arXiv subjects

Dominic W. Berry

Publications and source records attributed to Dominic W. Berry.

At least 91 records · Page 5Linked to original sources

arXiv2013

Swarm optimization for adaptive phase measurements with low visibility

Adaptive feedback normally provides the greatest accuracy for optical phase measurements. New advances in nitrogen vacancy centre technology have enabled magnetometry via individual spin measurements, which are similar to optical phase measurements but with low visibility. The adaptive measurements that previously worked well with high-visibility optical interferometry break down and give poor results for nitrogen vacancy centre measurements. We use advanced search techniques based on swarm optimisation to design better adaptive measurements that can provide improved measurement accuracy with low-visibility interferometry, with applications in nitrogen vacancy centre magnetometry.

quant-ph↗

arXiv2013

Exponential improvement in precision for Hamiltonian-evolution simulation

We provide a quantum method for simulating Hamiltonian evolution with complexity polynomial in the logarithm of the inverse error. This is an exponential improvement over existing methods for Hamiltonian simulation. In addition, its scaling with respect to time is close to linear, and its scaling with respect to the time derivative of the Hamiltonian is logarithmic. These scalings improve upon most existing methods. Our method is to use a compressed Lie-Trotter formula, based on recent ideas for efficient discrete-time simulations of continuous-time quantum query algorithms.

quant-ph↗

arXiv2013

Solovay-Kitaev Decomposition Strategy for Single-Qubit Channels

Inspired by the Solovay-Kitaev decomposition for approximating unitary operations as a sequence of operations selected from a universal quantum computing gate set, we introduce a method for approximating any single-qubit channel using single-qubit gates and the controlled-NOT (CNOT). Our approach uses the decomposition of the single-qubit channel into a convex combination of "quasiextreme" channels. Previous techniques for simulating general single-qubit channels would require as many as 20 CNOT gates, whereas ours only needs one, bringing it within the range of current experiments.

quant-ph↗

arXiv2013

Stochastic Heisenberg limit: Optimal estimation of a fluctuating phase

The ultimate limits to estimating a fluctuating phase imposed on an optical beam can be found using the recently derived continuous quantum Cramer-Rao bound. For Gaussian stationary statistics, and a phase spectrum scaling asymptotically as 1/omega^p with p>1, the minimum mean-square error in any (single-time) phase estimate scales as N^{-2(p-1)/(p+1)}, where N is the photon flux. This gives the usual Heisenberg limit for a constant phase (as the limit p--> infinity) and provides a stochastic Heisenberg limit for fluctuating phases. For p=2 (Brownian motion), this limit can be attained by phase tracking.

quant-ph↗

arXiv2013

Gate-efficient discrete simulations of continuous-time quantum query algorithms

We show how to efficiently simulate continuous-time quantum query algorithms that run in time T in a manner that preserves the query complexity (within a polylogarithmic factor) while also incurring a small overhead cost in the total number of gates between queries. By small overhead, we mean T within a factor that is polylogarithmic in terms of T and a cost measure that reflects the cost of computing the driving Hamiltonian. This permits any continuous-time quantum algorithm based on an efficiently computable driving Hamiltonian to be converted into a gate-efficient algorithm with similar running time.

quant-ph↗

arXiv2012

Optimal Heisenberg-style bounds for the average performance of arbitrary phase estimates

The ultimate bound to the accuracy of phase estimates is often assumed to be given by the Heisenberg limit. Recent work seemed to indicate that this bound can be violated, yielding measurements with much higher accuracy than was previously expected. The Heisenberg limit can be restored as a rigorous bound to the accuracy provided one considers the accuracy averaged over the possible values of the unknown phase, as we have recently shown [Phys. Rev. A 85, 041802(R) (2012)]. Here we present an expanded proof of this result together with a number of additional results, including the proof of a previously conjectured stronger bound in the asymptotic limit. Other measures of the accuracy are examined, as well as other restrictions on the generator of the phase shifts. We provide expanded numerical results for the minimum error and asymptotic expansions. The significance of the results claiming violation of the Heisenberg limit is assessed, followed by a detailed discussion of the limitations of the Cramer-Rao bound.

