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Quantum catalysis is a fascinating concept which demonstrates that certain transformations can only become possible when given access to a specific resource that has to be returned unaffected. It was first discovered in the context of entanglement theory and since then applied in a number of resource-theoretic frameworks, including quantum thermodynamics. Although in that case the necessary (and sometimes also sufficient) conditions on the existence of a catalyst are known, almost nothing is known about the precise form of the catalyst state required by the transformation. In particular, it is not clear whether it has to have some special properties or be finely tuned to the desired transformation. In this work we describe a surprising property of multi-copy states: we show that in resource theories governed by majorization all resourceful states are catalysts for all allowed transformations. In quantum thermodynamics this means that the so-called &quot;second laws of thermodynamics&quot; do not require a fine-tuned catalyst but rather any state, given sufficiently many copies, can serve as a useful catalyst.

Quantum 2020

All states are universal catalysts in quantum thermodynamics

thermal operations

catalysis

resource theory

entanglement

quantum thermodynamics

The Institute of Physics and IOP Publishing, in partnership with the Chinese Physical Society (CPS) and the University of Science and Technology of China (USTC) are proud to have brought together the international quantum science community online for this inaugural conference.


Early career and leading researchers from universities, industry and government worldwide came together to share, learn and collaborate on the latest research and emerging areas of high interest across quantum science and technology. The broad themes covered by Quantum 2020 included:

Quantum communication;
Quantum computing and quantum simulation;
Quantum sensing, metrology and imaging;
Quantum information theory, software and algorithms;
Quantum foundations;
Quantum technology in industry.
The four-day event featured talks from world-renowned scientists, interactive poster sessions and two exciting panel discussions on the themes of Quantum Technology in Industry and Quantum Technology Programmes Around the World.


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Quantum catalysis is a fascinating concept which demonstrates that certain transformations can only become possible when given access to a specific resource that has to be returned unaffected. It was first discovered in the context of entanglement theory and since then applied in a number of resource-theoretic frameworks, including quantum thermodynamics. Although in that case the necessary (and sometimes also sufficient) conditions on the existence of a catalyst are known, almost nothing is known about the precise form of the catalyst state required by the transformation. In particular, it is not clear whether it has to have some special properties or be finely tuned to the desired transformation. In this work we describe a surprising property of multi-copy states: we show that in resource theories governed by majorization all resourceful states are catalysts for all allowed transformations. In quantum thermodynamics this means that the so-called "second laws of thermodynamics" do not require a fine-tuned catalyst but rather any state, given sufficiently many copies, can serve as a useful catalyst.

poster

Binning a continuous degree of freedom of one particle creates an effective, finite-dimensional qudit. Photonic time-bin qubits and qudits are popular [1,2,3], though efficiently processing high-dimensional time-bins remains challenging. In this theoretical work, we devise a scheme using a single, binned degree of freedom of one particle as a system of multiple, effective qubits. Distinct qubits correspond to scales of the original, continuous variable. While general bin processing overhead scales polynomially with dimension [4,5], efficient quantum algorithms implemented on multi-qubit time-bins may use polynomial-size circuits optimized for conventional, multi-qubit quantum computing. Considering scales below accessible precision, we find intriguing analogies to infinite-dimensional von Neumann algebras. Finally, scale-separated qubits present an experimentally accessible medium to probe the quantum-classical transition of chaos.

[1] Bussieres et al. 2006. arXiv:quant-ph/0608183

[2] Islam et al. 2017 Sci. Adv. doi:10.1126/sciadv.1701491

[3] Victora et al. 2019. Quantum Photonics: Pioneering Advances and Emerging Applications, pp 179-206. doi:10.1007/978-3-319-98402-5_5

[4] Reck et al. 1994. Phys. Rev. Lett. doi:10.1103/PhysRevLett.73.58

[5] Kumar & Dhand. 2020. arXiv:2001.02012

Scale-Separated Qubits from Binned Continuous Variables

Introducing quantum entanglement into game theory led to a major milestone in the studies of quantum games. Such a breakthrough is achieved through the application of two-qubit operators which are uniquely represented by the geometrical points (c 1 , c 2 , c 3 ). While the quantization scheme proposed by Eisert et al involves controlled unitary operators, modification of the scheme includes a much wider class of two-qubit operators. It is known that altering the entangling operator in the quantization scheme has a direct effect on the average payoffs of the players involved in the game. However, we show in the present work that two different class of two-qubit entangling operators can produce the same average payoffs of the players. Such an analysis is carried out in the light of conversion of symmetric to potential games. While entangling operators play an inevitable role in quantum computing, we find its significance in game theory through this work.

