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Seth Lloyd

Publications and source records attributed to Seth Lloyd.

At least 109 records · Page 6Linked to original sources
arXiv2016

Decoherent histories approach to the cosmological measure problem

The method of decoherent histories allows probabilities to be assigned to sequences of quantum events in systems, such as the universe as a whole, where there is no external observer to make measurements. This paper applies the method of decoherent histories to address cosmological questions. Using a series of simple examples, beginning with the harmonic oscillator, we show that systems in a stationary state such as an energy eigenstate or thermal state can exhibit decoherent histories with non-trivial dynamics. We then examine decoherent histories in a universe that undergoes eternal inflation. Decoherent histories that assign probabilities to sequences of events in the vicinity of a timelike geodesic supply a natural cosmological measure. Under reasonable conditions, such sequences of events do not suffer from the presence of unlikely statistical fluctuations that mimic reality.

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arXiv2016

A Quantum Enigma Machine: Experimentally Demonstrating Quantum Data Locking

Claude Shannon proved in 1949 that information-theoretic-secure encryption is possible if the encryption key is used only once, is random, and is at least as long as the message itself. Notwithstanding, when information is encoded in a quantum system, the phenomenon of quantum data locking allows one to encrypt a message with a shorter key and still provide information-theoretic security. We present one of the first feasible experimental demonstrations of quantum data locking for direct communication and propose a scheme for a quantum enigma machine that encrypts 6 bits per photon (containing messages, new encryption keys, and forward error correction bits) with less than 6 bits per photon of encryption key while remaining information-theoretically secure.

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arXiv2016

Quantum singular value decomposition of non-sparse low-rank matrices

In this work, we present a method to exponentiate non-sparse indefinite low-rank matrices on a quantum computer. Given an operation for accessing the elements of the matrix, our method allows singular values and associated singular vectors to be found quantum mechanically in a time exponentially faster in the dimension of the matrix than known classical algorithms. The method extends to non-Hermitian and non-square matrices via embedding matrices. In the context of the generic singular value decomposition of a matrix, we discuss the Procrustes problem of finding a closest isometry to a given matrix.

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arXiv2016

Passive states as optimal inputs for single-jump lossy quantum channels

The passive states of a quantum system minimize the average energy among all the states with a given spectrum. We prove that passive states are the optimal inputs of single-jump lossy quantum channels. These channels arise from a weak interaction of the quantum system of interest with a large Markovian bath in its ground state, such that the interaction Hamiltonian couples only consecutive energy eigenstates of the system. We prove that the output generated by any input state $ρ$ majorizes the output generated by the passive input state $ρ_0$ with the same spectrum of $ρ$. Then, the output generated by $ρ$ can be obtained applying a random unitary operation to the output generated by $ρ_0$. This is an extension of De Palma et al., IEEE Trans. Inf. Theory 62, 2895 (2016), where the same result is proved for one-mode bosonic Gaussian channels. We also prove that for finite temperature this optimality property can fail already in a two-level system, where the best input is a coherent superposition of the two energy eigenstates.

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arXiv2016

The power of one qumode for quantum computation

Although quantum computers are capable of solving problems like factoring exponentially faster than the best-known classical algorithms, determining the resources responsible for their computational power remains unclear. An important class of problems where quantum computers possess an advantage is phase estimation, which includes applications like factoring. We introduce a new computational model based on a single squeezed state resource that can perform phase estimation, which we call the power of one qumode. This model is inspired by an interesting computational model known as deterministic quantum computing with one quantum bit (DQC1). Using the power of one qumode, we identify that the amount of squeezing is sufficient to quantify the resource requirements of different computational problems based on phase estimation. In particular, it establishes a quantitative relationship between the resources required for factoring and DQC1. For example, we find the squeezing required to factor has an exponential scaling whereas no squeezing (i.e., a coherent state) is already sufficient to solve the hardest problem in DQC1.

