arXiv subjects

Stephanie Wehner

Publications and source records attributed to Stephanie Wehner.

At least 91 records · Page 5Linked to original sources

arXiv2018

Work and reversibility in quantum thermodynamics

It is a central question in quantum thermodynamics to determine how irreversible is a process that transforms an initial state $ρ$ to a final state $σ$, and whether such irreversibility can be thought of as a useful resource. For example, we might ask how much work can be obtained by thermalizing $ρ$ to a thermal state $σ$ at temperature $T$ of an ambient heat bath. Here, we show that, for different sets of resource-theoretic thermodynamic operations, the amount of entropy produced along a transition is characterized by how reversible the process is. More specifically, this entropy production depends on how well we can return the state $σ$ to its original form $ρ$ without investing any work. At the same time, the entropy production can be linked to the work that can be extracted along a given transition, and we explore the consequences that this fact has for our results. We also exhibit an explicit reversal operation in terms of the Petz recovery channel coming from quantum information theory. Our result establishes a quantitative link between the reversibility of thermodynamical processes and the corresponding work gain.

quant-ph↗

arXiv2018

Representations of the multi-qubit Clifford group

The Clifford group is a fundamental structure in quantum information with a wide variety of applications. We discuss the tensor representations of the $q$-qubit Clifford group, which is defined as the normalizer of the $q$-qubit Pauli group in $U(2^q)$. In particular, we characterize all irreducible subrepresentations of the two-copy representation $φ^{\otimes2}$ of the Clifford group on the matrix space $\mathbb{C}^{d\times d}\otimes \mathbb{C}^{d\times d}$ with $d=2^q$. In an upcoming companion paper we applied this result to cut down the number of samples necessary to perform randomised benchmarking, a method for characterising quantum systems.

quant-ph↗

arXiv2018

How to transform graph states using single-qubit operations: computational complexity and algorithms

Graph states are ubiquitous in quantum information with diverse applications ranging from quantum network protocols to measurement based quantum computing. Here we consider the question whether one graph (source) state can be transformed into another graph (target) state, using a specific set of quantum operations (LC+LPM+CC): single-qubit Clifford operations (LC), single-qubit Pauli measurements (LPM) and classical communication (CC) between sites holding the individual qubits. We first show that deciding whether a graph state |G> can be transformed into another graph state |G'> using LC+LPM+CC is NP-Complete, even if |G'> is restricted to be the GHZ-state. However, we also provide efficient algorithms for two situations of practical interest: 1. |G> has Schmidt-rank width one and |G'> is a GHZ-state. The Schmidt-rank width is an entanglement measure of quantum states, meaning this algorithm is efficient if the original state has little entanglement. Our algorithm has runtime O(|V(G')||V(G)|^3), and is also efficient in practice even on small instances as further showcased by a freely available software implementation. 2. |G> is in a certain class of states with unbounded Schmidt-rank width, and |G'> is a GHZ-state of a constant size. Here the runtime is O(poly(|V(G)|)), showing that more efficient algorithms can in principle be found even for states holding a large amount of entanglement, as long as the output state has constant size. Our results make use of the insight that deciding whether a graph state |G> can be transformed to another graph state |G'> is equivalent to a known decision problem in graph theory, namely the problem of deciding whether a graph G' is a vertex-minor of a graph G. Many of the technical tools developed to obtain our results may be of independent interest.

quant-ph↗

arXiv2018

Parameter regimes for a single sequential quantum repeater

Quantum key distribution allows for the generation of a secret key between distant parties connected by a quantum channel such as optical fibre or free space. Unfortunately, the rate of generation of a secret key by direct transmission is fundamentally limited by the distance. This limit can be overcome by the implementation of so-called quantum repeaters. Here, we assess the performance of a specific but very natural setup called a single sequential repeater for quantum key distribution. We offer a fine-grained assessment of the repeater by introducing a series of benchmarks. The benchmarks, which should be surpassed to claim a working repeater, are based on finite-energy considerations, thermal noise and the losses in the setup. In order to boost the performance of the studied repeaters we introduce two methods. The first one corresponds to the concept of a cut-off, which reduces the effect of decoherence during storage of a quantum state by introducing a maximum storage time. Secondly, we supplement the standard classical post-processing with an advantage distillation procedure. Using these methods, we find realistic parameters for which it is possible to achieve rates greater than each of the benchmarks, guiding the way towards implementing quantum repeaters.

