Maris Ozols

Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)

In this paper we study the subset of generalized quantum measurements on finite dimensional systems known as local operations and classical communication (LOCC). While LOCC emerges as the natural class of operations in many important quantum information tasks, its mathematical structure is complex and difficult to characterize. Here we provide a precise description of LOCC and related operational classes in terms of quantum instruments. Our formalism captures both finite round protocols as well as those that utilize an unbounded number of communication rounds. While the set of LOCC is not topologically closed, we show that finite round LOCC constitutes a compact subset of quantum operations. Additionally we show the existence of an open ball around the completely depolarizing map that consists entirely of LOCC implementable maps. Finally, we demonstrate a two-qubit map whose action can be approached arbitrarily close using LOCC, but nevertheless cannot be implemented perfectly.

Bilateral photoplethysmography studies of the leg arterial stenosis

A newly developed portable multi-channel photoplethysmography (PPG) device has been used for comparative studies of 20 healthy control subjects and 45 patients with diagnosed arterial stenosis in a leg. The peripheral blood pulsations were detected simultaneously at four body sites-the same fingers and toes of both arms and legs. The PPG pulses recorded at the periphery of the stenotic leg, if compared with those of the healthy leg, were much weaker, with delayed arrival as a consequence of increased pulse wave transit time (PWTT) due to higher vascular resistance. The specific PWTT delays for the occluded legs were in the range of 20-80 ms, while in the case of healthy subjects the leg PPG signals arrived without delays or with smaller time-shifts not exceeding 14 ms. The reference bilateral PPG signals detected at the fingertips did not show any notable PWTT delays in both groups. Parallel measurements of local blood pressures by means of the oscillometry method with subsequent calculation of the ankle-brachial index were performed. Convincing correlation between the bilateral differences in the local blood pressure (a routine tool for diagnostics of leg stenosis) and in the corresponding PWTT delay (Pearsons coefficient r = 0.93), as well as between the PWTT delay and the ankle-brachial index (r = -0.96) has been established. From the point of view of PWTT delay, the average value of leg stenosis diagnostic threshold was established to be in the range of 23 +/- 9 ms, with full reliability above 32 ms. The obtained data may find further applications in alternative methodologies for detection and/or assessment of arterial occlusions in human extremities.

Entanglement can Increase Asymptotic Rates of Zero-Error Classical Communication over Classical Channels

It is known that the number of different classical messages which can be communicated with a single use of a classical channel with zero probability of decoding error can sometimes be increased by using entanglement shared between sender and receiver. It has been an open question to determine whether entanglement can ever increase the zero-error communication rates achievable in the limit of many channel uses. In this paper we show, by explicit examples, that entanglement can indeed increase asymptotic zero-error capacity, even to the extent that it is equal to the normal capacity of the channel.

Unbounded number of channel uses may be required to detect quantum capacity

Transmitting data reliably over noisy communication channels is one of the most important applications of information theory, and is well understood for channels modelled by classical physics. However, when quantum effects are involved, we do not know how to compute channel capacities. This is because the formula for the quantum capacity involves maximizing the coherent information over an unbounded number of channel uses. In fact, entanglement across channel uses can even increase the coherent information from zero to non-zero. Here we study the number of channel uses necessary to detect positive coherent information. In all previous known examples, two channel uses already sufficed. It might be that only a finite number of channel uses is always sufficient. We show that this is not the case: for any number of uses, there are channels for which the coherent information is zero, but which nonetheless have capacity.

Entropy power inequalities for qudits

Shannon’s entropy power inequality (EPI) can be viewed as a statement of concavity of an entropic function of a continuous random variable under a scaled addition rule: f(a X+1−a Y)≥af(X)+(1−a)f(Y)∀ a∈[0,1]. Here, X and Y are continuous random variables and the function f is either the differential entropy or the entropy power. Konig and Smith [IEEE Trans. Inf. Theory 60(3), 1536–1548 (2014)] and De Palma, Mari, and Giovannetti [Nat. Photonics 8(12), 958–964 (2014)] obtained quantum analogues of these inequalities for continuous-variable quantum systems, where X and Y are replaced by bosonic fields and the addition rule is the action of a beam splitter with transmissivity a on those fields. In this paper, we similarly establish a class of EPI analogues for d-level quantum systems (i.e., qudits). The underlying addition rule for which these inequalities hold is given by a quantum channel that depends on the parameter a ∈ [0, 1] and acts like a finite-dimensional analogue of a beam splitter with transmissiv...

Hamiltonian simulation with optimal sample complexity

We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd, Mohseni, and Rebentrost [Nat. Phys., 10(9):631–633, 2014] is optimal for this task. We further extend their method to the case of multiple input states, showing how to simulate any Hermitian polynomial of the states provided. As applications, we derive optimal algorithms for commutator simulation and orthogonality testing, and we give a protocol for creating a coherent superposition of pure states, when given sample access to those states. We also show that this sample-based Hamiltonian simulation can be used as the basis of a universal model of quantum computation that requires only partial swap operations and simple single-qubit states.Quantum Software from Quantum StatesOne of the hallmarks of quantum computation is the storage and extraction of information within quantum systems. Recently, Lloyd, Mohseni and Rebentrost created a protocol to treat multiple identical copies of a quantum state as “quantum software”, specifying a quantum program to be run on any other state. They use this approach to do principal component analysis of the software state. Here, we expand on their results, providing protocols for running more-complex quantum programs specified by several different states. Our protocols can be used to analyze the relationship between different states (for example, deciding whether states are orthogonal) and to create new states (such as coherent linear combinations of two states). We also outline the optimality of Lloyd et al.’s original protocol, as well as our new protocols.

The Complexity of Translationally Invariant Spin Chains with Low Local Dimension

We prove that estimating the ground state energy of a translationally invariant, nearest-neighbour Hamiltonian on a 1D spin chain is

A portable device for optical assessment of the cardiovascular condition

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