upper bounds on the rate at which quantum communication or entanglement preservation is possible by utilizing an arbitrary quantum channel a finite number of times, along with the assistance of k-extendible channels at no cost. We then show that the bounds obtained are significantly tighter than previously known bounds for quantum communication over both the depolarizing and erasure channels.

quant-ph↗

arXiv2021

Infinite-Dimensional Programmable Quantum Processors

A universal programmable quantum processor uses program quantum states to apply an arbitrary quantum channel to an input state. We generalize the concept of a finite-dimensional programmable quantum processor to infinite dimension assuming an energy constraint on the input and output of the target quantum channels. By proving reductions to and from finite-dimensional processors, we obtain upper and lower bounds on the program dimension required to approximately implement energy-limited quantum channels. In particular, we consider the implementation of Gaussian channels. Due to their practical relevance, we investigate the resource requirements for gauge-covariant Gaussian channels. Additionally, we give upper and lower bounds on the program dimension of a processor implementing all Gaussian unitary channels. These lower bounds rely on a direct information-theoretic argument, based on the generalization from finite to infinite dimension of a certain replication lemma for unitaries.

quant-ph↗

arXiv2021

Programmability of covariant quantum channels

A programmable quantum processor uses the states of a program register to specify one element of a set of quantum channels which is applied to an input register. It is well-known that such a device is impossible with a finite-dimensional program register for any set that contains infinitely many unitary quantum channels (Nielsen and Chuang's No-Programming Theorem), meaning that a universal programmable quantum processor does not exist. The situation changes if the system has symmetries. Indeed, here we consider group-covariant channels. If the group acts irreducibly on the channel input, these channels can be implemented exactly by a programmable quantum processor with finite program dimension (via teleportation simulation, which uses the Choi-Jamiolkowski state of the channel as a program). Moreover, by leveraging the representation theory of the symmetry group action, we show how to remove redundancy in the program and prove that the resulting program register has minimum Hilbert space dimension. Furthermore, we provide upper and lower bounds on the program register dimension of a processor implementing all group-covariant channels approximately.

quant-ph↗

arXiv2021

Belief-Invariant and Quantum Equilibria in Games of Incomplete Information

Drawing on ideas from game theory and quantum physics, we investigate nonlocal correlations from the point of view of equilibria in games of incomplete information. These equilibria can be classified in decreasing power as communication equilibria, belief-invariant equilibria, and correlated equilibria, all of which contain the familiar Nash equilibria. The notion of belief-invariant equilibrium appeared in game theory in the 90s. However, the class of non-signalling correlations associated to belief-invariance arose naturally already in the 80s in the foundations of quantum mechanics. In the present work, we explain and unify these two origins of the idea and study the above classes of equilibria, together with quantum correlated equilibria, using tools from quantum information but the language of (algorithmic) game theory. We present a general framework of belief-invariant communication equilibria, which contains correlated equilibria and quantum correlated equilibria as special cases. Our framework also contains the theory of Bell inequalities and their violations due to non-locality, which is a question of intense interest in the foundations of quantum mechanics, and it was indeed the original motivation for the aforementioned studies. Moreover, in our framework we can also model quantum games where players have conflicting interests, a recent developing topic in physics. We then use our framework to show new results related to the social welfare of equilibria. Namely, we exhibit a game where belief-invariance is socially better than any correlated equilibrium, and a game where all non-belief-invariant communication equilibria have a suboptimal social welfare. We also show that optimal social welfare can sometimes be achieved by quantum mechanical correlations, which do not need an informed mediator to be implemented, and go beyond the classical shared randomness approach.

cs.GT↗

arXiv2021

A genuinely natural information measure

The theoretical measuring of information was famously initiated by Shannon in his mathematical theory of communication, in which he proposed a now widely used quantity, the entropy, measured in bits. Yet, in the same paper, Shannon also chose to measure the information in continuous systems in nats, which differ from bits by the use of the natural rather than the binary logarithm. We point out that there is nothing natural about the choice of logarithm basis, rather it is arbitrary. We remedy this problematic state of affairs by proposing a genuinely natural measure of information, which we dub gnats. We show that gnats have many advantages in information theory, and propose to adopt the underlying methodology throughout science, arts and everyday life.

