Máté Farkas
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Máté Farkas has a total of 53 co-authors. Here are the top co-authors by number of shared publications:
- Arindam Mitra
Optics and Quantum Information Group, The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai 600113, India
4 shared publications Antonio Acín
ICFO
3 shared publications- Jędrzej Kaniewski
Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
3 shared publications - Antonio Acín
Institut de Ciencies Fotoniques
2 shared publications - Armin Tavakoli
Lund University
2 shared publications - Ashwin Nayak
Department of Combinatorics and Optimization, and Institute for Quantum Computing University of Waterloo 200 University Ave. W. N2L 3G1 Waterloo ON Canada
2 shared publications
Latest Publications
- 13 January 2026
- Published by Springer Nature in Nature Physics
- Vol. 22 (2) , 319-324
Maximal device-independent randomness in every dimension
- 13 January 2026
- Published by Springer Nature in Nature Physics
- Vol. 22 (2) , 319-324
Maximal device-independent randomness in every dimension
- Open Access
Extending quantum correlations to arbitrary distances via parallel repetition of routed Bell tests
Applications such as Device-Independent Quantum Key Distribution (DIQKD) require loophole-free certification of long-distance quantum correlations. However, these distances remain severely constrained by detector inefficiencies and unavoidable transmission losses. To overcome this challenge, we consider parallel repetitions of the recently proposed routed Bell experiments, where transmissions from the source are actively directed either to a nearby or a distant measurement device. We analytically show that the threshold detection efficiency of the distant device--needed to certify non-jointly-measurable measurements, a prerequisite of secure DIQKD--decreases exponentially, optimally, and robustly, following $η^*=1/2^N$, with the number $N$ of parallel repetitions.Open AccessExtending quantum correlations to arbitrary distances via parallel repetition of routed Bell tests
Applications such as Device-Independent Quantum Key Distribution (DIQKD) require loophole-free certification of long-distance quantum correlations. However, these distances remain severely constrained by detector inefficiencies and unavoidable transmission losses. To overcome this challenge, we consider parallel repetitions of the recently proposed routed Bell experiments, where transmissions from the source are actively directed either to a nearby or a distant measurement device. We analytically show that the threshold detection efficiency of the distant device--needed to certify non-jointly-measurable measurements, a prerequisite of secure DIQKD--decreases exponentially, optimally, and robustly, following $η^*=1/2^N$, with the number $N$ of parallel repetitions. - Open Access
- 25 February 2025
- Published by Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften in Quantum
- Vol. 9, 1643
Simple and general bounds on quantum random access codes
Random access codes are a type of communication task that is widely used in quantum information science. The optimal average success probability that can be achieved through classical strategies is known for any random access code. However, only a few cases are solved exactly for quantum random access codes. In this paper, we provide bounds for the fully general setting of n independent variables, each selected from a d-dimensional classical alphabet and encoded in a -dimensional quantum system subject to an arbitrary quantum measurement. The bound recovers the exactly known special cases, and we demonstrate numerically that even though the bound is not tight overall, it can still yield a good approximation.- 25 February 2025
- Published by Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften in Quantum
- Vol. 9, 1643
Open AccessSimple and general bounds on quantum random access codes
Random access codes are a type of communication task that is widely used in quantum information science. The optimal average success probability that can be achieved through classical strategies is known for any random access code. However, only a few cases are solved exactly for quantum random access codes. In this paper, we provide bounds for the fully general setting of n independent variables, each selected from a d-dimensional classical alphabet and encoded in a -dimensional quantum system subject to an arbitrary quantum measurement. The bound recovers the exactly known special cases, and we demonstrate numerically that even though the bound is not tight overall, it can still yield a good approximation. - Open Access
Maximal device-independent randomness in every dimension
Random numbers are used in a wide range of sciences. In many applications, generating unpredictable private random numbers is indispensable. Device-independent quantum random number generation is a framework that makes use of the intrinsic randomness of quantum processes to generate numbers that are fundamentally unpredictable according to our current understanding of physics. While device-independent quantum random number generation is an exceptional theoretical feat, the difficulty of controlling quantum systems makes it challenging to carry out in practice. It is therefore desirable to harness the full power of the quantum degrees of freedom (the dimension) that one can control. It is known that no more than $2 \log(d)$ bits of private device-independent randomness can be extracted from a quantum system of local dimension $d$. In this paper we demonstrate that this bound can be achieved for all dimensions $d$ by providing a family of explicit protocols. In order to obtain our result, we develop new certification techniques that can be of wider interest in device-independent applications for scenarios in which complete certification ('self-testing') is impossible or impractical.Open AccessMaximal device-independent randomness in every dimension