quant-ph↗

arXiv2018

Transforming graph states using single-qubit operations

Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from another stabilizer (source) state by single-qubit Clifford operations (LC), single-qubit Pauli measurements (LPM), and classical communication (CC) between sites holding the individual qubits. What's more, we provide a recipe to obtain the sequence of LC+LPM+CC operations which prepare the desired target state from the source state, and show how these operations can be applied in parallel to reach the target state in constant time. Our algorithm has applications in quantum networks, quantum computing, and can also serve as a design tool - for example, to find transformations between quantum error correcting codes. We provide a software implementation of our algorithm that makes this tool easier to apply. A key insight leading to our algorithm is to show that the problem is equivalent to one in graph theory, which is to decide whether some graph G' is a vertex-minor of another graph G. Here we show that the vertex-minor problem can be solved in time O(|G|^3) where |G| is the size of the graph G, whenever the rank-width of G and the size of G' are bounded. Our algorithm is based on techniques by Courcelle for solving fixed parameter tractable problems, where here the relevant fixed parameter is the rank width. The second half of this paper serves as an accessible but far from exhausting introduction to these concepts, that could be useful for many other problems in quantum information.

quant-ph↗

arXiv2017

Quantum error correction in crossbar architectures

A central challenge for the scaling of quantum computing systems is the need to control all qubits in the system without a large overhead. A solution for this problem in classical computing comes in the form of so called crossbar architectures. Recently we made a proposal for a large scale quantum processor~[Li et al. arXiv:1711.03807 (2017)] to be implemented in silicon quantum dots. This system features a crossbar control architecture which limits parallel single qubit control, but allows the scheme to overcome control scaling issues that form a major hurdle to large scale quantum computing systems. In this work, we develop a language that makes it possible to easily map quantum circuits to crossbar systems, taking into account their architecture and control limitations. Using this language we show how to map well known quantum error correction codes such as the planar surface and color codes in this limited control setting with only a small overhead in time. We analyze the logical error behavior of this surface code mapping for estimated experimental parameters of the crossbar system and conclude that logical error suppression to a level useful for real quantum computation is feasible.

quant-ph↗

arXiv2017

Smoothed generalized free energies for thermodynamics

In the study of thermodynamics for nanoscale quantum systems, a family of quantities known as generalized free energies have been derived as necessary and sufficient conditions that govern state transitions. These free energies become important especially in the regime where the system of interest consists of only a few (quantum) particles. In this work, we introduce a new family of smoothed generalized free energies, by constructing explicit smoothing procedures that maximize/minimize the free energies over an $ \varepsilon$-ball of quantum states. In contrast to previously known smoothed free energies, these quantities now allow us to make an operational statement for approximate thermodynamic state transitions. We show that these newly defined smoothed quantities converge to the standard free energy in the thermodynamic limit.

quant-ph↗

arXiv2017

Multiplexed entanglement generation over quantum networks using multi-qubit nodes

Quantum networks distributed over distances greater than a few kilometers will be limited by the time required for information to propagate between nodes. We analyze protocols that are able to circumvent this bottleneck by employing multi-qubit nodes and multiplexing. For each protocol, we investigate the key network parameters that determine its performance. We model achievable entangling rates based on the anticipated near-term performance of nitrogen-vacancy centres and other promising network platforms. This analysis allows us to compare the potential of the proposed multiplexed protocols in different regimes. Moreover, by identifying the gains that may be achieved by improving particular network parameters, our analysis suggests the most promising avenues for research and development of prototype quantum networks.

quant-ph↗

arXiv2017

Continuous-Variable Protocol for Oblivious Transfer in the Noisy-Storage Model

Cryptographic protocols are the backbone of our information society. This includes two-party protocols which offer protection against distrustful players. Such protocols can be built from a basic primitive called oblivious transfer. We present and experimentally demonstrate here the first quantum protocol for oblivious transfer for optical continuous-variable systems, and prove its security in the noisy-storage model. This model allows to establish security by sending more quantum signals than an attacker can reliably store during the protocol. The security proof is based on new uncertainty relations which we derive for continuous-variable systems, that differ from the ones used in quantum key distribution. We experimentally demonstrate the proposed oblivious transfer protocol for various channel losses by using entangled two-mode squeezed states measured with balanced homodyne detection. Our work enables the implementation of arbitrary two-party quantum cryptographic protocols with continuous-variable communication systems.