cs.IT↗

arXiv2021

Experimental quantum phase discrimination enhanced by controllable indistinguishability-based coherence

Quantum coherence, a basic feature of quantum mechanics residing in superpositions of quantum states, is a resource for quantum information processing. Coherence emerges in a fundamentally different way for nonidentical and identical particles, in that for the latter a unique contribution exists linked to indistinguishability which cannot occur for nonidentical particles. We experimentally demonstrate by an optical setup this additional contribution to quantum coherence, showing that its amount directly depends on the degree of indistinguishability and exploiting it to run a quantum phase discrimination protocol. Furthermore, the designed setup allows for simulating Fermionic particles with photons, thus assessing the role of particle statistics (Bosons or Fermions) in coherence generation and utilization. Our experiment proves that independent indistinguishable particles can supply a controllable resource of coherence for quantum metrology.

quant-ph↗

arXiv2021

Information theoretic parameters of non-commutative graphs and convex corners

We establish a second anti-blocker theorem for non-commutative convex corners, show that the anti-blocking operation is continuous on bounded sets of convex corners, and define optimisation parameters for a given convex corner that generalise well-known graph theoretic quantities. We define the entropy of a state with respect to a convex corner, characterise its maximum value in terms of a generalised fractional chromatic number and establish entropy splitting results that demonstrate the entropic complementarity between a convex corner and its anti-blocker. We identify two extremal tensor products of convex corners and examine the behaviour of the introduced parameters with respect to tensoring. Specialising to non-commutative graphs, we obtain quantum versions of the fractional chromatic number and the clique covering number, as well as a notion of non-commutative graph entropy of a state, which we show to be continuous with respect to the state and the graph. We define the Witsenhausen rate of a non-commutative graph and compute the values of our parameters in some specific cases.

math.OA↗

arXiv2021

Bosonic data hiding: power of linear vs non-linear optics

We show that the positivity of the Wigner function of Gaussian states and measurements provides an elegant way to bound the discriminating power of "linear optics", which we formalise as Gaussian measurement operations augmented by classical (feed-forward) communication (GOCC). This allows us to reproduce and generalise the result of Takeoka and Sasaki [PRA 78:022320, 2008], which tightly characterises the GOCC norm distance of coherent states, separating it from the optimal distinguishability according to Helstrom's theorem. Furthermore, invoking ideas from classical and quantum Shannon theory we show that there are states, each a probabilistic mixture of multi-mode coherent states, which are exponentially reliably discriminated in principle, but appear exponentially close judging from the output of GOCC measurements. In analogy to LOCC data hiding, which shows an irreversibility in the preparation and discrimination of states by the restricted class of local operations and classical communication (LOCC), we call the present effect GOCC data hiding. We also present general bounds in the opposite direction, guaranteeing a minimum of distinguishability under measurements with positive Wigner function, for any bounded-energy states that are Helstrom distinguishable. We conjecture that a similar bound holds for GOCC measurements.

quant-ph↗

arXiv2021

Capacities of Gaussian Quantum Channels with Passive Environment Assistance

Passive environment assisted communication takes place via a quantum channel modeled as a unitary interaction between the information carrying system and an environment, where the latter is controlled by a passive helper, who can set its initial state such as to assist sender and receiver, but not help actively by adjusting her behaviour depending on the message. Here we investigate the information transmission capabilities in this framework by considering Gaussian unitaries acting on Bosonic systems. We consider both quantum communication and classical communication with helper, as well as classical communication with free classical coordination between sender and helper (conferencing encoders). Concerning quantum communication, we prove general coding theorems with and without energy constraints, yielding multi-letter (regularized) expressions. In the search for cases where the capacity formula is computable, we look for Gaussian unitaries that are universally degradable or anti-degradable. However, we show that no Gaussian unitary yields either a degradable or anti-degradable channel for all environment states. On the other hand, restricting to Gaussian environment states, results in universally degradable unitaries, for which we thus can give single-letter quantum capacity formulas. Concerning classical communication, we prove a general coding theorem for the classical capacity under and energy constraint, given by a multi-letter expression. Furthermore, we derive an uncertainty-type relation between the classical capacities of the sender and the helper, helped respectively by the other party, showing a lower bound on the sum of the two capacities. Then, this is used to lower bound the classical information transmission rate in the scenario of classical communication between sender and helper.

