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Máté Farkas

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Arkady Berenstein

University of Oregon

Sergey Filippov

Hector Figueroa

Duoc Uc

Gelo Noel Tabia

University of Tartu

Francesco Giuseppe Russo

Jean-Yves Thibon

Université Paris-Est Marne-la-Vallée

Pantelis Damianou

University of Cyprus

Ronin Institute

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Papers by Máté Farkas

Characterizing and quantifying the incompatibility of quantum instruments

Physical Review A

Incompatibility of quantum devices is one of the cornerstones of quantum theory, and the incompat... more Incompatibility of quantum devices is one of the cornerstones of quantum theory, and the incompatibility of quantum measurements and channels has been linked to quantum advantage in certain information-theoretic tasks. In this work, we focus on the less well explored question of the incompatibility of quantum instruments, that is, devices that describe the measurement process in its entirety, accounting for both the classical measurement outcome and the quantum postmeasurement state. In particular, we focus on the recently introduced notion of parallel compatibility of instruments, which has been argued to be a natural notion of instrument compatibility. We introduce, in a manner similar to the case of measurements and channels, the incompatibility robustness of quantum instruments and derive universal bounds on it. We then prove that postprocessing of quantum instruments is a free operation for parallel compatibility. Last, we provide families of instruments for which our bounds are tight and families of compatible indecomposable instruments.

Three numerical approaches to find mutually unbiased bases using Bell inequalities

Quantum

Mutually unbiased bases correspond to highly useful pairs of measurements in quantum information ... more Mutually unbiased bases correspond to highly useful pairs of measurements in quantum information theory. In the smallest composite dimension, six, it is known that between three and seven mutually unbiased bases exist, with a decades-old conjecture, known as Zauner's conjecture, stating that there exist at most three. Here we tackle Zauner's conjecture numerically through the construction of Bell inequalities for every pair of integers n,d≥2 that can be maximally violated in dimension d if and only if n MUBs exist in that dimension. Hence we turn Zauner's conjecture into an optimisation problem, which we address by means of three numerical methods: see-saw optimisation, non-linear semidefinite programming and Monte Carlo techniques. All three methods correctly identify the known cases in low dimensions and all suggest that there do not exist four mutually unbiased bases in dimension six, with all finding the same bases that numerically optimise the corresponding Bell ine...

Upper Bounds on Key Rates in Device-Independent Quantum Key Distribution Based on Convex-Combination Attacks

Quantum 2.0 Conference and Exhibition

We provide an efficient, generic tool for upper-bounding key rates in device-independent quantum ... more

Self-Testing Mutually Unbiased Bases in Higher Dimensions with Space-Division Multiplexing Optical Fiber Technology

Physical Review Applied

Recently in Ref. [25], a method has been proposed for self-testing high-dimensional measurements ... more Recently in Ref. [25], a method has been proposed for self-testing high-dimensional measurements corresponding to mutually unbiased bases (MUBs) in the prepareand-measure scenario, under the dimension assumption. MUBs constitute a particularly useful family of quantum measurements, with myriad applications in quantum information. Among other tasks, they optimise state determination [26, 27], generate maximal amount of randomness [28], and give rise to secure cryptographic protocols

Mutually Unbiased Measurements, Hadamard Matrices, and Superdense Coding

arXiv (Cornell University), Apr 25, 2022

Mutually unbiased bases (MUBs) are highly symmetric bases on complex Hilbert spaces, and the corr... more 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.

Semi-device-independent random number generation with flexible assumptions

npj Quantum Information, 2021

Our ability to trust that a random number is truly random is essential for fields as diverse as c... more Our ability to trust that a random number is truly random is essential for fields as diverse as cryptography and fundamental tests of quantum mechanics. Existing solutions both come with drawbacks—device-independent quantum random number generators (QRNGs) are highly impractical and standard semi-device-independent QRNGs are limited to a specific physical implementation and level of trust. Here we propose a framework for semi-device-independent randomness certification, using a source of trusted vacuum in the form of a signal shutter. It employs a flexible set of assumptions and levels of trust, allowing it to be applied in a wide range of physical scenarios involving both quantum and classical entropy sources. We experimentally demonstrate our protocol with a photonic setup and generate secure random bits under three different assumptions with varying degrees of security and resulting data rates.

