Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session A58: Quantum Measurements, Channels, and Resource Theories |
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Sponsoring Units: DQI Chair: Gregory Bentsen, Brandeis University Room: Room 302 |
Monday, March 6, 2023 8:00AM - 8:12AM |
A58.00001: No-Go Theorem for a Quantum-Illumination Ranging Lior Cohen Quantum illumination promises high improvement in errors of target detection. However, currently it is uncertain if this improvement can be used for ranging applications. In this work, we use tools of quantum information theory to show that this improvement is impractical in time-of-flight (ToF) ranging. |
Monday, March 6, 2023 8:12AM - 8:24AM |
A58.00002: Quantum bounds and structured receiver performance for discriminating mixed states generated by weak measurement and thermal noise Piper C Wysocki, Jonathan Habif, Federico M Spedalieri Optimally discriminating between non-orthogonal states is critical to both quantum communications and quantum computation. As such, much work focuses on finding quantum bounds for minimal error discrimination and then comparing these quantum bounds with the performance of structured receivers. Pure state discrimination is well understood but deriving experimental strategies for discriminating mixed states has been less explored. We compute quantum bounds and receiver performance for discriminating between mixed states prepared by a pure coherent state mixed with thermal noise light in a channel and the same pure coherent state subject to weak measurement in a channel. We calculate the Helstrom bound for the case where a single copy of the quantum state is available for measurement and the quantum Chernoff bound, where copies of the quantum state occupy many modes and can be measured individually or with a joint measurement. We then compare these quantum bounds with the performance of different structured detection schemes, including direct and homodyne detection. The results have utility in quantum authentication, by enabling discrimination between a case of an attacker in a quantum key distribution system with weak measurement capabilities versus thermal noise in the channel. |
Monday, March 6, 2023 8:24AM - 8:36AM |
A58.00003: Only Classical Parameterized States have Optimal Measurements Wilfred Salmon, David R Arvidsson-Shukur, Sergii Strelchuk When estimating parameters encoded in quantum systems, it is natural to ask if there is an optimal quantum-measurement strategy. This question has been extensively studied when one has an a priori belief about the parameter (the Bayesian regime) or in the limit of infinitely many copies of a state (the asymptotic regime). In this talk, we address this question in a more experimentally realistic scenario. We assume that an experimenter has only finite resources and has no prior knowledge of the unknown parameter. We directly compare measurements without reference to an entropic quantity (e.g the Fisher information) and completely characterise when optimal measurements exist: there is an optimal measurement if and only if the parameterised state is classical. Furthermore, we discuss how one can consider approximately optimal measurements when a strictly optimal measurement does not exist. |
Monday, March 6, 2023 8:36AM - 8:48AM |
A58.00004: Power of sequential protocols in hidden channel discrimination SHO SUGIURA, Arkopal Dutt, Sina Zeytinoglu, William J Munro, Isaac L Chuang Any physical operation on a quantum system can be described as a quantum channel. Identification of quantum channels, referred to as quantum channel discrimination (QCD), is a fundamental task in experiments. A central achievement in QCD is unraveling the bounds of error probability in discrimination and the protocols used to achieve it. |
Monday, March 6, 2023 8:48AM - 9:00AM |
A58.00005: Approximate 2-localization of random matrices: The random matrix universe Nicolas Loizeau, Dries Sels Quantum many-body systems are endowed with a tensor product structure. This structure is essentially inherited from probability theory, where the probability of two independent events is the product of the probabilities. The tensor product structure of a Hamiltonian thus gives a natural decomposition of the system into smaller subsystems. Considering a particular Hamiltonian and a particular tensor product structure, one can ask: is there a basis in which this Hamiltonian has this desired tensor product structure? In general such an exact structure does not exist, however we will show (numerically) that large random matrices are approximately 2-local in a carefully chosen basis. These results suggest a mechanism for the emergence of locality from quantum theory itself. |
Monday, March 6, 2023 9:00AM - 9:12AM |
A58.00006: Maximum entropy methods for quantum state compatibility problems Bei Zeng Inferring a quantum system from incomplete information is a common problem in many aspects of quantum information science and applications, where the principle of maximum entropy (MaxEnt) plays an important role. The quantum state compatibility problem asks whether there exists a density matrix ρ compatible with some given measurement results. Such a compatibility problem can be naturally formulated as a semidefinite programming (SDP), which searches directly for the existence of a ρ. However, for large system dimensions, it is hard to represent ρ directly, since it needs too many parameters. In this work, we apply MaxEnt to solve various quantum state compatibility problems, including the quantum marginal problem. An immediate advantage of the MaxEnt method is that it only needs to represent ρ via a relatively small number of parameters, which is exactly the number of the operators measured. Furthermore, in case of incompatible measurement results, our method will further return a witness that is a supporting hyperplane of the compatible set. Our method has a clear geometric meaning and can be computed effectively with hybrid quantum-classical algorithms. |
