arXiv subjects

Renato Renner

Publications and source records attributed to Renato Renner.

At least 109 records · Page 6Linked to original sources

arXiv2013

Free randomness can be amplified

Are there fundamentally random processes in nature? Theoretical predictions, confirmed experimentally, such as the violation of Bell inequalities, point to an affirmative answer. However, these results are based on the assumption that measurement settings can be chosen freely at random, so assume the existence of perfectly free random processes from the outset. Here we consider a scenario in which this assumption is weakened and show that partially free random bits can be amplified to make arbitrarily free ones. More precisely, given a source of random bits whose correlation with other variables is below a certain threshold, we propose a procedure for generating fresh random bits that are virtually uncorrelated with all other variables. We also conjecture that such procedures exist for any non-trivial threshold. Our result is based solely on the no-signalling principle, which is necessary for the existence of free randomness.

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arXiv2013

Decoupling with unitary approximate two-designs

Consider a bipartite system, of which one subsystem, A, undergoes a physical evolution separated from the other subsystem, R. One may ask under which conditions this evolution destroys all initial correlations between the subsystems A and R, i.e. decouples the subsystems. A quantitative answer to this question is provided by decoupling theorems, which have been developed recently in the area of quantum information theory. This paper builds on preceding work, which shows that decoupling is achieved if the evolution on A consists of a typical unitary, chosen with respect to the Haar measure, followed by a process that adds sufficient decoherence. Here, we prove a generalized decoupling theorem for the case where the unitary is chosen from an approximate two-design. A main implication of this result is that decoupling is physical, in the sense that it occurs already for short sequences of random two-body interactions, which can be modeled as efficient circuits. Our decoupling result is independent of the dimension of the R system, which shows that approximate 2-designs are appropriate for decoupling even if the dimension of this system is large.

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arXiv2013

Efficient One-Way Secret-Key Agreement and Private Channel Coding via Polarization

We introduce explicit schemes based on the polarization phenomenon for the tasks of one-way secret key agreement from common randomness and private channel coding. For the former task, we show how to use common randomness and insecure one-way communication to obtain a strongly secure key such that the key construction has a complexity essentially linear in the blocklength and the rate at which the key is produced is optimal, i.e., equal to the one-way secret-key rate. For the latter task, we present a private channel coding scheme that achieves the secrecy capacity using the condition of strong secrecy and whose encoding and decoding complexity are again essentially linear in the blocklength.

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arXiv2013

Directed quantum communication

We raise the question whether there is a way to characterize the quantum information transport properties of a medium or material. For this analysis the special features of quantum information have to be taken into account. We find that quantum communication over an isotropic medium, as opposed to classical information transfer, requires the transmitter to direct the signal towards the receiver. Furthermore, for large classes of media there is a threshold, in the sense that `sufficiently much' of the signal has to be collected. Therefore, the medium's capacity for quantum communication can be characterized in terms of how the size of the transmitter and receiver has to scale with the transmission distance to maintain quantum information transmission. To demonstrate the applicability of this concept, an n-dimensional spin lattice is considered, yielding a sufficient scaling of d^(n/3) with the distance d.

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arXiv2013

A short note on the concept of free choice

We argue that the concepts of "freedom of choice" and of "causal order" are intrinsically linked: a choice is considered "free" if it is correlated only to variables in its causal future. We discuss the implications of this to Bell-type scenarios, where two separate measurements are carried out, neither of which lies in the causal future of the other, and where one typically assumes that the measurement settings are chosen freely. Furthermore, we refute a recent criticism made by Ghirardi and Romano in [arXiv:1301.5040] and [arXiv:1302.1635] that we used an unphysical freedom of choice assumption in our previous works, [Nat. Commun. 2, 411 (2011)] and [Phys. Rev. Lett. 108, 150402 (2012)].

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arXiv2013

One-Shot Classical-Quantum Capacity and Hypothesis Testing

The one-shot classical capacity of a quantum channel quantifies the amount of classical information that can be transmitted through a single use of the channel such that the error probability is below a certain threshold. In this work, we show that this capacity is well approximated by a relative-entropy-type measure defined via hypothesis testing. Combined with a quantum version of Stein's lemma, our results give a conceptually simple proof of the well-known Holevo-Schumacher-Westmoreland theorem for the capacity of memoryless channels. More generally, we obtain tight capacity formulas for arbitrary (not necessarily memoryless) channels.