$n$-fold unbiased bases: an extension of the MUB condition

I introduce a new notion, that extends the mutually unbiased bases (MUB) conditons to more than t... more I introduce a new notion, that extends the mutually unbiased bases (MUB) conditons to more than two bases. These, I call the nUB conditions, and the corresponding bases n-fold unbiased. They naturally appear while optimizing generic n-to-one quantum random access code (QRAC) strategies. While their existence in general dimensions is an open question, they nevertheless give close-to-tight upper bounds on QRAC success probabilities, and raise fundamental questions about the geometry of quantum states.

Robust self-test of high-dimension mutually unbiased bases with commercial multi-core fiber

2020 IEEE Photonics Society Summer Topicals Meeting Series (SUM), 2020

We perform a robust self-testing certification of two four-dimensional mutually unbiased bases in... more We perform a robust self-testing certification of two four-dimensional mutually unbiased bases in a high-quality optical configuration built with commercial multicore fiber. We also evaluate the randomness produced. Our results represent an important step towards practical self-testing in high-dimensional quantum information technologies.

Characterising and bounding the set of quantum behaviours in contextuality scenarios

Quantum, 2021

The predictions of quantum theory resist generalised noncontextual explanations. In addition to t... more The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum advantage in communication and information processing. In the first part of this work, we formally define contextuality scenarios via prepare-and-measure experiments, along with the polytope of general contextual behaviours containing the set of quantum contextual behaviours. This framework allows us to recover several properties of set of quantum behaviours in these scenarios, including contextuality scenarios and associated noncontextuality inequalities that require for their violation the individual quantum preparation and measurement procedures to be mixed states and unsharp measurements. With the framework in place, we formulate novel semidefinite programming relaxations for bounding these sets of quantum contextual behaviours. Most significantly, ...

Bell Nonlocality Is Not Sufficient for the Security of Standard Device-Independent Quantum Key Distribution Protocols

Physical Review Letters, 2021

Qudit homological product codes

Quantum Information and Computation, 2017

In this note we show that the random homological product code construction of Bravyi and Hastings... more

Quantum error-correction codes and absolutely maximally entangled states

Physical Review A, 2020

For every stabiliser N-qudit absolutely maximally entangled state, we present a method for determ... more For every stabiliser N-qudit absolutely maximally entangled state, we present a method for determining the stabiliser generators and logical operators of a corresponding quantum error correction code. These codes encode k qudits into N − k qudits, with k ≤ N/2 , where the local dimension d is prime. We use these methods to analyse the concatenation of such quantum codes and link this procedure to entanglement swapping. Using our techniques, we investigate the spread of quantum information on a tensor network code formerly used as a toy model for the AdS/CFT correspondence. In this network, we show how corrections arise to the Ryu-Takayanagi formula in the case of entangled input state, and that the bound on the entanglement entropy of the boundary state is saturated for absolutely maximally entangled input states.

The MRCC program system: Accurate quantum chemistry from water to proteins

The Journal of Chemical Physics, 2020

Incompatibility robustness of quantum measurements: a unified framework

New Journal of Physics, 2019

In quantum mechanics performing a measurement is an invasive process which generally disturbs the... more In quantum mechanics performing a measurement is an invasive process which generally disturbs the system. Due to this phenomenon, there exist incompatible quantum measurements, i.e. measurements that cannot be simultaneously performed on a single copy of the system. It is then natural to ask what the most incompatible quantum measurements are. To answer this question, several measures have been proposed to quantify how incompatible a set of measurements is, however their properties are not well-understood. In this work, we develop a general framework that encompasses all the commonly used measures of incompatibility based on robustness to noise. Moreover, we propose several conditions that a measure of incompatibility should satisfy, and investigate whether the existing measures comply with them. We find that some of the widely used measures do not fulfil these basic requirements. We also show that when looking for the most incompatible pairs of measurements, we obtain different ans...

Self-testing mutually unbiased bases in the prepare-and-measure scenario

Physical Review A, 2019

Certifying an Irreducible 1024-Dimensional Photonic State Using Refined Dimension Witnesses

Physical review letters, Jan 8, 2018

We report on a new class of dimension witnesses, based on quantum random access codes, which are ... more We report on a new class of dimension witnesses, based on quantum random access codes, which are a function of the recorded statistics and that have different bounds for all possible decompositions of a high-dimensional physical system. Thus, it certifies the dimension of the system and has the new distinct feature of identifying whether the high-dimensional system is decomposable in terms of lower dimensional subsystems. To demonstrate the practicability of this technique, we used it to experimentally certify the generation of an irreducible 1024-dimensional photonic quantum state. Therefore, certifying that the state is not multipartite or encoded using noncoupled different degrees of freedom of a single photon. Our protocol should find applications in a broad class of modern quantum information experiments addressing the generation of high-dimensional quantum systems, where quantum tomography may become intractable.

Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments

Science Advances, 2021

Quantum nonlocality is developed on the basis of the two most celebrated discrete structures in q... more

Characterizing and quantifying the incompatibility of quantum instruments

Physical Review A

Incompatibility of quantum devices is one of the cornerstones of quantum theory, and the incompat... more Incompatibility of quantum devices is one of the cornerstones of quantum theory, and the incompatibility of quantum measurements and channels has been linked to quantum advantage in certain information-theoretic tasks. In this work, we focus on the less well explored question of the incompatibility of quantum instruments, that is, devices that describe the measurement process in its entirety, accounting for both the classical measurement outcome and the quantum postmeasurement state. In particular, we focus on the recently introduced notion of parallel compatibility of instruments, which has been argued to be a natural notion of instrument compatibility. We introduce, in a manner similar to the case of measurements and channels, the incompatibility robustness of quantum instruments and derive universal bounds on it. We then prove that postprocessing of quantum instruments is a free operation for parallel compatibility. Last, we provide families of instruments for which our bounds are tight and families of compatible indecomposable instruments.

Three numerical approaches to find mutually unbiased bases using Bell inequalities

Quantum

Mutually unbiased bases correspond to highly useful pairs of measurements in quantum information ... more Mutually unbiased bases correspond to highly useful pairs of measurements in quantum information theory. In the smallest composite dimension, six, it is known that between three and seven mutually unbiased bases exist, with a decades-old conjecture, known as Zauner's conjecture, stating that there exist at most three. Here we tackle Zauner's conjecture numerically through the construction of Bell inequalities for every pair of integers n,d≥2 that can be maximally violated in dimension d if and only if n MUBs exist in that dimension. Hence we turn Zauner's conjecture into an optimisation problem, which we address by means of three numerical methods: see-saw optimisation, non-linear semidefinite programming and Monte Carlo techniques. All three methods correctly identify the known cases in low dimensions and all suggest that there do not exist four mutually unbiased bases in dimension six, with all finding the same bases that numerically optimise the corresponding Bell ine...

Upper Bounds on Key Rates in Device-Independent Quantum Key Distribution Based on Convex-Combination Attacks

Quantum 2.0 Conference and Exhibition

We provide an efficient, generic tool for upper-bounding key rates in device-independent quantum ... more

Self-Testing Mutually Unbiased Bases in Higher Dimensions with Space-Division Multiplexing Optical Fiber Technology

Physical Review Applied

Recently in Ref. [25], a method has been proposed for self-testing high-dimensional measurements ... more Recently in Ref. [25], a method has been proposed for self-testing high-dimensional measurements corresponding to mutually unbiased bases (MUBs) in the prepareand-measure scenario, under the dimension assumption. MUBs constitute a particularly useful family of quantum measurements, with myriad applications in quantum information. Among other tasks, they optimise state determination [26, 27], generate maximal amount of randomness [28], and give rise to secure cryptographic protocols

Mutually Unbiased Measurements, Hadamard Matrices, and Superdense Coding

arXiv (Cornell University), Apr 25, 2022

Mutually unbiased bases (MUBs) are highly symmetric bases on complex Hilbert spaces, and the corr... more 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.

Semi-device-independent random number generation with flexible assumptions

npj Quantum Information, 2021

Our ability to trust that a random number is truly random is essential for fields as diverse as c... more Our ability to trust that a random number is truly random is essential for fields as diverse as cryptography and fundamental tests of quantum mechanics. Existing solutions both come with drawbacks—device-independent quantum random number generators (QRNGs) are highly impractical and standard semi-device-independent QRNGs are limited to a specific physical implementation and level of trust. Here we propose a framework for semi-device-independent randomness certification, using a source of trusted vacuum in the form of a signal shutter. It employs a flexible set of assumptions and levels of trust, allowing it to be applied in a wide range of physical scenarios involving both quantum and classical entropy sources. We experimentally demonstrate our protocol with a photonic setup and generate secure random bits under three different assumptions with varying degrees of security and resulting data rates.

$n$-fold unbiased bases: an extension of the MUB condition

I introduce a new notion, that extends the mutually unbiased bases (MUB) conditons to more than t... more I introduce a new notion, that extends the mutually unbiased bases (MUB) conditons to more than two bases. These, I call the nUB conditions, and the corresponding bases n-fold unbiased. They naturally appear while optimizing generic n-to-one quantum random access code (QRAC) strategies. While their existence in general dimensions is an open question, they nevertheless give close-to-tight upper bounds on QRAC success probabilities, and raise fundamental questions about the geometry of quantum states.