quant-ph↗

arXiv2012

Quantum-enhanced optical phase tracking

Tracking a randomly varying optical phase is a key task in metrology, with applications in optical communication. The best precision for optical phase tracking has till now been limited by the quantum vacuum fluctuations of coherent light. Here we surpass this coherent-state limit by using a continuous-wave beam in a phase-squeezed quantum state. Unlike in previous squeezing-enhanced metrology, restricted to phases with very small variation, the best tracking precision (for a fixed light intensity) is achieved for a finite degree of squeezing, due to Heisenberg's uncertainty principle. By optimizing the squeezing we track the phase with a mean square error 15 \pm 4 % below the coherent-state limit.

quant-ph↗

arXiv2012

Universality of the Heisenberg limit for estimates of random phase shifts

The Heisenberg limit traditionally provides a lower bound on the phase uncertainty scaling as 1/ , where is the mean number of photons in the probe. However, this limit has a number of loopholes which potentially might be exploited, to achieve measurements with even greater accuracy. Here we close these loopholes by proving a completely rigorous form of the Heisenberg limit for the average error over all phase shifts. Our result gives the first completely general, constraint-free and non-asymptotic statement of the Heisenberg limit. It holds for all phase estimation schemes, including multiple passes, nonlinear phase shifts, multimode probes, and arbitrary measurements.

quant-ph↗

arXiv2011

Black-box Hamiltonian simulation and unitary implementation

We present general methods for simulating black-box Hamiltonians using quantum walks. These techniques have two main applications: simulating sparse Hamiltonians and implementing black-box unitary operations. In particular, we give the best known simulation of sparse Hamiltonians with constant precision. Our method has complexity linear in both the sparseness D (the maximum number of nonzero elements in a column) and the evolution time t, whereas previous methods had complexity scaling as D^4 and were superlinear in t. We also consider the task of implementing an arbitrary unitary operation given a black-box description of its matrix elements. Whereas standard methods for performing an explicitly specified N x N unitary operation use O(N^2) elementary gates, we show that a black-box unitary can be performed with bounded error using O(N^{2/3} (log log N)^{4/3}) queries to its matrix elements. In fact, except for pathological cases, it appears that most unitaries can be performed with only O(sqrt{N}) queries, which is optimal.

quant-ph↗

arXiv2011

Preservation of loss in linear-optical processing

We propose a measure of quantum efficiency of a multimode state of light that quantifies the amount of optical loss this state has experienced, and prove that this efficiency cannot increase in any linear-optical processing with destructive conditional measurements. Any loss that has affected a state can neither be removed nor redistributed so as to further increase the efficiency in higher-efficiency modes at the expense of lower-efficiency modes. This result eliminates the possibility of catalytically improving photon sources.

quant-ph↗

arXiv2011

Simulating Quantum Dynamics On A Quantum Computer

We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are significant because they are the first to have time-complexities that are comparable to the best known methods for simulating time-independent Hamiltonian evolution, given appropriate smoothness criteria on the Hamiltonian are satisfied. We provide a thorough cost analysis of these algorithms that considers discretizion errors in both the time and the representation of the Hamiltonian. In addition, we provide the first upper bounds for the error in Lie-Trotter-Suzuki approximations to unitary evolution operators, that use adaptively chosen time steps.

quant-ph↗

arXiv2009

The standard fair sampling assumption is not necessary to test local realism

Almost all Bell-inequality experiments to date have used postselection, and therefore relied on the fair sampling assumption for their interpretation. The standard form of the fair sampling assumption is that the loss is independent of the measurement settings, so the ensemble of detected systems provides a fair statistical sample of the total ensemble. This is often assumed to be needed to interpret Bell inequality experiments as ruling out hidden-variable theories. Here we show that it is not necessary; the loss can depend on measurement settings, provided the detection efficiency factorises as a function of the measurement settings and any hidden variable. This condition implies that Tsirelson's bound must be satisfied for entangled states. On the other hand, we show that it is possible for Tsirelson's bound to be violated while the CHSH-Bell inequality still holds for unentangled states, and present an experimentally feasible example.

