All talks are taking place in the JILA auditorium. In the afternoons, the collaborations and informal discussions will take place in the Foothills room (10th floor, JILA tower), and in JILA X317.
| Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | |
|---|---|---|---|---|---|---|
| 09.00-10.00 | A. Winter | N. Datta | G. Gour | D. Leung | M. Junge | |
| 10.30-11.15 | M. Walter | S. Das | N. LaRacuente | C. Hirche | A. Anshu | |
| 11.30-12.00 | K. Mayer | M.B. Ruskai | K. Fang | L. Gao | K. Sharma | |
| 12.00-12.30 | H. Ma | T. Zhang | X. Wang | K. Noh | ||
| Lunch | ||||||
| Afternoon | 16.30: Chautauqua Park hike (meet at JILA tower) |
Discussions | 15.00: Poster session 16.00: Open problem session |
Discussions | Discussions | Discussions |
| Evening | 19.00: Meet & Greet at Backcountry Pizza |
18.00: Conference dinner at Sanitas Brew. Co. |
17.00: Group hike |
This list is being updated as speakers and titles are confirmed.
We consider a variation of the well-studied quantum state redistribution task, in which the starting state is known only to the receiver Bob and not to the sender Alice. We refer to this as quantum state redistribution with a one-sided promise. In addition, we consider communication from Alice to Bob over a noisy channel N, instead of the noiseless channel, as is usually considered in state redistribution. We take a natural approach towards solution of this problem where we "embed" the promise as part of the state and then invoke known protocols for quantum state redistribution composed with known protocols for transfer of quantum information over noisy channels. We interpret the communication primitive Alpha-bit, recently introduced in Ref. [arXiv:1706.09434], as an instance of state transfer (a sub-task of state redistribution) with a one-sided promise over noisy channels. Using our approach, we are able to reproduce the Alpha-bit capacities with or without entanglement assistance in Ref. [arXiv:1706.09434], using known protocols for quantum state redistribution and quantum communication over noisy channels. Furthermore, we generalize the entanglement assisted classical capacity of the Alpha-bit, showing that any quantum state redistribution protocol can be used as a black box to simulate classical communication.
Joint work with Min-Hsiu Hsieh and Rahul Jain.
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Resource theories in quantum information science are helpful for the study and quantification of the performance of information-processing tasks that involve quantum systems. These resource theories also find applications in the study of other areas; e.g., the resource theories of entanglement and coherence have found use and implications in the study of quantum thermodynamics and memory effects in quantum dynamics. In this paper, we introduce the resource theory of unextendibility, which is associated to the inability of extending quantum entanglement in a given quantum state to multiple parties. The free states in this resource theory are the k-extendible states, and the free channels are k-extendible channels, which preserve the class of k-extendible states. We make use of this resource theory to derive non-asymptotic, upper bounds on the rate at which quantum communication or entanglement preservation is possible by utilizing an arbitrary quantum channel a finite number of times, along with the assistance of k-extendible channels at no cost. We then show that the bounds we obtain are significantly tighter than previously known bounds for both the depolarizing and erasure channels. Joint work with Eneet Kaur, Mark M. Wilde, and Andreas Winter.
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Quantum functional inequalities (e.g.~the logarithmic Sobolev- and Poincar\'{e} inequalities) have found widespread application in the study of the behavior of primitive quantum Markov semigroups. The classical counterparts of these inequalities are related to each other via a so-called transportation cost inequality of order 2 (T2). The latter inequality relies on the notion of a metric on the set of probability distributions called the Wasserstein distance of order 2. (T2) in turn implies a transportation cost inequality of order 1 (T1). In this talk, we introduce quantum generalizations of the inequalities (T1) and (T2), making use of appropriate quantum versions of the Wasserstein distances, one recently defined by Carlen and Maas and the other defined by us. We establish that these inequalities are related to each other, and to the quantum modified logarithmic Sobolev- and Poincar\'{e} inequalities, as in the classical case. We also show that these inequalities imply certain concentration-type results for the invariant state of the underlying semigroup. We consider the example of the generalized depolarizing semigroup to derive concentration inequalities for any finite dimensional full-rank quantum state. These inequalities are then applied to derive upper bounds on the error probabilities occurring in the setting of finite blocklength quantum parameter estimation. This is joint work with Cambyse Rouz\'e.
