Piotr Badziag

University of Bristol, Bristol, England, United Kingdom

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Publications (18)58.91 Total impact

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    ABSTRACT: We report on an experimental test of classical and quantum dimension. We have used a dimension witness that can distinguish between quantum and classical systems of dimensions two, three, and four and performed the experiment for all five cases. The witness we have chosen is a base of semi-device-independent cryptographic and randomness expansion protocols. Therefore, the part of the experiment in which qubits were used is a realization of these protocols. In our work we also present an analytic method for finding the maximum quantum value of the witness along with corresponding measurements and preparations. This method is quite general and can be applied to any linear dimension witness.
    03/2014; 112(14).
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    ABSTRACT: Kochen-Specker (KS) theorem is a fundamental result that shows that quantum theory cannot be explained if measurement results were predefined. Its proof requires a set of yes-no questions each of them in several contexts. The original KS proof required 132 contexts and, so far, the simplest known proof requires 9 contexts. Here we present a proof with only 7 contexts and show that, under some assumptions, this is the smallest number of contexts possible in a KS proof. Finally, we use our 7-context proof to derive an experimentally testable state-independent noncontextuality inequality.
    08/2013;
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    ABSTRACT: A fundamental resource in any communication and computation task is the amount of information that can be transmitted and processed. Information encoded in a classical system is limited by the dimension d_c of the system, i.e., the number of distinguishable states. A system with d_c=2^n classical states can carry n bits of classical information. Information encoded in a quantum system is limited by the dimension d_q of the Hilbert space of the system, i.e., the number of perfectly distinguishable quantum states. A system with d_q=2^n perfectly distinguishable quantum states can carry n qubits of quantum information. Physical systems of higher dimensions may enable more efficient and powerful information processing protocols. The dimension is fundamental in quantum cryptography and random number generation, where the security of many schemes crucially relies on the system's dimension. From a fundamental perspective, the dimension can be used to quantify the non-classicality of correlations, since classical simulation of correlations produced by a quantum system of dimension d_q may require a classical system of dimension d_c >> d_q. For all these reasons, a fundamental problem in information theory is to assess the (classical or quantum) dimension of a physical system in a "device-independent" scenario, i.e., without referring to the system's specifications, which may be under control of a dishonest supplier, eavesdropper or saboteur. In this contribution we report experiments realizing this goal for systems emitted by a black box. Our results indicate that dimension witnesses utilized in the experiments may become a powerful tool for testing systems provided by unreliable sources.
    Nature Physics 11/2011; · 19.35 Impact Factor
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    ABSTRACT: Which is the simplest logical structure for which there is quantum nonlocality? We show that there are only three bipartite Bell inequalities with quantum violation associated with the simplest graph of relationships of exclusivity with a quantum-classical gap. These are the most elementary logical Bell inequalities. We show that the quantum violation of some well-known Bell inequalities is related to them. We test the three Bell inequalities with pairs of polarization-entangled photons and report violations in good agreement with the quantum predictions. Unlike other experiments testing noncontextuality inequalities with pentagonal exclusivity, the ones reported here are free of the compatibility loophole.
    Physical Review A 06/2011; 87(1). · 3.04 Impact Factor
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    ABSTRACT: Every nontrivial Bell inequality can be associated to a graph with some special properties. The simplest of these graphs is the pentagon. In this sense, any Bell inequality associated to a pentagon can be regarded as elementary. We show that there are three of them: one is a primitive Bell inequality inside the Clauser-Horne-Shimony-Holt inequality and, surprisingly, it is not maximally violated by maximally entangled states. The other two are maximally violated by maximally entangled states and are related to the Clauser-Horne inequality and the I3322 inequality, respectively. We report experimental violations of the three inequalities with pairs of photons entangled in polarization.
    01/2011;
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    ABSTRACT: We show that the state-independent violation of inequalities for noncontextual hidden variable theories introduced in [Phys. Rev. Lett. 101, 210401 (2008)] is universal, i.e., occurs for any quantum mechanical system in which noncontextuality is meaningful. We describe a method to obtain state-independent violations for any system of dimension d> or =3. This universality proves that, according to quantum mechanics, there are no "classical" states.
    Physical Review Letters 07/2009; 103(5):050401. · 7.73 Impact Factor
  • Yu-Chun Wu, Piotr Badziag, Marek Żukowski
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    ABSTRACT: We construct a simple algorithm to generate any Clauser-Horne-Shimony-Holt- (CHSH-) type Bell inequality involving a party with two local binary measurements from two CHSH-type inequalities without this party. The algorithm readily generalizes to situations where the additional observer uses three measurement settings. There, each inequality involving the additional party is constructed from three inequalities with this party excluded. With this generalization at hand, we construct and analyze a class of symmetric inequalities for four observers and three experimental settings per observer.
    Physical Review A 02/2009; 79(2). · 3.04 Impact Factor
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    Yu-Chun Wu, Piotr Badziag, Marek Zukowski
