arXiv subjects

Gilles Brassard

Publications and source records attributed to Gilles Brassard.

At least 37 records · Page 2Linked to original sources

arXiv2009

Fair Loss-Tolerant Quantum Coin Flipping

Coin flipping is a cryptographic primitive in which two spatially separated players, who in principle do not trust each other, wish to establish a common random bit. If we limit ourselves to classical communication, this task requires either assumptions on the computational power of the players or it requires them to send messages to each other with sufficient simultaneity to force their complete independence. Without such assumptions, all classical protocols are so that one dishonest player has complete control over the outcome. If we use quantum communication, on the other hand, protocols have been introduced that limit the maximal bias that dishonest players can produce. However, those protocols would be very difficult to implement in practice because they are susceptible to realistic losses on the quantum channel between the players or in their quantum memory and measurement apparatus. In this paper, we introduce a novel quantum protocol and we prove that it is completely impervious to loss. The protocol is fair in the sense that either player has the same probability of success in cheating attempts at biasing the outcome of the coin flip. We also give explicit and optimal cheating strategies for both players.

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arXiv2009

Flipping quantum coins

Coin flipping is a cryptographic primitive in which two distrustful parties wish to generate a random bit in order to choose between two alternatives. This task is impossible to realize when it relies solely on the asynchronous exchange of classical bits: one dishonest player has complete control over the final outcome. It is only when coin flipping is supplemented with quantum communication that this problem can be alleviated, although partial bias remains. Unfortunately, practical systems are subject to loss of quantum data, which restores complete or nearly complete bias in previous protocols. We report herein on the first implementation of a quantum coin-flipping protocol that is impervious to loss. Moreover, in the presence of unavoidable experimental noise, we propose to use this protocol sequentially to implement many coin flips, which guarantees that a cheater unwillingly reveals asymptotically, through an increased error rate, how many outcomes have been fixed. Hence, we demonstrate for the first time the possibility of flipping coins in a realistic setting. Flipping quantum coins thereby joins quantum key distribution as one of the few currently practical applications of quantum communication. We anticipate our findings to be useful for various cryptographic protocols and other applications, such as an online casino, in which a possibly unlimited number of coin flips has to be performed and where each player is free to decide at any time whether to continue playing or not.

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arXiv2009

Entanglement Cost of Nonlocal Measurements

For certain joint measurements on a pair of spatially separated particles, we ask how much entanglement is needed to carry out the measurement exactly. For a class of orthogonal measurements on two qubits with partially entangled eigenstates, we present upper and lower bounds on the entanglement cost. The upper bound is based on a recent result by D. Berry [Phys. Rev. A 75, 032349 (2007)]. The lower bound, based on the entanglement production capacity of the measurement, implies that for almost all measurements in the class we consider, the entanglement required to perform the measurement is strictly greater than the average entanglement of its eigenstates. On the other hand, we show that for any complete measurement in d x d dimensions that is invariant under all local Pauli operations, the cost of the measurement is exactly equal to the average entanglement of the states associated with the outcomes.

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arXiv2007

Anonymous quantum communication

We present the first protocol for the anonymous transmission of a quantum state that is information-theoretically secure against an active adversary, without any assumption on the number of corrupt participants. The anonymity of the sender and receiver is perfectly preserved, and the privacy of the quantum state is protected except with exponentially small probability. Even though a single corrupt participant can cause the protocol to abort, the quantum state can only be destroyed with exponentially small probability: if the protocol succeeds, the state is transferred to the receiver and otherwise it remains in the hands of the sender (provided the receiver is honest).

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arXiv2006

Can quantum-mechanical description of physical reality be considered incomplete?

In loving memory of Asher Peres, we discuss a most important and influential paper written in 1935 by his thesis supervisor and mentor Nathan Rosen, together with Albert Einstein and Boris Podolsky. In that paper, the trio known as EPR questioned the completeness of quantum mechanics. The authors argued that the then-new theory should not be considered final because they believed it incapable of describing physical reality. The epic battle between Einstein and Bohr intensified following the latter's response later the same year. Three decades elapsed before John S. Bell gave a devastating proof that the EPR argument was fatally flawed. The modest purpose of our paper is to give a critical analysis of the original EPR paper and point out its logical shortcomings in a way that could have been done 70 years ago, with no need to wait for Bell's theorem. We also present an overview of Bohr's response in the interest of showing how it failed to address the gist of the EPR argument.

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arXiv2006

Brief History of Quantum Cryptography: A Personal Perspective

Quantum cryptography is the only approach to privacy ever proposed that allows two parties (who do not share a long secret key ahead of time) to communicate with provably perfect secrecy under the nose of an eavesdropper endowed with unlimited computational power and whose technology is limited by nothing but the fundamental laws of nature. This essay provides a personal historical perspective on the field. For the sake of liveliness, the style is purposely that of a spontaneous after-dinner speech.