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The ability to distill quantum coherence is essential for the implementation of quantum technologies. In this talk, We explore coherence distillation in various scenarios and study the tradeoff between key parameters: distillation rate, error tolerance, and success probability. We investigate the distillation process under different classes of free operations, highlighting differences in their capabilities and establishing their fundamental limitations in state transformations.
This talk is based on two arXiv papers:
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Quantum correlations are probabilistic correlations arose from measurement on bipartite quantum systems. The matrix-valued quantum correlation can be viewed as the outcome of partial measurements. In this talk, I will show that the set of matrix-valued correlation arose from separable infinite dimensional bipartite system is not closed. In particular, our non-closeness result exists for systems with small sizes of measurements (e.g. 3 two-valued PVMs), hence complements with the results of Slofstra and of Dykema-Paulsen-Prakash in the scalar value setting. For the argument, we will also mention some interesting correspondences of embezzlement and dense coding & teleportation in $C^*$-algebras. This is joint work with Samuel J. Harris and Marius Junge.
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A common theme in Chemistry, Thermodynamics, and Information Theory is how one type of resource -- be it chemicals, heat baths, or communication channels -- can be used to produce another. These processes of conversion and their applications are studied under the general heading of "resource theories". While resource theories use a wide range of sophisticated and apparently unrelated mathematical techniques, there is also an emerging general mathematical framework which seems to underpin all of them. In this talk, I will give a short overview on some of these common mathematical structures that appear in resource theories, particularly those appearing in resource theories of quantum processes. I will end with an application of these techniques to the problem of discrimination of quantum channels.
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"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in classical information theory, particularly in coding and Shannon theory; entropy power inequalities are special instances of them. The arguably most elementary kind of information combining is the addition of two binary random variables (a CNOT gate), and the resulting quantities play an important role in belief propagation and polar coding. In previous work we have investigated extensions of the classical bounds on information combining to the setting with quantum side information. This has been done using e.g. recent lower bounds on the conditional mutual information in terms of recovery quantities, leading to a non-trivial lower bound with applications to coding. Furthermore a conjecture for the optimal bounds was proposed. In this talk we extend on the previous work, by considering three main points:
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We show how group and quantum group representations can lead to natural constructions of Stinespring isometries. Based on interpolation theory we then discuss perturbative estimates for quantum and private capacity. We will also discuss the relation to recent estimates by Collins and his collaborators.
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Coherence, entanglement and uncertainty are three quintessential aspects of quantumness. A fundamental question is how these aspects relate. In the von Neumann algebra formalism, strong subadditivity and several entropic uncertainty relations are actually special cases of a single inequality. We generalize quantities such as conditional mutual information from tensor subsystems to subalgebras, proving basic properties and inequalities in this broader setting. Via complex interpolation, we show uncertainty-like relations for the outputs of quantum channels applied to a common input state. We begin to develop a general form of resource theory that includes notions of both entanglement and coherence. Our setting is closely related to the resource theory of asymmetry. It presents a unified picture of several quantum notions as the asymmetry of one channel's output with respect to another.
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We first summarize recently found nonlocal games (with finite number of classical questions and answers) whose optimal winning probability can only be attained as a limit of strategies using arbitrarily high dimensional entangled states. Then, we focus on one such game, an explicit three-player game with very few classical questions and answers. This game is based on the coherent state exchange game introduced in arXiv:0804.4118, which in turns is based on embezzlement of entanglement due to van Dam and Hayden. We discuss the main ideas behind each of these ingredients, and how they can be put together to obtain a quantitative tradeoff in the winning probability vs the dimension of the entangled state shared by the players.