quant-ph↗

arXiv2017

Quantum preparation uncertainty and lack of information

The quantum uncertainty principle famously predicts that there exist measurements that are inherently incompatible, in the sense that their outcomes cannot be predicted simultaneously. In contrast, no such uncertainty exists in the classical domain, where all uncertainty results from ignorance about the exact state of the physical system. Here, we critically examine the concept of preparation uncertainty and ask whether similarly in the quantum regime, some of the uncertainty that we observe can actually also be understood as a lack of information (LOI), albeit a lack of quantum information. We answer this question affirmatively by showing that for the well known measurements employed in BB84 quantum key distribution, the amount of uncertainty can indeed be related to the amount of available information about additional registers determining the choice of the measurement. We proceed to show that also for other measurements the amount of uncertainty is in part connected to a LOI. Finally, we discuss the conceptual implications of our observation to the security of cryptographic protocols that make use of BB84 states.

quant-ph↗

arXiv2017

Entropic Uncertainty Relations and their Applications

Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty principle and, hence, play an important role in quantum foundations. More recently, entropic uncertainty relations have emerged as the central ingredient in the security analysis of almost all quantum cryptographic protocols, such as quantum key distribution and two-party quantum cryptography. This review surveys entropic uncertainty relations that capture Heisenberg's idea that the results of incompatible measurements are impossible to predict, covering both finite- and infinite-dimensional measurements. These ideas are then extended to incorporate quantum correlations between the observed object and its environment, allowing for a variety of recent, more general formulations of the uncertainty principle. Finally, various applications are discussed, ranging from entanglement witnessing to wave-particle duality to quantum cryptography.

quant-ph↗

arXiv2016

Capacity estimation and verification of quantum channels with arbitrarily correlated errors

One of the main figures of merit for quantum memories and quantum communication devices is their quantum capacity. It has been studied for arbitrary kinds of quantum channels, but its practical estimation has so far been limited to devices that implement independent and identically distributed (i.i.d.) quantum channels, where each qubit is affected by the same noise process. Real devices, however, typically exhibit correlated errors. Here, we overcome this limitation by presenting protocols that estimate a channel's one-shot quantum capacity for the case where the device acts on (an arbitrary number of) qubits. The one-shot quantum capacity quantifies a device's ability to store or communicate quantum information, even if there are correlated errors across the different qubits. We present a protocol which is easy to implement and which comes in two versions. The first version estimates the one-shot quantum capacity by preparing and measuring in two different bases, where all involved qubits are used as test qubits. The second version verifies on-the-fly that a channel's one-shot quantum capacity exceeds a minimal tolerated value while storing or communicating data, therefore combining test qubits and data qubits in one protocol. We discuss the performance of our method using simple examples, such as the dephasing channel for which our method is asymptotically optimal. Finally, we apply our method to estimate the one-shot capacity in an experiment using a transmon qubit.

quant-ph↗

arXiv2016

Contextuality without nonlocality in a superconducting quantum system

Classical realism demands that system properties exist independently of whether they are measured, while noncontextuality demands that the results of measurements do not depend on what other measurements are performed in conjunction with them. The Bell-Kochen-Specker theorem states that noncontextual realism cannot reproduce the measurement statistics of a single three-level quantum system (qutrit). Noncontextual realistic models may thus be tested using a single qutrit without relying on the notion of quantum entanglement in contrast to Bell inequality tests. It is challenging to refute such models experimentally, since imperfections may introduce loopholes that enable a realist interpretation. Here we use a superconducting qutrit with deterministic, binary-outcome readouts to violate a noncontextuality inequality while addressing the detection, individual-existence and compatibility loopholes. This evidence of state-dependent contextuality also demonstrates the fitness of superconducting quantum circuits for fault-tolerant quantum computation in surface-code architectures, currently the most promising route to scalable quantum computing.

quant-ph↗

arXiv2016

Shortcuts to quantum network routing

A quantum network promises to enable long distance quantum communication, and assemble small quantum devices into a large quantum computing cluster. Each network node can thereby be seen as a small few qubit quantum computer. Qubits can be sent over direct physical links connecting nearby quantum nodes, or by means of teleportation over pre-established entanglement amongst distant network nodes. Such pre-shared entanglement effectively forms a shortcut - a virtual quantum link - which can be used exactly once. Here, we present an abstraction of a quantum network that allows ideas from computer science to be applied to the problem of routing qubits, and manage entanglement in the network. Specifically, we consider a scenario in which each quantum network node can create EPR pairs with its immediate neighbours over a physical connection, and perform entanglement swapping operations in order to create long distance virtual quantum links. We proceed to discuss the features unique to quantum networks, which call for the development of new routing techniques. As an example, we present two simple hierarchical routing schemes for a quantum network of N nodes for a ring and sphere topology. For these topologies we present efficient routing algorithms requiring O(log N) qubits to be stored at each network node, O(polylog N) time and space to perform routing decisions, and O(log N) timesteps to replenish the virtual quantum links in a model of entanglement generation.