Entangling operators and their interplay with average payoffs in quantum games

In many current experimental setups and quantum information technologies, protocols that maximize a case-specific figure of merit are highly desirable. In this talk we focus on the preparation of cat states, i.e., quantum superposition of two opposite-phase coherent states, in a nonlinear optical Kerr resonator. To solve this quantum state control problem, we implement the dynamics of the system as part of a fully differentiable program [1]. This framework ultimately combines machine learning and the knowledge of the differential equations governing the dynamics of the physical system. We employ a neural network that maps the state of the system at a given time to a control pulse. Finally, we verify the robustness of the method against noise in the initial states.

[1] F. Schäfer, M. Kloc, C. Bruder, N. Lörch, Mach. Learn.: Sci Technol. 1 035009

A differentiable programming method for optimal preparation of cat states

In High Energy Physics (HEP), calorimeter outputs play an essential role in understanding low distance processes occurring during particle collisions. Due to the complexity of underlying physics, the traditional Monte-Carlo simulation is computationally expensive, and thus, the HEP community has suggested Generative Adversarial Networks (GAN) for fast simulation. Meanwhile, it has also been proposed that, in certain circumstances, simulation using GANs can itself be sped-up by using quantum GANs (qGANs).
Our work presents an advanced prototype of qGAN, that we call the dual-Parameterized Quantum Circuit (PQC) GAN, with a classical discriminator and two quantum generators which take the form of PQCs. The first PQC learns the probability distribution over the images of N pixels, while the second generates normalized pixel intensities of an individual image for each PQC input. The dual-PQC architecture exhibits an apparent quantum advantage, by using only O(log(N)) qubits, unlike the classical GAN with O(N) neurons. Its performance has been evaluated through the application in HEP to imitate calorimeter outputs, translated into pixelated images. The results demonstrate that the model can reproduce a fixed number of images with a reduced size as well as their probability distribution and allows us to scale up to real calorimeter outputs. 


Dual-Parameterized Quantum Circuit GAN Model in High Energy Physics

In oblivious transfer, a sender Alice sends two bits to a receiver Bob, who only receives one of them. Alice does not know which bit Bob received. Oblivious transfer is a useful cryptographic primitive. It is universal for multiparty computation, where two or more parties want to compute something together, while not revealing more than necessary about their input data to the other party. Perfect quantum oblivious transfer is impossible, but imperfect variants remain possible. We show that it is possible to “reverse” a quantum oblivious transfer protocol by Amiri et al., arXiv:2007.04712, so that one can achieve quantum oblivious transfer “both ways” even if one of the parties can only send quantum states, and the other one can only measure quantum states. This can be useful for applications.


Reversing quantum oblivious transfer

1-2 Oblivious Transfer is a cryptographic primitive in which a sender holds two bits, and a receiver receives one of them in such a way that the receiver does not learn both bits, and the sender does not know which of the bits the receiver has obtained. Perfect Quantum Oblivious Transfer is not possible, but it is possible to have protocols where cheating probabilities for the parties are bounded. Previous
research has found security bounds of 2=3 for general and 0:749 for symmetric pure quantum states. Here we examine a series of incomplete protocols, which means protocols with inherent probability for errors, that allow for security against the sender by no-signalling without allowing the receiver to cheat with unity success probability.
We characterise all incomplete protocols using symmetric states and compare dierent examples for implementable protocols with particular focus on the use of coherent states. Easiest to implement is a protocol in which classical bit value pairs are mapped to four phases +,-,+i,-i of a coherent state, which are distinguished using a single homodyne detection measurement. We show that using single photon BB84 like states provides better performance in terms of security than our coherent state protocols.