quant-ph↗

arXiv2020

Multi-User Distillation of Common Randomness and Entanglement from Quantum States

We construct new protocols for the tasks of converting noisy multipartite quantum correlations into noiseless classical and quantum ones using local operations and classical communications (LOCC). For the former, known as common randomness (CR) distillation, two new lower bounds on the "distillable common randomness", an operational measure of the total genuine (classical) correlations in a quantum state, are obtained. Our proof relies on a generalization of communication for omniscience (CO) [Csiszar and Narayan, IEEE Trans. Inf. Theory 50:3047-3061, 2004]. Our contribution here is a novel simultaneous decoder for the compression of correlated classical sources by random binning with quantum side information at the decoder. For the latter, we derive two new lower bounds on the rate at which Greenberger-Horne-Zeilinger (GHZ) states can be asymptotically distilled from any given pure state under LOCC. Our approach consists in "making coherent" the proposed CR distillation protocols and recycling of resources [Devetak et al. IEEE Trans. Inf. Theory 54(10):4587-4618, 2008]. The first lower bound is identical to a recent result by Vrana and Christandl [IEEE Trans. Inf. Theory 65(9):5945-5958, 2019], which is based on a combinatorial method to achieve the same rate. Our second lower bound generalises and improves upon this result, and unifies a number of other known lower bounds on GHZ distillation.

quant-ph↗

arXiv2020

Proton and Li-Ion Permeation through Graphene with Eight-Atom-Ring Defects

Defect-free graphene is impermeable to gases and liquids but highly permeable to thermal protons. Atomic-scale defects such as vacancies, grain boundaries and Stone-Wales defects are predicted to enhance graphene's proton permeability and may even allow small ions through, whereas larger species such as gas molecules should remain blocked. These expectations have so far remained untested in experiment. Here we show that atomically thin carbon films with a high density of atomic-scale defects continue blocking all molecular transport, but their proton permeability becomes ~1,000 times higher than that of defect-free graphene. Lithium ions can also permeate through such disordered graphene. The enhanced proton and ion permeability is attributed to a high density of 8-carbon-atom rings. The latter pose approximately twice lower energy barriers for incoming protons compared to the 6-atom rings of graphene and a relatively low barrier of ~0.6 eV for Li ions. Our findings suggest that disordered graphene could be of interest as membranes and protective barriers in various Li-ion and hydrogen technologies.

cond-mat.mtrl-sci↗

arXiv2020

Reference frames which separately store non-commuting conserved quantities

Even in the presence of conservation laws, one can perform arbitrary transformations on a system if given access to a suitable reference frame, since conserved quantities may be exchanged between the system and the frame. Here we explore whether these quantities can be separated into different parts of the reference frame, with each part acting as a `battery' for a distinct quantity. For systems composed of spin-$\frac12$ particles, we show that the components of angular momentum $S_x$, $S_y$ and $S_z$ (non-commuting conserved quantities) may be separated in this way, and also provide several extensions of this result. These results also play a key role in the quantum thermodynamics of non-commuting conserved quantities.

quant-ph↗

arXiv2020

Quantum Godwin's Law

Godwin's law, i.e. the empirical observation that as an online discussion grows in time, the probability of a comparison with Nazis or Hitler quickly approaches unity, is one of the best-documented facts of the internet. Anticipating the quantum internet, here we show under reasonable model assumptions a polynomial quantum speedup of Godwin's law. Concretely, in quantum discussions, Hitler will be mentioned on average quadratically earlier, and we conjecture that under specific network topologies, even cubic speedups are possible. We also show that the speedup cannot be more than exponential, unless the polynomial hierarchy collapses to a certain finite level. We report on numerical experiments to simulate the appearance of the quantum Godwin law in future quantum internets; the most amazing finding of our studies is that -- unlike quantum computational speedups -- the quantum Godwin effect is not only robust against noise, but actually enhanced by decoherence. We have as yet no theoretical explanation, nor a good application, for this astonishing behaviour, which we dub quantum hyperpiesia.