cs.NI↗

arXiv2016

Device-independence for two-party cryptography and position verification

Quantum communication has demonstrated its usefulness for quantum cryptography far beyond quantum key distribution. One domain is two-party cryptography, whose goal is to allow two parties who may not trust each other to solve joint tasks. Another interesting application is position-based cryptography whose goal is to use the geographical location of an entity as its only identifying credential. Unfortunately, security of these protocols is not possible against an all powerful adversary. However, if we impose some realistic physical constraints on the adversary, there exist protocols for which security can be proven, but these so far relied on the knowledge of the quantum operations performed during the protocols. In this work we give device-independent security proofs of two-party cryptography and Position Verification for memoryless devices under different physical constraints on the adversary. We assess the quality of the devices by observing a Bell violation and we show that security can be attained for any violation of the Clauser-Holt-Shimony-Horne inequality.

quant-ph↗

arXiv2016

Surpassing the Carnot Efficiency by extracting imperfect work

A suitable way of quantifying work for microscopic quantum systems has been constantly debated in the field of quantum thermodynamics. One natural approach is to measure the average increase in energy of an ancillary system, called the battery, after a work extraction protocol. The quality of energy extracted is usually argued to be good by quantifying higher moments of the energy distribution, or by restricting the amount of entropy to be low. This limits the amount of heat contribution to the energy extracted, but does not completely prevent it. We show that the definition of "work" is crucial. If one allows for a definition of work that tolerates a non-negligible entropy increase in the battery, then a small scale heat engine can possibly exceed the Carnot efficiency. This can be achieved even when one of the heat baths is finite in size.

quant-ph↗

arXiv2016

Entropic uncertainty and measurement reversibility

The entropic uncertainty relation with quantum side information (EUR-QSI) from [Berta et al., Nat. Phys. 6, 659 (2010)] is a unifying principle relating two distinctive features of quantum mechanics: quantum uncertainty due to measurement incompatibility, and entanglement. In these relations, quantum uncertainty takes the form of preparation uncertainty where one of two incompatible measurements is applied. In particular, the "uncertainty witness" lower bound in the EUR-QSI is not a function of a post-measurement state. An insightful proof of the EUR-QSI from [Coles et al., Phys. Rev. Lett. 108, 210405 (2012)] makes use of a fundamental mathematical consequence of the postulates of quantum mechanics known as the non-increase of quantum relative entropy under quantum channels. Here, we exploit this perspective to establish a tightening of the EUR-QSI which adds a new state-dependent term in the lower bound, related to how well one can reverse the action of a quantum measurement. As such, this new term is a direct function of the post-measurement state and can be thought of as quantifying how much disturbance a given measurement causes. Our result thus quantitatively unifies this feature of quantum mechanics with the others mentioned above. We have experimentally tested our theoretical predictions on the IBM Quantum Experience and find reasonable agreement between our predictions and experimental outcomes.

quant-ph↗

arXiv2016

Sifting attacks in finite-size quantum key distribution

A central assumption in quantum key distribution (QKD) is that Eve has no knowledge about which rounds will be used for parameter estimation or key distillation. Here we show that this assumption is violated for iterative sifting, a sifting procedure that has been employed in some (but not all) of the recently suggested QKD protocols in order to increase their efficiency. We show that iterative sifting leads to two security issues: (1) some rounds are more likely to be key rounds than others, (2) the public communication of past measurement choices changes this bias round by round. We analyze these two previously unnoticed problems, present eavesdropping strategies that exploit them, and find that the two problems are independent. We discuss some sifting protocols in the literature that are immune to these problems. While some of these would be inefficient replacements for iterative sifting, we find that the sifting subroutine of an asymptotically secure protocol suggested by Lo et al (2005 J. Cryptol. 18 133-65), which we call LCA sifting, has an efficiency on par with that of iterative sifting. One of our main results is to show that LCA sifting can be adapted to achieve secure sifting in the finite-key regime. More precisely, we combine LCA sifting with a certain parameter estimation protocol, and we prove the finite-key security of this combination. Hence we propose that LCA sifting should replace iterative sifting in future QKD implementations. More generally, we present two formal criteria for a sifting protocol that guarantee its finite-key security. Our criteria may guide the design of future protocols and inspire a more rigorous QKD analysis, which has neglected sifting-related attacks so far.

quant-ph↗