Monday, March 6, 2023 9:12AM - 9:24AM |
A58.00007: The quantum low-rank approximation problem Nic Ezzell, Zoe Holmes, Patrick J Coles, Elliott M Ball, Aliza U Siddiqui, Mark M Wilde, Andrew T Sornborger In the presence of noise, a quantum system is described by a density matrix often labeled ρ. Intuitively, noise creates uncertainty in our knowledge of the exact state, and ρ is the average state across many identical experiments. Under thermal noise, for example, the state of a system with hamiltonian H relaxes to a thermal state, ρth, which weighs the eigenstates of H with a Gibbs weight. In principal, ρth therefore consists of a convex combination of an exponential number of pure states, but for small temperatures, it's a good approximation to truncate to a small low-energy subspace. We make this truncation rigorous by defining and solving the quantum analog of the famous "low-rank approximation problem" which asks for the matrix B closest to A satisfying rank(B) <= R. The solution is intuitive: B is the truncation of A to the eigenspace with R largest eigenvalues which are known as the principal values. In the quantum case, A and B become quantum states ρ and σ which must be normalized, i.e. Tr[ρ] = Tr[σ] = 1, so simple truncation alone cannot work. A reasonable guess is that the quantum solution is just the classical one with renormalization. We show that this is correct, but by an additive renormalization and not a multiplicative one. Further, this additive renormalization solution is unique for any Schatten p-norm with p >= 2, but highly degenerate for p = 1 which the trace distance. We then develop a hybrid quantum-classical variational algorithm to solve the quantum low-rank approximation problem for p = 2. In particular, we show how to either learn a rank-constrained approximation of ρ by finding a circuit which prepares an approximate purification or by probabilistically sampling states generated from a fixed unitary acting on different computational basis states. This algorithm--which we call "quantum mixed state compiling," therefore provides a means to (i) learn a mixed state, (ii) learn a lower-rank approximation of a mixed state, (iii) perform principal components analysis, and more. |
Monday, March 6, 2023 9:24AM - 9:36AM |
A58.00008: Detecting entanglement by pure bosonic extension Xuanran Zhu Detecting and quantifying quantum entanglement is a central task in quantum information theory. Relative entropy of entanglement (REE) is one of the most famous quantities for measuring entanglement and has various applications in many other fields. One well-studied and efficient approach for calculating the lower bound of REE is the positive partial transpose (PPT) criterion. But it fails in the bound entangled area. In this work, we use a method called pure bosonic extension to significantly improve the feasibility of k-symmetric/bosonic extensions which characterize the separable set from outside by a hierarchy structure. Based on this method, we can efficiently approximate the boundaries of k-bosonic extendible sets and obtain the desired lower bound of REE. Compared to the Semi-Definite Programming method, for example, the symmetric extension function in QETLAB, our algorithm can support much larger single particle dimensions and much larger k. |
Monday, March 6, 2023 9:36AM - 9:48AM |
A58.00009: Experimental study of quantum uncertainty from lack of information Filip D Rozpedek, Yuan-Yuan Zhao, Zhibo Hou, Kang-Da Wu, Guo-Yong Xiang, Chuan-Feng Li, Guang-Can Guo Quantum uncertainty is a well-known property of quantum mechanics that states the impossibility of predicting measurement outcomes of multiple incompatible observables simultaneously. In contrast, the uncertainty in the classical domain comes from the lack of information about the exact state of the system. One may naturally ask, whether the quantum uncertainty is indeed a fully intrinsic property of the quantum theory, or whether similar to the classical domain lack of knowledge about specific parts of the physical system might be the source of this uncertainty. This question has been addressed in the previous literature where the authors argue that in the entropic formulation of the uncertainty principle that can be illustrated using the so-called, guessing games, indeed such lack of information has a significant contribution to the arising quantum uncertainty. Here we investigate this issue experimentally by implementing the corresponding two-dimensional and three-dimensional guessing games. Our results confirm that within the guessing-game framework, the quantum uncertainty to a large extent relies on the fact that quantum information determining the key properties of the game is stored in the degrees of freedom that remain inaccessible to the guessing party. Moreover, we offer an experimentally compact method to construct the high-dimensional Fourier gate which is a major building block for various tasks in quantum computation, quantum communication, and quantum metrology. |
