Author(s): Jae-Mo Lihm, Kyungjoo Noh, and Uwe R. Fischer

Autonomous quantum error correction utilizes the engineered coupling of a quantum system to a dissipative ancilla to protect quantum logical states from decoherence. We show that the Knill-Laflamme condition, stating that the environmental error operators should act trivially on a subspace, which th...

[Phys. Rev. A 98, 012317] Published Mon Jul 16, 2018

A recommendation system suggests products to users based on data about user preferences. It is typically modeled by a problem of completing an $m\times n$ matrix of small rank $k$. We give the first classical algorithm to produce a recommendation in $O(\text{poly}(k)\text{polylog}(m,n))$ time, which is an exponential improvement on previous algorithms that run in time linear in $m$ and $n$. Our strategy is inspired by a quantum algorithm by Kerenidis and Prakash: like the quantum algorithm, instead of reconstructing a user's full list of preferences, we only seek a randomized sample from the user's preferences. Our main result is an algorithm that samples high-weight entries from a low-rank approximation of the input matrix in time independent of $m$ and $n$, given natural sampling assumptions on that input matrix. As a consequence, we show that Kerenidis and Prakash's quantum machine learning (QML) algorithm, one of the strongest candidates for provably exponential speedups in QML, does not in fact give an exponential speedup over classical algorithms.

We demonstrate niobium nitride based superconducting single-photon detectors sensitive in the spectral range $457$ nm - $2300$ nm. The system performance was tested in a real-life experiment with correlated photons generated by means of spontaneous parametric down conversion, where one of photon was in the visible range and the other was in the infrared range. We measured a signal to noise ratio as high as $4\times 10^4$ in our detection setting. A photon detection efficiency as high as $64$ % at $1550$ nm and $15$ % at $2300$ nm was observed.

Security analyses of quantum cryptographic protocols typically rely on certain conditions; one such condition is that the sender (Alice) and receiver (Bob) have isolated devices inaccessible to third parties. If an eavesdropper (Eve) has a side-channel into one of the devices, then the key rate may be sensibly reduced. In this paper, we consider an attack on a coherent-state protocol, where Eve not only taps the main communication channel but also hacks Alice's device. This is done by introducing a Trojan horse mode with low mean number of photons $\bar{n}$ which is then modulated in a similar way to the signal state. First we show that this strategy can be reduced to an attack without side channels but with higher loss and noise in the main channel. Then we show how the key rate rapidly deteriorates for increasing photons $\bar{n}$, being halved at long distances each time $\bar{n}+1$ doubles. Our work suggests that Alice's device should also be equipped with sensing systems that are able to detect and estimate the total number of incoming and outgoing photons.

There has been a concerted effort to identify problems computable with quantum technology which are intractable with classical technology or require far fewer resources to compute. Recently, randomness processing in a Bernoulli factory has been identified as one such task. Here, we report two quantum photonic implementations of a Bernoulli factory, one utilising quantum coherence and single-qubit measurements and the other which uses quantum coherence and entangling measurements of two qubits. We show that the former consumes three orders of magnitude fewer resources than the best known classical method, while entanglement offers a further five-fold reduction. These concepts may provide a means for quantum enhanced-performance in the simulation of stochastic processes and sampling tasks.

A quantum particle in an infinite one-dimensional well potential is considered. Let the boundaries of well changes in a finite time $T$. The standard methods for calculating probability of transition from an initial to the final state are in general inapplicable since the states of different wells belong to different Hilbert spaces. If the final well covers only a part of the initial well (and, possibly, some outer part of the configuration space), the total probability of the transition from any stationary state of the initial well into {\bf all} possible states of the final well is less than 1 at $T\to 0$. If the problem is regularized with a finite-height potential well, this missing probability can be understood as a non-zero probability of transitions into the continuous spectrum, despite the fact that this spectrum disappears at the removal of regularization. This phenomenon ("transition to nowhere") can result important phenomena in some fundamental problems. We discuss also how to calculate the probabilities of discussed transitions at final $T$ for some ranges of parameters.

We consider a bipartite quantum conductor and analyze fluctuations of heat quantity in a subsystem as well as self-information associated with the reduced-density matrix of the subsystem. By exploiting the multi-contour Keldysh technique, we calculate the R\'enyi entropy, or the information generating function, subjected to the constraint of the local heat quantity of the subsystem, from which the probability distribution of conditional self-information is derived. We present an equality that relates the optimum capacity of information transmission and the R\'enyi entropy of order 0, which is the number of integer partitions into distinct parts. We apply our formalism to a two-terminal quantum dot. We point out that in the steady state, the reduced-density matrix and the operator of the local heat quantity of the subsystem may be commutative.