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Many-body entanglement gives rise to various exotic phenomena. Especially, in some strong correlated systems, the new discovered topological ordered phase interpreted as a non-trivial pattern of many-body entanglement has novel properties, such as fractional charges, anyonic braiding statistics, topological ground state degeneracy and so on. Here, I focus on a special topological order, called fracton order, where the mobility of fractional charges is strongly restricted and the ground state degeneracy is sub-extensive, depending on system size. The three-dimensional fracton order is shown to be characterized by a universal structure of the entanglement entropy, whose non-local contribution scales linearly in subsystem size, different from regular topological entanglement entropy which is a constant. This non-local contribution is extracted by suitably combining the results of bipartition entanglement entropy. Alternatively, a new quantity called recoverable information is also defined to detect the non-local (topological) nature of this order.
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We investigate the problem of bounding the quantum process fidelity given bounds on the fidelities between target states and the action of a process on a set of pure input states. We formulate the problem as a semidefinite program and prove convexity of the minimum process fidelity as a function of the errors on the output states. We characterize the conditions required to uniquely determine a process in the case of no errors, and derive a lower bound on its fidelity in the limit of small errors for any set of input states satisfying these conditions. We then consider sets of input states whose one-dimensional projectors form a symmetric positive operator-valued measure (POVM). We prove that for such sets the minimum fidelity is bounded by a linear function of the average output state error. The minimal non-orthogonal symmetric POVM contains d + 1 states, where d is the Hilbert space dimension. Our bounds applied to these states provide an efficient method for estimating the process fidelity without the use of full process tomography.
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Gaussian thermal loss channels are of particular importance since they model realistic optical communication channels. In this talk, I will review basic properties of Gaussian channels and show how they can be used to establish (1) an upper bound of the quantum capacity of the Gaussian thermal loss channel and (2) an achievable rate of the Gottesman-Kitaev-Preskill (GKP) codes for the Gaussian thermal loss channel. In particular, I will show that, in the energy-unconstrained case, a family of the GKP codes achieves the quantum capacity of the Gaussian thermal loss channel up to at most a constant gap (~log_{2}e=1.44269…) from the presented upper bound of the quantum capacity. In the energy-constrained case, I will formulate a biconvex encoding and decoding optimization problem to maximize entanglement fidelity. Using an alternating semidefinite programming (SDP) method to solve the biconvex optimization, I will show that the (hexagonal) GKP code emerges as an optimal encoding from Haar random initial codes. (This talk is based on arXiv:1801.07271.)
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Several new classes of extreme points of unital and trace-preserving completely positive (CP) maps are analyzed. One class is not extreme in either the convex set of unital CP maps or the set of trace-preserving CP maps and is factorizable. Another class is extreme for both the set of unital CP maps and the set of trace-preserving CP maps, except for certain critical parameters. For those parameters the linear dependence of the matrices in the Choi product condition are associated with representations of the symmetric group. Joint work with U. Haagerup and M. Musat.
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We establish several upper bounds on the energy-constrained quantum and private capacities of all single-mode phase-insensitive bosonic Gaussian channels. The first upper bound, which we call the "data-processing bound," is the simplest and is obtained by decomposing a phase-insensitive channel as a pure-loss channel followed by a quantum-limited amplifier channel. We prove that the data-processing bound can be at most 1.45 bits larger than a known lower bound on these capacities of the phase-insensitive Gaussian channel. We discuss another data-processing upper bound as well. Two other upper bounds, which we call the ``$\varepsilon$-degradable bound'' and the ``$\varepsilon$-close-degradable bound,'' are established using the notion of approximate degradability along with energy constraints. We find a strong limitation on any potential superadditivity of the coherent information of any phase-insensitive Gaussian channel in the low-noise regime, as the data-processing bound is very near to a known lower bound in such cases. We also find improved achievable rates of private communication through bosonic thermal channels, by employing coding schemes that make use of displaced thermal states. We end by proving that an optimal Gaussian input state for the energy-constrained, generalized channel divergence of two particular Gaussian channels is the two-mode squeezed vacuum state that saturates the energy constraint.