Monday, March 6, 2023 9:48AM - 10:00AM |
A58.00010: Master Equation Emulation and Coherence Preservation with Classical Control of a Superconducting Qubit Evangelos Vlachos, Haimeng Zhang, Vivek Maurya, Jeffrey Marshall, Tameem Albash, Eli Levenson-Falk Open quantum systems are a topic of intense theoretical research. The use of master equations to model a system's evolution subject to an interaction with an external environment is one of the most successful theoretical paradigms. General experimental tools to study different open system realizations have been limited, and so it is highly desirable to develop experimental tools which emulate diverse master equation dynamics and give a way to test open systems theories. We demonstrate a systematic method for engineering specific system-environment interactions and emulating non-Markovian master equations of a particular form–generalized Markovian master equations–using classical stochastic noise. We show numerical simulations and experimental data demonstrating the successful emulation of generalized Markovian environments. We also demonstrate that non-Markovian noise can be used as a resource to extend the coherence of a quantum system and counteract the adversarial effects of Markovian environments. Lastly, we present a method for generating noise of arbitrary memory kernels, thus enabling the emulation of more complicated dynamics. |
Monday, March 6, 2023 10:00AM - 10:12AM |
A58.00011: Amplitude damping channels in multilevel systems: there's more than you think Stefano Chessa, Vittorio Giovannetti The amplitude damping channel (ADC) is one of the stantdard textbook instances of noise affecting 2-dimensional quantum systems (qubits). It can describe effectively ubiquitous relaxation processes affecting quantum devices such as superconducting circuits or losses in optical fibers. Many of its information theoretic properties, notably its quantum capacity, are understood. |
Monday, March 6, 2023 10:12AM - 10:24AM |
A58.00012: Randomized channel-state duality Bin Yan, Nikolai Sinitsyn Channel-state duality is a central result in quantum information science. It refers to the correspondence between a dynamical process (quantum channel) and a static quantum state in an enlarged Hilbert space. Since the corresponding dual state is generally mixed, it is described by a Hermitian matrix. In this talk, we present a randomized channel-state duality. In other words, a quantum channel is represented by a collection of $N$ pure quantum states that are produced from a random source. The accuracy of this randomized duality relation is given by $1/N$, with regard to an appropriate distance measure. For large systems, $N$ is much smaller than the dimension of the exact dual matrix of the quantum channel. This provides a highly accurate low-rank approximation of any quantum channel, and, as a consequence of the duality relation, an efficient data compression scheme for mixed quantum states. We demonstrate these two immediate applications of the randomized channel-state duality with a chaotic $1$-dimensional spin system. |
Monday, March 6, 2023 10:24AM - 10:36AM |
A58.00013: Magic Phase Transitions in Random Quantum Circuits Christopher D White, Pradeep Niroula, Qingfeng Wang, Christopher Monroe, Crystal Noel, Michael J Gullans In recent years, measurement-induced phase transition, wherein unitary gates and projective measurements compete to determine the entanglement structure of a quantum state, have received intense interest. While entanglement is an important resource in quantum communication, it does not capture the non-classicality needed for quantum computation. Magic refers to the family of measures used to determine how useful the state is for fault-tolerant synthesis of non-Clifford operations in qudit-based error correction architectures — a good magic monotone is zero for a stabilizer state and does not increase under stabilizer operations. In this work, we show that a random stabilizer code subject to coherent errors exhibits a phase transition in magic. Below an error-rate threshold, stabilizer syndrome measurements remove the accumulated magic in the circuit, effectively protecting against the coherent errors. Above the threshold, the syndrome measurements concentrate magic. This "magic" phase transition is intimately related to the error-correction threshold. In this work, we present numerical and analytic characterizations of the magic transition. |
Monday, March 6, 2023 10:36AM - 10:48AM |
A58.00014: Magic: a new perspective on quantum chaos Lorenzo Leone, Salvatore Francesco Emanuele Oliviero, Alioscia Hamma Magic in quantum states is the resource that allows quantum computers to attain the quantum computational advantage over classical computers. Without magic, a quantum computer cannot do anything that a classical computer cannot do. In this work, we show that the resource theory of magic is closely connected to the theory of quantum chaos: we provide a measure of non-Cliffordness for unitary operators based on high order OTOCs and, as a consequence, only those quantum evolutions that attain a quantum computational advantage over classical computation can be considered chaotic. |
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