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arXiv2012

Reliable Quantum State Tomography

Quantum state tomography is the task of inferring the state of a quantum system by appropriate measurements. Since the frequency distributions of the outcomes of any finite number of measurements will generally deviate from their asymptotic limits, the estimates computed by standard methods do not in general coincide with the true state, and therefore have no operational significance unless their accuracy is defined in terms of error bounds. Here we show that quantum state tomography, together with an appropriate data analysis procedure, yields reliable and tight error bounds, specified in terms of confidence regions - a concept originating from classical statistics. Confidence regions are subsets of the state space in which the true state lies with high probability, independently of any prior assumption on the distribution of the possible states. Our method for computing confidence regions can be applied to arbitrary measurements including fully coherent ones; it is practical and particularly well suited for tomography on systems consisting of a small number of qubits, which are currently in the focus of interest in experimental quantum information science.

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arXiv2012

Tight Finite-Key Analysis for Quantum Cryptography

Despite enormous progress both in theoretical and experimental quantum cryptography, the security of most current implementations of quantum key distribution is still not established rigorously. One of the main problems is that the security of the final key is highly dependent on the number, M, of signals exchanged between the legitimate parties. While, in any practical implementation, M is limited by the available resources, existing security proofs are often only valid asymptotically for unrealistically large values of M. Here, we demonstrate that this gap between theory and practice can be overcome using a recently developed proof technique based on the uncertainty relation for smooth entropies. Specifically, we consider a family of Bennett-Brassard 1984 quantum key distribution protocols and show that security against general attacks can be guaranteed already for moderate values of M.

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arXiv2012

The Uncertainty Relation for Smooth Entropies

Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data (e.g., a description of the system's state before measurement), an extended relation which remains valid in the presence of quantum information has been proposed recently [Berta et al., Nat. Phys. 6, 659 (2010)]. Here, we generalize this uncertainty relation to one formulated in terms of smooth entropies. Since these entropies measure operational quantities such as extractable secret key length, our uncertainty relation is of immediate practical use. To illustrate this, we show that it directly implies security of a family of quantum key distribution protocols including BB84. Our proof remains valid even if the measurement devices used in the experiment deviate arbitrarily from the theoretical model.

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arXiv2012

Reply to recent scepticism about the foundations of quantum cryptography

In a series of recent papers, Hirota and Yuen claim to have identified a fundamental flaw in the theory underlying quantum cryptography, which would invalidate existing security proofs. In this short note, we sketch their argument and show that their conclusion is unjustified --- it originates from a confusion between necessary and sufficient criteria for secrecy.

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arXiv2012

An intuitive proof of the data processing inequality

The data processing inequality (DPI) is a fundamental feature of information theory. Informally it states that you cannot increase the information content of a quantum system by acting on it with a local physical operation. When the smooth min-entropy is used as the relevant information measure, then the DPI follows immediately from the definition of the entropy. The DPI for the von Neumann entropy is then obtained by specializing the DPI for the smooth min-entropy by using the quantum asymptotic equipartition property (QAEP). We provide a new, simplified proof of the QAEP and therefore obtain a self-contained proof of the DPI for the von Neumann entropy.

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arXiv2012

Achieving the Capacity of any DMC using only Polar Codes

We construct a channel coding scheme to achieve the capacity of any discrete memoryless channel based solely on the techniques of polar coding. In particular, we show how source polarization and randomness extraction via polarization can be employed to "shape" uniformly-distributed i.i.d. random variables into approximate i.i.d. random variables distributed ac- cording to the capacity-achieving distribution. We then combine this shaper with a variant of polar channel coding, constructed by the duality with source coding, to achieve the channel capacity. Our scheme inherits the low complexity encoder and decoder of polar coding. It differs conceptually from Gallager's method for achieving capacity, and we discuss the advantages and disadvantages of the two schemes. An application to the AWGN channel is discussed.

cs.IT↗

arXiv2012

Security of continuous-variable quantum key distribution against general attacks

We prove the security of Gaussian continuous-variable quantum key distribution against arbitrary attacks in the finite-size regime. The novelty of our proof is to consider symmetries of quantum key distribution in phase space in order to show that, to good approximation, the Hilbert space of interest can be considered to be finite-dimensional, thereby allowing for the use of the postselection technique introduced by Christandl, Koenig and Renner (Phys. Rev. Lett. 102, 020504 (2009)). Our result greatly improves on previous work based on the de Finetti theorem which could not provide security for realistic, finite-size, implementations.