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Schur-Weyl duality is a ubiquitous tool in quantum information. At its heart is the statement that the space of operators that commute with the tensor powers of all unitaries is spanned by the permutations of the tensor factors. In this work, we describe a similar duality theory for tensor powers of Clifford unitaries. The Clifford group is a central object in many subfields of quantum information, most prominently in the theory of fault-tolerance. The duality theory has a simple and clean description in terms of finite geometries. We demonstrate its effectiveness in several applications: (1) We resolve an open problem in quantum property testing by showing that "stabilizerness" is efficiently testable: There is a protocol that, given access to six copies of an unknown state, can determine whether it is a stabilizer state, or whether it is far away from the set of stabilizer states. We give a related membership test for the Clifford group. (2) We find that tensor powers of stabilizer states have an increased symmetry group. We provide corresponding de Finetti theorems, showing that the reductions of arbitrary states with this symmetry are well-approximated by mixtures of stabilizer tensor powers (in some cases, exponentially well). (3) We show that the distance of a pure state to the set of stabilizers can be lower-bounded in terms of the sum-negativity of its Wigner function. This gives a new quantitative meaning to the sum-negativity (and the related mana) -- a measure relevant to fault-tolerant quantum computation. The result constitutes a robust generalization of the discrete Hudson theorem. (4) We show that complex projective designs of arbitrary order can be obtained from a finite number (independent of the number of qudits) of Clifford orbits. To prove this result, we give explicit formulas for arbitrary moments of random stabilizer states.
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Quantum state redistribution is a fundamental task in quantum information theory, where two parties A and B aim to redistribute a quantum system C via communication and shared entanglement. In this work, we investigate quantum state redistribution in various settings. We first study the optimal fidelity of zero-communication quantum state redistribution and explore its connection to the recoverability of quantum information. Furthermore, we characterize the communication cost and fidelity of the no-signalling-assisted quantum state redistribution. This talk is based on a joint work with Mario Berta, Kun Fang, and Marco Tomamichel (in preparation).
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The distributed compression of correlated sources, as well as its descendant problems of compression with side- information at the decoder, associated with the names of David Slepian and Jack Wolf in the classical setting, are a corner stone of multi-user Shannon theory. The attempts to generalise these fundamental tools to the quantum Shannon setting have met with mixed success, ranging from the deep (quantum state merging) to the disappointing (quantum data compression with classical side information). I will take up the latter problem and show some recent advances made in joint work with Zahra Khanian [to appear]. We show that, while for the classical case compression all the way down to the conditional entropy is possible, meaning that the rate sum always equals the Shannon limit, in the quantum case the minimum rate is generally strictly larger than the conditional entropy (of the quantum source conditioned on the classical side information). In other words, the rate sum is in general strictly larger than the Schumacher limit. We interpret this as the cost of ignorance of the encoder: If he had access to the side information as well as the decoder, the conditional entropy could be achieved, without it the compression rate is strictly larger.
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In ordinary, non-relativistic quantum theory, especially in quantum information, states are defined across all the space but only at one time, which goes against our intuition from relativity. Pseudo-density matrix is a generalisation of density matrix to spacetime domain and treats space and time on an equal footing. It remains to have unit trace and be Hermitian but not positive semi-definite so it is called pseudo. In pseudo-density matrix formulation, temporal correlations are treated analogous to spatial correlations and there is a symmetry between spatial and temporal correlations in bipartite states. Here, we define time crystals in terms of long-range order in time, which is temporal correlation in the long period, and use quantum error correction to counteract the quantum decoherence. An NMR experiment is carried out to verify the existence of this time crystal for one step. Also, we generalise pseudo-density matrix formulation to continuous variables and quantum fields, discuss the role of partial transpose in spacetime swapping and plan to apply it in black hole information paradox for a better understanding.
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