Robust self-test of high-dimension mutually unbiased bases with commercial multi-core fiber

2020 IEEE Photonics Society Summer Topicals Meeting Series (SUM), 2020

We perform a robust self-testing certification of two four-dimensional mutually unbiased bases in... more We perform a robust self-testing certification of two four-dimensional mutually unbiased bases in a high-quality optical configuration built with commercial multicore fiber. We also evaluate the randomness produced. Our results represent an important step towards practical self-testing in high-dimensional quantum information technologies.

Characterising and bounding the set of quantum behaviours in contextuality scenarios

Quantum, 2021

The predictions of quantum theory resist generalised noncontextual explanations. In addition to t... more The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum advantage in communication and information processing. In the first part of this work, we formally define contextuality scenarios via prepare-and-measure experiments, along with the polytope of general contextual behaviours containing the set of quantum contextual behaviours. This framework allows us to recover several properties of set of quantum behaviours in these scenarios, including contextuality scenarios and associated noncontextuality inequalities that require for their violation the individual quantum preparation and measurement procedures to be mixed states and unsharp measurements. With the framework in place, we formulate novel semidefinite programming relaxations for bounding these sets of quantum contextual behaviours. Most significantly, ...

Bell Nonlocality Is Not Sufficient for the Security of Standard Device-Independent Quantum Key Distribution Protocols

Physical Review Letters, 2021

Qudit homological product codes

Quantum Information and Computation, 2017

In this note we show that the random homological product code construction of Bravyi and Hastings... more

Quantum error-correction codes and absolutely maximally entangled states

Physical Review A, 2020

For every stabiliser N-qudit absolutely maximally entangled state, we present a method for determ... more For every stabiliser N-qudit absolutely maximally entangled state, we present a method for determining the stabiliser generators and logical operators of a corresponding quantum error correction code. These codes encode k qudits into N − k qudits, with k ≤ N/2 , where the local dimension d is prime. We use these methods to analyse the concatenation of such quantum codes and link this procedure to entanglement swapping. Using our techniques, we investigate the spread of quantum information on a tensor network code formerly used as a toy model for the AdS/CFT correspondence. In this network, we show how corrections arise to the Ryu-Takayanagi formula in the case of entangled input state, and that the bound on the entanglement entropy of the boundary state is saturated for absolutely maximally entangled input states.

The MRCC program system: Accurate quantum chemistry from water to proteins

The Journal of Chemical Physics, 2020

Incompatibility robustness of quantum measurements: a unified framework

New Journal of Physics, 2019

In quantum mechanics performing a measurement is an invasive process which generally disturbs the... more In quantum mechanics performing a measurement is an invasive process which generally disturbs the system. Due to this phenomenon, there exist incompatible quantum measurements, i.e. measurements that cannot be simultaneously performed on a single copy of the system. It is then natural to ask what the most incompatible quantum measurements are. To answer this question, several measures have been proposed to quantify how incompatible a set of measurements is, however their properties are not well-understood. In this work, we develop a general framework that encompasses all the commonly used measures of incompatibility based on robustness to noise. Moreover, we propose several conditions that a measure of incompatibility should satisfy, and investigate whether the existing measures comply with them. We find that some of the widely used measures do not fulfil these basic requirements. We also show that when looking for the most incompatible pairs of measurements, we obtain different ans...

Self-testing mutually unbiased bases in the prepare-and-measure scenario

Physical Review A, 2019

Certifying an Irreducible 1024-Dimensional Photonic State Using Refined Dimension Witnesses

Physical review letters, Jan 8, 2018

We report on a new class of dimension witnesses, based on quantum random access codes, which are ... more We report on a new class of dimension witnesses, based on quantum random access codes, which are a function of the recorded statistics and that have different bounds for all possible decompositions of a high-dimensional physical system. Thus, it certifies the dimension of the system and has the new distinct feature of identifying whether the high-dimensional system is decomposable in terms of lower dimensional subsystems. To demonstrate the practicability of this technique, we used it to experimentally certify the generation of an irreducible 1024-dimensional photonic quantum state. Therefore, certifying that the state is not multipartite or encoded using noncoupled different degrees of freedom of a single photon. Our protocol should find applications in a broad class of modern quantum information experiments addressing the generation of high-dimensional quantum systems, where quantum tomography may become intractable.

Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments

Science Advances, 2021

Quantum nonlocality is developed on the basis of the two most celebrated discrete structures in q... more