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arXiv2012

Tsirelson's bound from a Generalised Data Processing Inequality

The strength of quantum correlations is bounded from above by Tsirelson's bound. We establish a connection between this bound and the fact that correlations between two systems cannot increase under local operations, a property known as the data processing inequality. More specifically, we consider arbitrary convex probabilistic theories. These can be equipped with an entropy measure that naturally generalizes the von Neumann entropy, as shown recently in [Short and Wehner, Barnum et al.]. We prove that if the data processing inequality holds with respect to this generalized entropy measure then the underlying theory necessarily respects Tsirelson's bound. We moreover generalise this statement to any entropy measure satisfying certain minimal requirements. A consequence of our result is that not all of the entropic relations used to derive Tsirelson's bound via information causality in [Pawlowski et al.] are necessary.

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arXiv2012

Trevisan's extractor in the presence of quantum side information

Randomness extraction involves the processing of purely classical information and is therefore usually studied in the framework of classical probability theory. However, such a classical treatment is generally too restrictive for applications, where side information about the values taken by classical random variables may be represented by the state of a quantum system. This is particularly relevant in the context of cryptography, where an adversary may make use of quantum devices. Here, we show that the well known construction paradigm for extractors proposed by Trevisan is sound in the presence of quantum side information. We exploit the modularity of this paradigm to give several concrete extractor constructions, which, e.g, extract all the conditional (smooth) min-entropy of the source using a seed of length poly-logarithmic in the input, or only require the seed to be weakly random.

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arXiv2012

Is a system's wave function in one-to-one correspondence with its elements of reality?

Although quantum mechanics is one of our most successful physical theories, there has been a long-standing debate about the interpretation of the wave function---the central object of the theory. Two prominent views are that (i) it corresponds to an element of reality, i.e. an objective attribute that exists before measurement, and (ii) it is a subjective state of knowledge about some underlying reality. A recent result [Pusey et al. arXiv:1111.3328] has placed the subjective interpretation into doubt, showing that it would contradict certain physically plausible assumptions, in particular that multiple systems can be prepared such that their elements of reality are uncorrelated. Here we show, based only on the assumption that measurement settings can be chosen freely, that a system's wave function is in one-to-one correspondence with its elements of reality. This also eliminates the possibility that it can be interpreted subjectively.

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arXiv2012

Efficient Quantum Polar Coding

Polar coding, introduced 2008 by Arikan, is the first (very) efficiently encodable and decodable coding scheme whose information transmission rate provably achieves the Shannon bound for classical discrete memoryless channels in the asymptotic limit of large block sizes. Here we study the use of polar codes for the transmission of quantum information. Focusing on the case of qubit Pauli channels and qubit erasure channels, we use classical polar codes to construct a coding scheme which, using some pre-shared entanglement, asymptotically achieves a net transmission rate equal to the coherent information using efficient encoding and decoding operations and code construction. Furthermore, for channels with sufficiently low noise level, we demonstrate that the rate of preshared entanglement required is zero.

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arXiv2012

Noisy channel coding via privacy amplification and information reconciliation

We show that optimal protocols for noisy channel coding of public or private information over either classical or quantum channels can be directly constructed from two more primitive information-theoretic tools: privacy amplification and information reconciliation, also known as data compression with side information. We do this in the one-shot scenario of structureless resources, and formulate our results in terms of the smooth min- and max-entropy. In the context of classical information theory, this shows that essentially all two-terminal protocols can be reduced to these two primitives, which are in turn governed by the smooth min- and max-entropies, respectively. In the context of quantum information theory, the recently-established duality of these two protocols means essentially all two-terminal protocols can be constructed using just a single primitive.

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