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arXiv2005

Experimental Heat-Bath Cooling of Spins

Algorithmic cooling is a novel technique to generate ensembles of highly polarized spins, which could significantly improve the signal strength in Nuclear Magnetic Resonance (NMR) spectroscopy. It combines reversible (entropy-preserving) manipulations and irreversible controlled interactions with the environment, using simple quantum computing techniques to increase spin polarization far beyond the Shannon entropy-conservation bound. Notably, thermalization is beneficially employed as an integral part of the cooling scheme, contrary to its ordinary destructive implications. We report the first cooling experiments bypassing Shannon's entropy-conservation bound, performed on a standard liquid-state NMR spectrometer. We believe that this experimental success could pave the way for the first near-future application of quantum computing devices.

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arXiv2005

A limit on nonlocality in any world in which communication complexity is not trivial

Bell proved that quantum entanglement enables two space-like separated parties to exhibit classically impossible correlations. Even though these correlations are stronger than anything classically achievable, they cannot be harnessed to make instantaneous (faster than light) communication possible. Yet, Popescu and Rohrlich have shown that even stronger correlations can be defined, under which instantaneous communication remains impossible. This raises the question: Why are the correlations achievable by quantum mechanics not maximal among those that preserve causality? We give a partial answer to this question by showing that slightly stronger correlations would result in a world in which communication complexity becomes trivial.

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arXiv2005

Recasting Mermin's multi-player game into the framework of pseudo-telepathy

Entanglement is perhaps the most non-classical manifestation of quantum mechanics. Among its many interesting applications to information processing, it can be harnessed to reduce the amount of communication required to process a variety of distributed computational tasks. Can it be used to eliminate communication altogether? Even though it cannot serve to signal information between remote parties, there are distributed tasks that can be performed without any need for communication, provided the parties share prior entanglement: this is the realm of pseudo-telepathy. One of the earliest uses of multi-party entanglement was presented by Mermin in 1990. Here we recast his idea in terms of pseudo-telepathy: we provide a new computer-scientist-friendly analysis of this game. We prove an upper bound on the best possible classical strategy for attempting to play this game, as well as a novel, matching lower bound. This leads us to considerations on how well imperfect quantum-mechanical apparatus must perform in order to exhibit a behaviour that would be classically impossible to explain. Our results include improved bounds that could help vanquish the infamous detection loophole.

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arXiv2004

Minimum entangled state dimension required for pseudo-telepathy

Pseudo-telepathy provides an intuitive way of looking at Bell's inequalities, in which it is often obvious that feats achievable by use of quantum entanglement would be classically impossible. A two-player pseudo-telepathy game proceeds as follows: Alice and Bob are individually asked a question and they must provide an answer. They are not allowed any form of communication once the questions are asked, but they may have agreed on a common strategy prior to the execution of the game. We say that they win the game if the questions and answers fulfil a specific relation. A game exhibits pseudo-telepathy if there is a quantum strategy that makes Alice and Bob win the game for all possible questions, provided they share prior entanglement, whereas it would be impossible to win this game systematically in a classical setting. In this paper, we show that any two-player pseudo-telepathy game requires the quantum players to share an entangled quantum system of dimension at least 3x3. This is optimal for two-player games, but the most efficient pseudo-telepathy game possible, in terms of total dimension, involves three players who share a quantum system of dimension 2x2x2.

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arXiv2004

Quantum Pseudo-Telepathy

Quantum information processing is at the crossroads of physics, mathematics and computer science. It is concerned with that we can and cannot do with quantum information that goes beyond the abilities of classical information processing devices. Communication complexity is an area of classical computer science that aims at quantifying the amount of communication necessary to solve distributed computational problems. Quantum communication complexity uses quantum mechanics to reduce the amount of communication that would be classically required. Pseudo-telepathy is a surprising application of quantum information processing to communication complexity. Thanks to entanglement, perhaps the most nonclassical manifestation of quantum mechanics, two or more quantum players can accomplish a distributed task with no need for communication whatsoever, which would be an impossible feat for classical players. After a detailed overview of the principle and purpose of pseudo-telepathy, we present a survey of recent and no-so-recent work on the subject. In particular, we describe and analyse all the pseudo-telepathy games currently known to the authors.

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arXiv2003

Quantum Computing Without Entanglement

It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability of the outcome after a xed number of oracle calls. Using a separable (that is, unentangled) n-qubit state, we show that the Deutsch-Jozsa problem and the Simon problem can be solved more reliably by a quantum computer than by the best possible classical algorithm, even probabilistic. We conclude that: (a) entanglement is not essential for quantum computing; and (b) some advantage of quantum algorithms over classical algorithms persists even when the quantum state contains an arbitrarily small amount of information|that is, even when the state is arbitrarily close to being totally mixed.

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arXiv2003

Multi-Party Pseudo-Telepathy

Quantum entanglement, perhaps the most non-classical manifestation of quantum information theory, cannot be used to transmit information between remote parties. Yet, it can be used to reduce the amount of communication required to process a variety of distributed computational tasks. We speak of pseudo-telepathy when quantum entanglement serves to eliminate the classical need to communicate. In earlier examples of pseudo-telepathy, classical protocols could succeed with high probability unless the inputs were very large. Here we present a simple multi-party distributed problem for which the inputs and outputs consist of a single bit per player, and we present a perfect quantum protocol for it. We prove that no classical protocol can succeed with a probability that differs from 1/2 by more than a fraction that is exponentially small in the number of players. This could be used to circumvent the detection loophole in experimental tests of nonlocality.