Random numbers are used in a wide range of sciences. In many applications, generating unpredictable private random numbers is indispensable. Device-independent quantum random number generation is a framework that makes use of the intrinsic randomness of quantum processes to generate numbers that are fundamentally unpredictable according to our current understanding of physics. While device-independent quantum random number generation is an exceptional theoretical feat, the difficulty of controlling quantum systems makes it challenging to carry out in practice. It is therefore desirable to harness the full power of the quantum degrees of freedom (the dimension) that one can control. It is known that no more than $2 \log(d)$ bits of private device-independent randomness can be extracted from a quantum system of local dimension $d$. In this paper we demonstrate that this bound can be achieved for all dimensions $d$ by providing a family of explicit protocols. In order to obtain our result, we develop new certification techniques that can be of wider interest in device-independent applications for scenarios in which complete certification ('self-testing') is impossible or impractical. - 8 July 2024
- Published by American Physical Society (APS) in Physical Review A
- Vol. 110 (1) , L010403
Maximal intrinsic randomness of a quantum state
One of the most counterintuitive aspects of quantum theory is its claim that there is “intrinsic” randomness in the physical world. Quantum information science has greatly progressed in the study of intrinsic, or secret, quantum randomness in the past decade. With much emphasis on device-independent and semi-device-independent bounds, one of the most basic questions has escaped attention: how much intrinsic randomness can be extracted from a given state , and what measurements achieve this bound? We answer this question for three different randomness quantifiers: the conditional min-entropy, the conditional von Neumann entropy, and the conditional max-entropy. For the first, we solve the min-max problem of finding the projective measurement that minimizes the maximal guessing probability of an eavesdropper. The result is that one can guarantee an amount of conditional min-entropy with by performing suitable projective measurements. For the conditional von Neumann entropy, we find that the maximal value is , with the von Neumann entropy of , while for the conditional max-entropy, we find the maximal value , where is the largest eigenvalue of . Optimal values for , and are achieved by measuring in any basis that is unbiased with respect to the eigenbasis of , as well as by other, less intuitive, measurements.- 8 July 2024
- Published by American Physical Society (APS) in Physical Review A
- Vol. 110 (1) , L010403
Maximal intrinsic randomness of a quantum state
One of the most counterintuitive aspects of quantum theory is its claim that there is “intrinsic” randomness in the physical world. Quantum information science has greatly progressed in the study of intrinsic, or secret, quantum randomness in the past decade. With much emphasis on device-independent and semi-device-independent bounds, one of the most basic questions has escaped attention: how much intrinsic randomness can be extracted from a given state , and what measurements achieve this bound? We answer this question for three different randomness quantifiers: the conditional min-entropy, the conditional von Neumann entropy, and the conditional max-entropy. For the first, we solve the min-max problem of finding the projective measurement that minimizes the maximal guessing probability of an eavesdropper. The result is that one can guarantee an amount of conditional min-entropy with by performing suitable projective measurements. For the conditional von Neumann entropy, we find that the maximal value is , with the von Neumann entropy of , while for the conditional max-entropy, we find the maximal value , where is the largest eigenvalue of . Optimal values for , and are achieved by measuring in any basis that is unbiased with respect to the eigenbasis of , as well as by other, less intuitive, measurements.- Open Access
- 22 May 2024
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 132 (21) , 210803
Unbounded Device-Independent Quantum Key Rates from Arbitrarily Small Nonlocality
Device-independent quantum key distribution allows for proving the security of a shared cryptographic key between two distant parties with potentially untrusted devices. The security proof is based on the measurement outcome statistics (correlation) of a Bell experiment, and security is guaranteed by the laws of quantum theory. While it is known that the observed correlation must be Bell nonlocal in order to prove security, recent results show that Bell nonlocality is in general not sufficient for standard device-independent quantum key distribution. In this work, we show that conversely, there is no lower bound on the amount of nonlocality that is sufficient for device-independent quantum key distribution. Even more so, we show that from certain correlations that exhibit arbitrarily small nonlocality, one can still extract unbounded device-independent key rates. Therefore, a quantitative relation between device-independent key rates and Bell nonlocality cannot be drawn in general. Our main technique comprises a rigorous connection between self-testing and device-independent quantum key distribution, applied to a recently discovered family of Bell inequalities with arbitrarily many measurement outcomes. Published by the American Physical Society 2024