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arXiv2016

Quantum data hiding in the presence of noise

When classical or quantum information is broadcast to separate receivers, there exist codes that encrypt the encoded data such that the receivers cannot recover it when performing local operations and classical communication, but they can decode reliably if they bring their systems together and perform a collective measurement. This phenomenon is known as quantum data hiding and hitherto has been studied under the assumption that noise does not affect the encoded systems. With the aim of applying the quantum data hiding effect in practical scenarios, here we define the data-hiding capacity for hiding classical information using a quantum channel. Using this notion, we establish a regularized upper bound on the data hiding capacity of any quantum broadcast channel, and we prove that coherent-state encodings have a strong limitation on their data hiding rates. We then prove a lower bound on the data hiding capacity of channels that map the maximally mixed state to the maximally mixed state (we call these channels "mictodiactic"---they can be seen as a generalization of unital channels when the input and output spaces are not necessarily isomorphic) and argue how to extend this bound to generic channels and to more than two receivers.

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arXiv2016

Chiral Quantum Walks

Given its importance to many other areas of physics, from condensed matter physics to thermodynamics, time-reversal symmetry has had relatively little influence on quantum information science. Here we develop a network-based picture of time-reversal theory, classifying Hamiltonians and quantum circuits as time-symmetric or not in terms of the elements and geometries of their underlying networks. Many of the typical circuits of quantum information science are found to exhibit time-asymmetry. Moreover, we show that time-asymmetry in circuits can be controlled using local gates only, and can simulate time-asymmetry in Hamiltonian evolution. We experimentally implement a fundamental example in which controlled time-reversal asymmetry in a palindromic quantum circuit leads to near-perfect transport. Our results pave the way for using time-symmetry breaking to control coherent transport, and imply that time-asymmetry represents an omnipresent yet poorly understood effect in quantum information science.

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arXiv2016

Global coherence of quantum evolutions based on decoherent histories: theory and application to photosynthetic quantum energy transport

Assessing the role of interference in natural and artificial quantum dyanamical processes is a crucial task in quantum information theory. To this aim, an appopriate formalism is provided by the decoherent histories framework. While this approach has been deeply explored from different theoretical perspectives, it still lacks of a comprehensive set of tools able to concisely quantify the amount of coherence developed by a given dynamics. In this paper we introduce and test different measures of the (average) coherence present in dissipative (Markovian) quantum evolutions, at various time scales and for different levels of environmentally induced decoherence. In order to show the effectiveness of the introduced tools, we apply them to a paradigmatic quantum process where the role of coherence is being hotly debated: exciton transport in photosynthetic complexes. To spot out the essential features that may determine the performance of the transport we focus on a relevant trimeric subunit of the FMO complex and we use a simplified (Haken-Strobl) model for the system-bath interaction. Our analysis illustrates how the high efficiency of environmentally assisted transport can be traced back to a quantum recoil avoiding effect on the exciton dynamics, that preserves and sustains the benefits of the initial fast quantum delocalization of the exciton over the network. Indeed, for intermediate levels of decoherence, the bath is seen to selectively kill the negative interference between different exciton pathways, while retaining the initial positive one. The concepts and tools here developed show how the decoherent histories approach can be used to quantify the relation between coherence and efficiency in quantum dynamical processes.

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arXiv2016

Time Independent Universal Computing with Spin Chains: Quantum Plinko Machine

We present a scheme for universal quantum computing using XY Heisenberg spin chains. Information is encoded into packets propagating down these chains, and they interact with each other to perform universal quantum computation. A circuit using g gate blocks on m qubits can be encoded into chains of length $O(g^{3+δ} m^{3+δ})$ for all $δ>0$ with vanishingly small error.

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arXiv2015

Core-halo instability in dynamical systems

This paper proves an instability theorem for dynamical systems. As one adds interactions between subystems in a complex system, structured or random, a threshold of connectivity is reached beyond which the overall dynamics inevitably goes unstable. The threshold occurs at the point at which flows and interactions between subsystems (`surface' effects) overwhelm internal stabilizing dynamics (`volume' effects). The theorem is used to identify instability thresholds in systems that possess a core-halo or core-periphery structure, including the gravo-thermal catastrophe -- i.e., star collapse and explosion -- and the interbank payment network. In the core-halo model, the same dynamical instability underlies both gravitational and financial collapse.