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arXiv2003

Quantum Arithmetic on Galois Fields

In this paper we discuss the problem of performing elementary finite field arithmetic on a quantum computer. Of particular interest, is the controlled-multiplication operation, which is the only group-specific operation in Shor's algorithms for factoring and solving the Discrete Log Problem. We describe how to build quantum circuits for performing this operation on the generic Galois fields GF($p^k$), as well as the boundary cases GF($p$) and GF($2^k$). We give the detailed size, width and depth complexity of such circuits, which ultimately will allow us to obtain detailed upper bounds on the amount of quantum resources needed to solve instances of the DLP on such fields.

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arXiv2001

Quantum Communication Complexity (A Survey)

Can quantum communication be more efficient than its classical counterpart? Holevo's theorem rules out the possibility of communicating more than n bits of classical information by the transmission of n quantum bits --- unless the two parties are entangled, in which case twice as many classical bits can be communicated but no more. In apparent contradiction, there are distributed computational tasks for which quantum communication cannot be simulated efficiently by classical means. In extreme cases, the effect of transmitting quantum bits cannot be achieved classically short of transmitting an exponentially larger number of bits. In a similar vein, can entanglement be used to save on classical communication? It is well known that entanglement on its own is useless for the transmission of information. Yet, there are distributed tasks that cannot be accomplished at all in a classical world when communication is not allowed, but that become possible if the non-communicating parties share prior entanglement. This leads to the question of how expensive it is, in terms of classical communication, to provide an exact simulation of the spooky power of entanglement.

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arXiv2000

Quantum Amplitude Amplification and Estimation

Consider a Boolean function $χ: X \to \{0,1\}$ that partitions set $X$ between its good and bad elements, where $x$ is good if $χ(x)=1$ and bad otherwise. Consider also a quantum algorithm $\mathcal A$ such that $A |0\rangle= \sum_{x\in X} α_x |x\rangle$ is a quantum superposition of the elements of $X$, and let $a$ denote the probability that a good element is produced if $A |0\rangle$ is measured. If we repeat the process of running $A$, measuring the output, and using $χ$ to check the validity of the result, we shall expect to repeat $1/a$ times on the average before a solution is found. *Amplitude amplification* is a process that allows to find a good $x$ after an expected number of applications of $A$ and its inverse which is proportional to $1/\sqrt{a}$, assuming algorithm $A$ makes no measurements. This is a generalization of Grover's searching algorithm in which $A$ was restricted to producing an equal superposition of all members of $X$ and we had a promise that a single $x$ existed such that $χ(x)=1$. Our algorithm works whether or not the value of $a$ is known ahead of time. In case the value of $a$ is known, we can find a good $x$ after a number of applications of $A$ and its inverse which is proportional to $1/\sqrt{a}$ even in the worst case. We show that this quadratic speedup can also be obtained for a large family of search problems for which good classical heuristics exist. Finally, as our main result, we combine ideas from Grover's and Shor's quantum algorithms to perform amplitude estimation, a process that allows to estimate the value of $a$. We apply amplitude estimation to the problem of *approximate counting*, in which we wish to estimate the number of $x\in X$ such that $χ(x)=1$. We obtain optimal quantum algorithms in a variety of settings.

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arXiv1999

Security Aspects of Practical Quantum Cryptography

The use of quantum bits (qubits) in cryptography holds the promise of secure cryptographic quantum key distribution schemes. Unfortunately, the implemented schemes can be totally insecure. We provide a thorough investigation of security issues for practical quantum key distribution, taking into account channel losses, a realistic detection process, and modifications of the ``qubits'' sent from the sender to the receiver. We first show that even quantum key distribution with perfect qubits cannot be achieved over long distances when fixed channel losses and fixed dark count errors are taken into account. Then we show that existing experimental schemes (based on ``weak-pulse'') are usually totally insecure. Finally we show that parametric downconversion offers enhanced performance compared to its weak coherent pulse counterpart.

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arXiv1999

Quantum cryptography via parametric downconversion

The use of quantum bits (qubits) in cryptography holds the promise of secure cryptographic quantum key distribution schemes. It is based usually on single-photon polarization states. Unfortunately, the implemented ``qubits'' in the usual weak pulse experiments are not true two-level systems, and quantum key distribution based on these imperfect qubits is totally insecure in the presence of high (realistic) loss rate. In this work, we investigate another potential implementation: qubits generated using a process of parametric downconversion. We find that, to first (two-photon) and second (four-photon) order in the parametric downconversion small parameter, this implementation of quantum key distribution is equivalent to the theoretical version. Once realistic measurements are taken into account, quantum key distribution based on parametric downconversion suffers also from sensitivity to extremely high (nonrealistic) losses. By choosing the small parameter of the process according to the loss rates, both implementations of quantum key distribution can in principle become secure against the attack studied in this paper. However, adjusting the small parameter to the required levels seems to be impractical in the weak pulse process. On the other hand, this can easily be done in the parametric downconversion process, making it a much more promising implementation.

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