Imperfect quantum oblivious transfer where the sender cannot cheat

Photon interference and bunching are widely studied quantum effects that have also been proposed for high-precision measurements. We construct and use a theoretical description of photon interferometry on rotating
platforms, specifically exploring the relation between noninertial motion, relativity, and quantum mechanics. We propose an experiment testing these relations where photon entanglement can be revealed or concealed solely by controlling the rotational motion of an interferometer.

Revealing and concealing entanglement with noninertial motion

The Google announcement of the first experimentally achieved result of the so-called quantum supremacy, based on exploiting the multiqubit entanglement to the problem of randomness verification [https://doi.org/10.1038/s41586-019-1666-5], attracted attention to the classically ungrasped nature of the randomness itself and its verification. The elusive infiniteness of true randomness correlating with the quantum entanglement of the infinite number of entangled qubits asks for a fundamental description. We proposed a simplistic theoretical concept linking the multiqubit entanglement with the randomness in the public patent application in 2017 [PCT/PL2017/000133-WO/2019/132679] and in Sci. Rep. in 2020 [https://doi.org/10.1038/s41598-019-56706-2], the latter coincided in time with Google team announcement. We show that on the theoretical level, the presented concepts are equivalent in the fundamental sense. We discuss our quantum multiqubit entanglement based protocol for quantum random number generation, with unique features, like secure public randomness testing, overcoming local computational restrictions, or arbitrarily diminishing of the average time of the complex randomness testing of finite length bit sequence at the cost of multi-qubit entanglement level. Here, the randomness of the generated single sequence proves the randomness of all the other simultaneously generated sequences (or the randomness of the shorter sequence proves the randomness of longer sequence), which is a crucial result based on the multiqubit quantum entanglement.

Multiqubit entanglement for public randomness testing vs Google's quantum supremacy

The initial research undertaken was aimed at examining the feasibility of adapting and implementing Topological Data Analysis (TDA) methods using Persistent Homology to meet requirements in the telecom domain. Persistent Homology based methods are especially useful in detecting anomalies in time series data and show good prospects of being useful in telecom network alarm data. Here, the special interest to this technique is a metric called the Wasserstein Distance, which shows how much two persistence diagrams correspondingly differ from one another. Calculating this metric is a minimum weight maximum matching problem on a bipartite graph. Existing classical methods of calculating the Wasserstein distance show polynomial time complexity O(n power 3).
We carried out a quantum study which involved converting this Wasserstein matching problem into a Quadratic Unconstrained Binary Optimization problem and minimizing it using a Quantum Annealer approach.
Our final focus on the TDA Wasserstein distance problem is the implementation of an alternate Combinatorial Optimization Quantum Algorithm which should theoretically be faster than existing classical methods, potentially yielding a quantum speedup in detecting anomalies in the future.

Quantum Topological Data Analysis for Anomaly Detection

The violation of seminal Bell-type inequalities in spin polarization correlation experiments stimulated speculations about quantum magic and nonlocality. Some authors claim that the quantum correlations are due to some instantaneous influences between distant quantum systems, that an individual quantum system may be at the same time here and a meter away or that the experimenters’ free will is an illusion. The narrative about the quantum magic is not only grounded in some failed attempts of providing more detailed description of quantum phenomena but also in the disturbing fact that there is no consensus about the interpretation of quantum theory. Nevertheless if one starts talking about magic this is the end of the science. Robert Griffith and several other authors came recently to the conclusion that the quantum nonlocality and the quantum steering are misleading notions which should be abandoned or renamed . The quantum correlations between the outcomes of real experiments with entangled physical systems are strong but imperfect and they can be explained in a locally causal way. it is not true that the entangled systems behave as pairs of fair dice showing always the same outcomes. The important message for quantum information community is that qubits are not the attributes of individual physical systems which can be changed instantaneously by the measurements performed on distant entangled partners.

All states are universal catalysts in quantum thermodynamics

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Scale-Separated Qubits from Binned Continuous Variables

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