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    ABSTRACT: We construct a simple algorithm to generate any CHSH type Bell inequality involving a party with two local binary measurements from two CHSH type inequalities without this party. The algorithm readily generalizes to situations, where the additional observer uses three measurement settings. There, each inequality involving the additional party is constructed from three inequalities with this party excluded. With this generalization at hand, we construct and analyze new symmetric inequalities for four observers and three experimental settings per observer. Comment: 8 pages, no figure
    10/2008;
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    ABSTRACT: A simple geometrical criterion gives experimentally friendly sufficient conditions for entanglement. Its generalization gives a necessary and sufficient condition. It is linked with a family of entanglement identifiers, which is strictly richer than the family of entanglement witnesses.
    Physical Review Letters 04/2008; 100(14):140403. · 7.73 Impact Factor
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    ABSTRACT: We describe a method of extending Bell inequalities from $n$ to $n+1$ parties and formulate sufficient conditions for our method to produce tight inequalities from tight inequalities. The method is non trivial in the sense that the inequalities produced by it, when applied to entangled quantum states may be violated stronger than the original inequalities. In other words, the method is capable of generating inequalities which are more powerfull indicators of non-classical correlations than the original inequalities.
    Physical Review A 01/2008; · 3.04 Impact Factor
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    ABSTRACT: We present an intuitive geometrical entanglement criterion. It allows formulation of simple and experimentally friendly sufficient conditions for entanglement. The conditions are illustrated with several examples. Moreover, a generalization of our approach is a necessary and sufficient separability condition. It can be associated with a family of entanglement identifiers, which is strictly richer than the family of entanglement witnesses.
    12/2007;
  • Piotr Badziag, Marek Zukowski
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    ABSTRACT: Derivation of the full set of Bell inequalities involving correlation functions, for two parties, with binary observables, and N possible local settings is not as easy as it seemed. The proof of v1 is wrong. Additionaly one can find a counterexample, which will be presented soon. Thus our thesis is dead. Still the series of Bell inequalities discussed in the manuscript (v1) form a necessary condition for local realism, and are tight. They are tight and complete (sufficient) only for N=3 settings per observer (as shown in quant-ph/0611086, fortunately using an entirely different approach).
    05/2007;
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    ABSTRACT: We present a method to derive explicit forms of tight correlation function Bell inequalities for three systems and dichotomic observables, which involve three settings for each observer. We also give sufficient conditions for quantum predictions to satisfy the new inequalities.
    Physical Review A 12/2006; · 3.04 Impact Factor
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    ABSTRACT: It is pointed out that separability problem for arbitrary multi-partite states can be fully solved by a finite size, elementary recursive algorithm. In the worse case scenario, the underlying numerical procedure, may grow doubly exponentially with the state's rank. Nevertheless, we argue that for generic states, analysis of concurrence matrices essentially reduces the task of solving separability problem in $m \times n$ dimensions to solving a set of linear equations in about $\binom{mn+D-1}{D}$ variables, where $D$ decreases with $mn$ and for large $mn$ it should not exceed 4. Moreover, the same method is also applicable to multipartite states where it is at least equally efficient.
    05/2005;
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    ABSTRACT: We investigate measurements of bipartite ensembles restricted to local operations and classical communication and find a universal Holevo-like upper bound on the locally accessible information. We analyze our bound and exhibit a class of states which saturate it. Finally, we link the bound to the problem of quantification of the nonlocality of the operations necessary to extract locally inaccessible information.
    Physical Review Letters 10/2003; 91(11):117901. · 7.73 Impact Factor
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    ABSTRACT: We argue that a complete characterisation of quantum correlations in bipartite systems of many dimensions may require a quantity which, even for pure states, does not reduce to a single number. Subsequently, we introduce multi-dimensional generalizations of concurrence and find evidence that they may provide useful tools for the analysis of quantum correlations in mixed bipartite states. We also introudce {\it biconcurrence} that leads to a necessary and sufficient condition for separability. Comment: RevTeX 7 pages
    Journal of Modern Optics 07/2001; · 1.16 Impact Factor
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    ABSTRACT: We show how an interaction with the environment can enhance fidelity of quantum teleportation. To this end, we present examples of states which cannot be made useful for teleportation by any local unitary transformations; nevertheless, after being subjected to a dissipative interaction with the local environment, the states allow for teleportation with genuinely quantum fidelity. The surprising fact here is that the necessary interaction does not require any intelligent action from the parties sharing the states. In passing, we produce some general results regarding optimization of teleportation fidelity by local action. We show that bistochastic processes cannot improve fidelity of two-qubit states. We also show that in order to have their fidelity improvable by a local process, the bipartite states must violate the so-called reduction criterion of separability. Comment: 9 pages, Revtex
    Physical Review A 12/1999; · 3.04 Impact Factor
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Publication Stats

205 Citations
58.91 Total Impact Points

Institutions

  • 2014
    • University of Bristol
      • School of Mathematics
      Bristol, England, United Kingdom
  • 2008–2009
    • University of Gdansk
      • Department of Theoretical Physics and Astrophysics
      Gdańsk, Pomeranian Voivodeship, Poland
    • Stockholm University
      • Department of Physics
      Stockholm, Stockholm, Sweden
  • 2003
    • Mälardalens högskola i Eskilstuna och Västerås
      Västerås, Västmanland, Sweden