We have measured the low-frequency time instability known as charge offset drift of Si/SiO$_2$ single electron devices (SEDs) with and without an overall poly-Si top gate. We find that SEDs with a poly-Si top gate have significantly less charge offset drift, exhibiting fewer isolated jumps and a factor of two reduction in fluctuations about a stable mean value. The observed reduction can be accounted for by the electrostatic reduction in the mutual capacitance $C_m$ between defects and the quantum dot, and increase in the total defect capacitance $C_d$ due to the top gate. These results depart from the accepted understanding that the level of charge offset drift in SEDs is determined by the intrinsic material properties, forcing consideration of the device design as well. We expect these results to be of importance in developing SEDs for applications from quantum information to metrology or wherever charge noise or integrability of devices is a challenge.

Recently, physicists have started applying quantum information theory to black holes. This led to the conjecture that black holes are the fastest scramblers of information, and that they scramble it in time order M log M, where M is the mass of the black hole in natural units. As stated above, the conjecture is not completely defined, as there are several possible definitions of scrambling times. It appears that not all papers that refer to this conjecture interpret it the same way. We consider a definition of scrambling time stronger than the one given in the paper that first proposed this conjecture [Sekino and Susskind, JHEP 0810:065 (2008)], and show that this stronger version of the conjecture appears to be incompatible with a number of other widely-believed and reasonable-sounding properties of black holes.

We argue that for the scrambling time of a black hole to be this fast, either relativity is violated or non-standard physics must be occurring outside the stretched event horizon of a black hole. More specifically, either information is being transferred faster than relativity would permit, the information is not carried by the Hawking radiation and thus must be carried by unknown physics, or the Hawking radiation carries much more information than standard thermodynamics would permit.

In classical mechanics, external constraints on the dynamical variables can be easily implemented within the Lagrangian formulation and form the basis for several interesting mechanical phenomena and devices. Conversely, the extension of this idea to the quantum realm, which dates back to Dirac, has proven notoriously difficult due to the non-commutativity of observables. Motivated by recent progress in the experimental control of quantum systems, we propose here an implementation of quantum constraints based on the idea of work protocols, which are dynamically engineered to enfore the constraints. As a proof of principle, we consider a quantum harmonic oscillator and show how the combination of two work protocols can be used to implement non-trivial constraints in quantum phase space which couple together the first and second moments of the quadrature operators. We find that such constraints affect the equations of motion for the system in a non-trivial way, inducing non-linear behavior and even classical chaos, although Gaussianity is preserved at all times. A discussion concerning the robustness of this approach to possible experimental errors is also presented.

Silicon photonics holds the promise of the miniaturization of quantum communication devices. Recently, silicon chip optical transmitters for quantum key distribution (QKD) have been built and demonstrated experimentally. Nonetheless, these silicon chips suffer substantial polarization and phase dependent loss which, if unchecked, could compromise the security of QKD systems. Here, we first restore the security by regarding the single photons without phase and polarization dependence as untagged and secure qubits. Next, by using a post-selection technique, one could implement a secure QKD protocol that provides a high key generation rate even in the presence of severe phase and polarization dependent loss. Our solution is simple to realize in a practical experiment as it does not require any hardware modification.

We consider two quantization approaches to the Bateman oscillator model. One is Feshbach-Tikochinsky's quantization approach reformulated concisely without invoking the ${\mathit{SU}(1,1)}$ Lie algebra, and the other is the imaginary-scaling quantization approach developed originally for the Pais-Uhlenbeck oscillator model. The latter approach overcomes the problem of unbounded-below energy spectrum that is encountered in the former approach. In both the approaches, the positive-definiteness of the squared-norms of the Hamiltonian eigenvectors is ensured. Unlike Feshbach-Tikochinsky's quantization approach, the imaginary-scaling quantization approach allows to have stable states in addition to decaying and growing states.

We formulate Nielsen's geometric approach to complexity in the context of two dimensional conformal field theories, where series of conformal transformations are interpreted as "unitary circuits". We argue that, at large central charge, this approach naturally leads to the geometric action on the coadjoint orbits of the Virasoro group. This action is directly connected to the Polyakov action of two dimensional gravity, which therefore sets the rules for optimal quantum computation in conformal field theories.

Reversible lattice dynamics embody basic features of physics that govern the time evolution of classical information. They have finite resolution in space and time, don't allow information to be erased, and easily accommodate other structural properties of microscopic physics, such as finite distinct state and locality of interaction. In an ideal quantum realization of a reversible lattice dynamics, finite classical rates of state-change at lattice sites determine average energies and momenta. This is very different than traditional continuous models of classical dynamics, where the number of distinct states is infinite, the rate of change between distinct states is infinite, and energies and momenta are not tied to rates of distinct state change. Here we discuss a family of classical mechanical models that have the informational and energetic realism of reversible lattice dynamics, while retaining the continuity and mathematical framework of classical mechanics. These models may help to clarify the informational foundations of mechanics.