quant-ph↗

arXiv2020

Fundamental limits on key rates in device-independent quantum key distribution

In this paper, we introduce intrinsic non-locality as a quantifier for Bell non-locality, and we prove that it satisfies certain desirable properties such as faithfulness, convexity, and monotonicity under local operations and shared randomness. We then prove that intrinsic non-locality is an upper bound on the secret-key-agreement capacity of any device-independent protocol conducted using a device characterized by a correlation $p$. We also prove that intrinsic steerability is an upper bound on the secret-key-agreement capacity of any semi-device-independent protocol conducted using a device characterized by an assemblage $\hatρ$. We also establish the faithfulness of intrinsic steerability and intrinsic non-locality. Finally, we prove that intrinsic non-locality is bounded from above by intrinsic steerability.

quant-ph↗

arXiv2019

General Mixed State Quantum Data Compression with and without Entanglement Assistance

We consider the most general (finite-dimensional) quantum mechanical information source, which is given by a quantum system $A$ that is correlated with a reference system $R$. The task is to compress $A$ in such a way as to reproduce the joint source state $ρ^{AR}$ at the decoder with asymptotically high fidelity. This includes Schumacher's original quantum source coding problem of a pure state ensemble and that of a single pure entangled state, as well as general mixed state ensembles. Here, we determine the optimal compression rate (in qubits per source system) in terms of the Koashi-Imoto decomposition of the source into a classical, a quantum, and a redundant part. The same decomposition yields the optimal rate in the presence of unlimited entanglement between compressor and decoder, and indeed the full region of feasible qubit-ebit rate pairs.

quant-ph↗

arXiv2019

How to quantify a dynamical quantum resource

We show that the generalization of the relative entropy of a resource from states to channels is not unique, and there are at least six such generalizations. We then show that two of these generalizations are asymptotically continuous, satisfy a version of the asymptotic equipartition property, and their regularizations appear in the power exponent of channel versions of the quantum Stein's Lemma. To obtain our results, we use a new type of "smoothing" that can be applied to functions of channels (with no state analog). We call it "liberal smoothing" as it allows for more spread in the optimization. Along the way, we show that the diamond norm can be expressed as a D_max distance to the set of quantum channels, and prove a variety of properties of all six generalizations of the relative entropy of a resource.

quant-ph↗

arXiv2019

Distributed Private Randomness Distillation

We develop the resource theory of private randomness extraction in the distributed and device-dependent scenario. We begin by introducing the notion of independent random bits, which are bipartite states containing ideal private randomness for each party, and motivate the natural set of free operations. As a conceptual tool, we introduce Virtual Quantum State Merging, which is essentially the flip side of Quantum State Merging, without communication. We focus on the bipartite case and find the rate regions achievable in different settings. Surprisingly, it turns out that local noise can boost randomness extraction. As a consequence of our analysis, we resolve a long-standing problem by giving an operational interpretation for the reverse coherent information (up to a constant term $\log d$) as the number of private random bits obtained by sending quantum states from one honest party (server) to another one (client) via the eavesdropped quantum channel.

quant-ph↗

arXiv2019

All tight correlation Bell inequalities have quantum violations

It is by now well-established that there exist non-local games for which the best entanglement-assisted performance is not better than the best classical performance. Here we show in contrast that any two-player XOR game, for which the corresponding Bell inequality is tight, has a quantum advantage. In geometric terms, this means that any correlation Bell inequality for which the classical and quantum maximum values coincide, does not define a facet, i.e. a face of maximum dimension, of the local Bell polytope. Indeed, using semidefinite programming duality, we prove upper bounds on the dimension of these faces, bounding it far away from the maximum. In the special case of non-local computation games, it had been shown before that they are not facet-defining; our result generalises and improves this. As a by-product of our analysis, we find a similar upper bound on the dimension of the faces of the convex body of quantum correlation matrices, showing that (except for the trivial ones expressing the non-negativity of probability) it does not have facets.

quant-ph↗