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arXiv2015

Quantum algorithms for topological and geometric analysis of big data

Extracting useful information from large data sets can be a daunting task. Topological methods for analyzing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying such topological features -- connected components, holes, or voids -- and for determining how such features persist as the data is viewed at different scales. This paper provides quantum algorithms for calculating Betti numbers in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian. The algorithms provide an exponential speedup over classical algorithms for topological data analysis.

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arXiv2015

Continuous-variable quantum enigma machines for long-distance key distribution

Quantum physics allows for unconditionally secure communication through insecure communication channels. The achievable rates of quantum-secured communication are fundamentally limited by the laws of quantum physics and in particular by the properties of entanglement. For a lossy communication line, this implies that the secret-key generation rate vanishes at least exponentially with the communication distance. We show that this fundamental limitation can be violated in a realistic scenario where the eavesdropper can store quantum information for only a finite, yet arbitrarily long, time. We consider communication through a lossy bononic channel (modeling linear loss in optical fibers) and we show that it is in principle possible to achieve a constant rate of key generation of one bit per optical mode over arbitrarily long communication distances.

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arXiv2015

Adiabatic and Hamiltonian computing on a 2D lattice with simple 2-qubit interactions

We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this construction, the movement of one particle is controlled by the presence or absence of other particles, an effective quantum field effect transistor that allows the construction of controlled-NOT and controlled-rotation gates. The construction translates into a model for universal quantum computation with time-independent 2-qubit ZZ and XX+YY interactions on an (almost) planar grid. The effective Hamiltonian is arrived at by a single use of first-order perturbation theory avoiding the use of perturbation gadgets. The dynamics and spectral properties of the effective Hamiltonian can be fully determined as it corresponds to a particular realization of a mapping between a quantum circuit and a Hamiltonian called the space-time circuit-to-Hamiltonian construction. Because of the simple interactions required, and because no higher-order perturbation gadgets are employed, our construction is potentially realizable using superconducting or other solid-state qubits.

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arXiv2015

Quantum Time

We give a consistent quantum description of time, based on Page and Wootters' conditional probabilities mechanism, that overcomes the criticisms that were raised against similar previous proposals. In particular we show how the model allows to reproduce the correct statistics of sequential measurements performed on a system at different times.

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arXiv2015

MDI-QKD: Continuous- versus discrete-variables at metropolitan distances

In a comment, Xu, Curty, Qi, Qian, and Lo claimed that discrete-variable (DV) measurement device independent (MDI) quantum key distribution (QKD) would compete with its continuous-variable (CV) counterpart at metropolitan distances. Actually, Xu et al.'s analysis supports exactly the opposite by showing that the experimental rate of our CV protocol (achieved with practical room-temperature devices) remains one order of magnitude higher than their purely-numerical and over-optimistic extrapolation for qubits, based on nearly-ideal parameters and cryogenic detectors (unsuitable solutions for a realistic metropolitan network, which is expected to run on cheap room-temperature devices, potentially even mobile). The experimental rate of our protocol (expressed as bits per relay use) is confirmed to be two-three orders of magnitude higher than the rate of any realistic simulation of practical DV-MDI-QKD over short-medium distances. Of course this does not mean that DV-MDI-QKD networks should not be investigated or built, but increasing their rate is a non-trivial practical problem clearly beyond the analysis of Xu et al. Finally, in order to clarify the facts, we also refute a series of incorrect arguments against CV-MDI-QKD and, more generally, CV-QKD, which were made by Xu et al. with the goal of supporting their thesis.

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arXiv2015

Quantum data locking for high-rate private communication

We show that, if the accessible information is used as a security quantifier, quantum channels with a certain symmetry can convey private messages at a tremendously high rate, as high as less than one bit below the rate of non-private classical communication. This result is obtained by exploiting the quantum data locking effect. The price to pay to achieve such a high private communication rate is that accessible information security is in general not composable. However, composable security holds against an eavesdropper who is forced to measure her share of the quantum system within a finite time after she gets it.

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