Toward an alternative approach to the quantum mechanic ground state search, we theoretically introduce a protocol in which energy of two identical systems are deterministically exchanged. The protocol utilizes a quantum interference between "forward" and "backward" time evolved states with respect to a given Hamiltonian. In addition, to make use the protocol for the ground state search, we construct a network with which we may be able to efficiently apply the protocol successively among multiple systems so that energy of one of them is gradually approaching the lowest one. Although rigorous analysis on the validity of the network is left as a future challenge, some properties of the network are also investigated.

The nitrogen-vacancy (NV) center in diamond allows room-temperature wide-field quantum magnetometry and metrology for a small volume, which is an important technology for applications in biology. Although coherence of the NV center has a limited frequency resolution of diamond magnetometry to 10-100 kHz, recent studies have shown that a phase sensitive protocol can beat the coherence limit on a confocal setup. Here, we report a new measurement protocol, "iQdyne," for improving the frequency resolution of wide-field imaging beyond the coherence limit of the NV center. We demonstrate wide-field magnetometry with a frequency resolution of 238 mHz and a magnetic sensitivity of 65 nT/sqrtHz, which are superior to the conventional XY8-based technique, which paves the way to in vivo microscale nuclear magnetic resonance imaging. We find that the experimental performance of iQdyne agrees well with that of an analytical model.

We analyze the security of two multipartite quantum key distribution (QKD) protocols, specifically we introduce an $N$-partite version of the BB84 protocol and we discuss the $N$-partite six-state protocol proposed in arXiv:1612.05585v2 . The security analysis proceeds from the generalization of known results in bipartite QKD to the multipartite scenario, and takes into account finite resources. In this context we derive a computable expression for the achievable key rate of both protocols by employing the best-known strategies: the uncertainty relation and the postselection technique. We compare the performances of the two protocols both for finite resources and infinitely many signals.

The correlation properties of the pump field in spontaneous parametric down-conversion are crucial in determining the degree of entanglement of generated signal and idler photons. We find theoretically that continuous-variable entanglement of the transverse positions and momenta of these photons can be achieved only if the coherence of the pump beam is sufficiently high. The positions of signal and idler photons are found to be correlated, even for an incoherent pump. However, the momenta of the signal and idler photons are not anti-correlated, even though transverse momentum is conserved.

Berry phase, the geometric phase accumulated in cyclic adiabatic evolution, has been commonly used to define topological invariants for equilibrium states. Pancharatnam geometric phase, a purely geometric phase accumulated in generic time-evolution, extends the Berry phase to non-adiabatic and non-cyclic dynamics. Theoretically, the Pancharatnam geometric phase can perfectly identify dynamical phase transitions in quenched systems, which are analog to equilibrium phase transitions in the Ginzburg-Landau paradigm. However, due to the great challenge in eliminating the dynamical phase during a non-cyclic evolution, it is hard to observe the Pancharatnam geometric phase in dynamical phase transitions. Here, we directly observe the Pancharatnam geometric phase after sudden quenches from a topological edge state in the Su-Schrieffer-Heeger model, which is realized by a reconfigurable array of nanomechanical oscillators. Due to the chiral symmetry in our system, the initial edge state equally populates all symmetrical pairs of final eigenstates and so that the dynamical phase is naturally eliminated. We found that, the Pancharatnam geometric phase jumps $\pi$ at each critical time when dynamical phase transition takes place, otherwise the Pancharatnam geometric phase keeps unchanged. This work not only provides a quantitative method to identify dynamical phase transitions, but also paves the way to reveal the bulk-edge correspondence for dynamical phase transitions in topological systems.

We report the first quantum key distribution (QKD) systems capable of delivering sustainable, real-time secure keys continuously at rates exceeding 10 Mb/s. To achieve such rates, we developed high speed post-processing modules, achieving maximum data throughputs of 60 MC/s, 55 Mb/s, and 108 Mb/s for standalone operation of sifting, error correction and privacy amplification modules, respectively. The photonic layer of the QKD systems features high-speed single photon detectors based on self-differencing InGaAs avalanche photodiodes, phase encoding using asymmetric Mach-Zehnder interferometer, and active stabilization of the interferometer phase and photon polarisation. An efficient variant of the decoy-state BB84 protocol is implemented for security analysis, with a large dataset size of $10^8$ bits selected to mitigate finite-size effects. Over a 2 dB channel, a record secure key rate of 13.72 Mb/s has been achieved averaged over 4.4 days of operation. We confirm the robustness and long-term stability on a second QKD system continuously running for 1 month without any user intervention.