- 22 May 2024
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 132 (21) , 210803
Open AccessUnbounded Device-Independent Quantum Key Rates from Arbitrarily Small Nonlocality
Device-independent quantum key distribution allows for proving the security of a shared cryptographic key between two distant parties with potentially untrusted devices. The security proof is based on the measurement outcome statistics (correlation) of a Bell experiment, and security is guaranteed by the laws of quantum theory. While it is known that the observed correlation must be Bell nonlocal in order to prove security, recent results show that Bell nonlocality is in general not sufficient for standard device-independent quantum key distribution. In this work, we show that conversely, there is no lower bound on the amount of nonlocality that is sufficient for device-independent quantum key distribution. Even more so, we show that from certain correlations that exhibit arbitrarily small nonlocality, one can still extract unbounded device-independent key rates. Therefore, a quantitative relation between device-independent key rates and Bell nonlocality cannot be drawn in general. Our main technique comprises a rigorous connection between self-testing and device-independent quantum key distribution, applied to a recently discovered family of Bell inequalities with arbitrarily many measurement outcomes. Published by the American Physical Society 2024
- Open Access
An invertible map between Bell non-local and contextuality scenarios
We present an invertible map between correlations in any bipartite Bell scenario and behaviours in a family of contextuality scenarios. The map takes local, quantum and non-signalling correlations to non-contextual, quantum and contextual behaviours, respectively. Consequently, we find that the membership problem of the set of quantum contextual behaviours is undecidable, the set cannot be fully realised via finite dimensional quantum systems and is not closed. Finally, we show that neither this set nor its closure is the limit of a sequence of computable supersets, due to the result MIP*=RE.
Open AccessAn invertible map between Bell non-local and contextuality scenarios
We present an invertible map between correlations in any bipartite Bell scenario and behaviours in a family of contextuality scenarios. The map takes local, quantum and non-signalling correlations to non-contextual, quantum and contextual behaviours, respectively. Consequently, we find that the membership problem of the set of quantum contextual behaviours is undecidable, the set cannot be fully realised via finite dimensional quantum systems and is not closed. Finally, we show that neither this set nor its closure is the limit of a sequence of computable supersets, due to the result MIP*=RE.
- 27 November 2023
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 131 (22) , 220202
Invertible Map between Bell Nonlocal and Contextuality Scenarios
We present an invertible map between correlations in any bipartite Bell scenario and behaviors in a family of contextuality scenarios. The map takes local, quantum, and no-signaling correlations to noncontextual, quantum, and contextual behaviors, respectively. Consequently, we find that the membership problem of the set of quantum contextual behaviors is undecidable, the set cannot be fully realized via finite dimensional quantum systems and is not closed. Finally, we show that neither this set nor its closure is the limit of a sequence of computable supersets due to the result .- 27 November 2023
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 131 (22) , 220202
Invertible Map between Bell Nonlocal and Contextuality Scenarios
We present an invertible map between correlations in any bipartite Bell scenario and behaviors in a family of contextuality scenarios. The map takes local, quantum, and no-signaling correlations to noncontextual, quantum, and contextual behaviors, respectively. Consequently, we find that the membership problem of the set of quantum contextual behaviors is undecidable, the set cannot be fully realized via finite dimensional quantum systems and is not closed. Finally, we show that neither this set nor its closure is the limit of a sequence of computable supersets due to the result .- Open Access
Unbounded device-independent quantum key rates from arbitrarily small non-locality
Device-independent quantum key distribution allows for proving the security of a shared cryptographic key between two distant parties with potentially untrusted devices. The security proof is based on the measurement outcome statistics (correlation) of a Bell experiment, and security is guaranteed by the laws of quantum theory. While it is known that the observed correlation must be Bell non-local in order to prove security, recent results show that Bell non-locality is in general not sufficient for standard device-independent quantum key distribution. In this work, we show that conversely, there is no lower bound on the amount of non-locality that is sufficient for device-independent quantum key distribution. Even more so, we show that from certain correlations that exhibit arbitrarily small non-locality, one can still extract unbounded device-independent key rates. Therefore, a quantitative relation between device-independent key rates and Bell non-locality cannot be drawn in general. Our main technique comprises a rigorous connection between self-testing and device-independent quantum key distribution, applied to a recently discovered family of Bell inequalities with arbitrarily many measurement outcomes.