quant-ph↗

arXiv2008

Higher Order Decompositions of Ordered Operator Exponentials

We present a decomposition scheme based on Lie-Trotter-Suzuki product formulae to represent an ordered operator exponential as a product of ordinary operator exponentials. We provide a rigorous proof that does not use a time-displacement superoperator, and can be applied to non-analytic functions. Our proof provides explicit bounds on the error and includes cases where the functions are not infinitely differentiable. We show that Lie-Trotter-Suzuki product formulae can still be used for functions that are not infinitely differentiable, but that arbitrary order scaling may not be achieved.

math-ph↗

arXiv2007

Lower bounds for communication capacities of two-qudit unitary operations

We show that entangling capacities based on the Jamiolkowski isomorphism may be used to place lower bounds on the communication capacities of arbitrary bipartite unitaries. Therefore, for these definitions, the relations which have been previously shown for two-qubit unitaries also hold for arbitrary dimensions. These results are closely related to the theory of the entanglement-assisted capacity of channels. We also present more general methods for producing ensembles for communication from initial states for entanglement creation.

quant-ph↗

arXiv2006

Implementation of multipartite unitary operations with limited resources

A general method for implementing weakly entangling multipartite unitary operations using a small amount of entanglement and classical communication is presented. For the simple Hamiltonian σ_z\otimesσ_z this method requires less entanglement than previously known methods. In addition, compression of multiple operations is applied to reduce the average communication required.

quant-ph↗

arXiv2006

Two qubits can be entangled in two distinct temperature regions

We have found that for a wide range of two-qubit Hamiltonians the canonical-ensemble thermal state is entangled in two distinct temperature regions. In most cases the ground state is entangled; however we have also found an example where the ground state is separable and there are still two regions. This demonstrates that the qualitative behavior of entanglement with temperature can be much more complicated than might otherwise have been expected; it is not simply determined by the entanglement of the ground state, even for the simple case of two qubits. Furthermore, we prove a finite bound on the number of possible entangled regions for two qubits, thus showing that arbitrarily many transitions from entanglement to separability are not possible. We also provide an elementary proof that the spectrum of the thermal state at a lower temperature majorizes that at a higher temperature, for any Hamiltonian, and use this result to show that only one entangled region is possible for the special case of Hamiltonians without magnetic fields.

quant-ph↗

arXiv2006

Efficiency limits for linear optical processing of single photons and single-rail qubits

We analyze the problem of increasing the efficiency of single-photon sources or single-rail photonic qubits via linear optical processing and destructive conditional measurements. In contrast to previous work we allow for the use of coherent states and do not limit to photon-counting measurements. We conjecture that it is not possible to increase the efficiency, prove this conjecture for several important special cases, and provide extensive numerical results for the general case.

quant-ph↗

arXiv2006

Adaptive phase measurements for narrowband squeezed beams

We have previously [Phys. Rev. A 65, 043803 (2002)] analyzed adaptive measurements for estimating the continuously varying phase of a coherent beam, and a broadband squeezed beam. A real squeezed beam must have finite photon flux N and hence can be significantly squeezed only over a limited frequency range. In this paper we analyze adaptive phase measurements of this type for a realistic model of a squeezed beam. We show that, provided it is possible to suitably choose the parameters of the beam, a mean-square phase uncertainty scaling as (N/kappa)^{-5/8} is possible, where kappa is the linewidth of the beam resulting from the fluctuating phase. This is an improvement over the (N/kappa)^{-1/2} scaling found previously for coherent beams. In the experimentally realistic case where there is a limit on the maximum squeezing possible, the variance will be reduced below that for coherent beams, though the scaling is unchanged.

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