Open AccessUnbounded device-independent quantum key rates from arbitrarily small non-locality
Device-independent quantum key distribution allows for proving the security of a shared cryptographic key between two distant parties with potentially untrusted devices. The security proof is based on the measurement outcome statistics (correlation) of a Bell experiment, and security is guaranteed by the laws of quantum theory. While it is known that the observed correlation must be Bell non-local in order to prove security, recent results show that Bell non-locality is in general not sufficient for standard device-independent quantum key distribution. In this work, we show that conversely, there is no lower bound on the amount of non-locality that is sufficient for device-independent quantum key distribution. Even more so, we show that from certain correlations that exhibit arbitrarily small non-locality, one can still extract unbounded device-independent key rates. Therefore, a quantitative relation between device-independent key rates and Bell non-locality cannot be drawn in general. Our main technique comprises a rigorous connection between self-testing and device-independent quantum key distribution, applied to a recently discovered family of Bell inequalities with arbitrarily many measurement outcomes.
- Open Access
Mutually Unbiased Measurements, Hadamard Matrices, and Superdense Coding
Mutually unbiased bases (MUBs) are highly symmetric bases on complex Hilbert spaces, and the corresponding rank-1 projective measurements are ubiquitous in quantum information theory. In this work, we study a recently introduced generalization of MUBs called mutually unbiased measurements (MUMs). These measurements inherit the essential property of complementarity from MUBs, but the Hilbert space dimension is no longer required to match the number of outcomes. This operational complementarity property renders MUMs highly useful for device-independent quantum information processing. It has been shown that MUMs are strictly more general than MUBs. In this work we provide a complete proof of the characterization of MUMs that are direct sums of MUBs. We then proceed to construct new examples of MUMs that are not direct sums of MUBs. A crucial technical tool for these construction is a correspondence with quaternionic Hadamard matrices, which allows us to map known examples of such matrices to MUMs that are not direct sums of MUBs. Furthermore, we show that -- in stark contrast with MUBs -- the number of MUMs for a fixed outcome number is unbounded. Next, we focus on the use of MUMs in quantum communication. We demonstrate how any pair of MUMs with d outcomes defines a d-dimensional superdense coding protocol. Using MUMs that are not direct sums of MUBs, we disprove a recent conjecture due to Nayak and Yuen on the rigidity of superdense coding for infinitely many dimensions. The superdense coding protocols arising in the refutation reveal how shared entanglement may be used in a manner heretofore unknown.
Open AccessMutually Unbiased Measurements, Hadamard Matrices, and Superdense Coding
Mutually unbiased bases (MUBs) are highly symmetric bases on complex Hilbert spaces, and the corresponding rank-1 projective measurements are ubiquitous in quantum information theory. In this work, we study a recently introduced generalization of MUBs called mutually unbiased measurements (MUMs). These measurements inherit the essential property of complementarity from MUBs, but the Hilbert space dimension is no longer required to match the number of outcomes. This operational complementarity property renders MUMs highly useful for device-independent quantum information processing. It has been shown that MUMs are strictly more general than MUBs. In this work we provide a complete proof of the characterization of MUMs that are direct sums of MUBs. We then proceed to construct new examples of MUMs that are not direct sums of MUBs. A crucial technical tool for these construction is a correspondence with quaternionic Hadamard matrices, which allows us to map known examples of such matrices to MUMs that are not direct sums of MUBs. Furthermore, we show that -- in stark contrast with MUBs -- the number of MUMs for a fixed outcome number is unbounded. Next, we focus on the use of MUMs in quantum communication. We demonstrate how any pair of MUMs with d outcomes defines a d-dimensional superdense coding protocol. Using MUMs that are not direct sums of MUBs, we disprove a recent conjecture due to Nayak and Yuen on the rigidity of superdense coding for infinitely many dimensions. The superdense coding protocols arising in the refutation reveal how shared entanglement may be used in a manner heretofore unknown.