Solution to time-energy costs of quantum channels

We derive a formula for the time-energy costs of general quantum channels proposed in [Phys. Rev. A {\bf 88}, 012307 (2013)]. This formula allows us to numerically find the time-energy cost of any quantum channel using positive semidefinite programming. We also derive a lower bound to the time-energy cost for any channels and the exact the time-energy cost for a class of channels which includes the qudit depolarizing channels and projector channels as special cases.

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Some bounds on the minimum number of queries required for quantum channel perfect discrimination

Quantum Information and Computation ◽

10.26421/qic12.1-2-9 ◽

2012 ◽

Vol 12 (1&2) ◽

pp. 138-148

Author(s):

Cheng Lu ◽

Jianxin Chen ◽

Runyao Duan

Keyword(s):

Lower Bound ◽

Lower Bounds ◽

Upper Bound ◽

Quantum Channel ◽

Necessary Condition ◽

Quantum Channels ◽

Sequential Scheme ◽

Minimum Number ◽

Perfect Discrimination ◽

Sufficient And Necessary Condition

We prove a lower bound on the $q$-maximal fidelities between two quantum channels $\E_0$ and $\E_1$ and an upper bound on the $q$-maximal fidelities between a quantum channel $\E$ and an identity $\I$. Then we apply these two bounds to provide a simple sufficient and necessary condition for sequential perfect distinguishability between $\E$ and $\I$ and provide both a lower bound and an upper bound on the minimum number of queries required to sequentially perfectly discriminating $\E$ and $\I$. Interestingly, in the $2$-dimensional case, both bounds coincide. Based on the optimal perfect discrimination protocol presented in \cite{DFY09}, we can further generalize the lower bound and upper bound to the minimum number of queries to perfectly discriminating $\E$ and $I$ over all possible discrimination schemes. Finally the two lower bounds are shown remain working for perfectly discriminating general two quantum channels $\E_0$ and $\E_1$ in sequential scheme and over all possible discrimination schemes respectively.

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Defining quantum divergences via convex optimization

Quantum ◽

10.22331/q-2021-01-26-387 ◽

2021 ◽

Vol 5 ◽

pp. 387

Author(s):

Hamza Fawzi ◽

Omar Fawzi

Keyword(s):

Convex Optimization ◽

Semidefinite Programming ◽

Quantum Channel ◽

Upper Bounds ◽

Chain Rule ◽

Quantum Channels ◽

Optimization Program ◽

Rényi Divergence ◽

Strong Converse ◽

A Chain

We introduce a new quantum Rényi divergence Dα# for α∈(1,∞) defined in terms of a convex optimization program. This divergence has several desirable computational and operational properties such as an efficient semidefinite programming representation for states and channels, and a chain rule property. An important property of this new divergence is that its regularization is equal to the sandwiched (also known as the minimal) quantum Rényi divergence. This allows us to prove several results. First, we use it to get a converging hierarchy of upper bounds on the regularized sandwiched α-Rényi divergence between quantum channels for α>1. Second it allows us to prove a chain rule property for the sandwiched α-Rényi divergence for α>1 which we use to characterize the strong converse exponent for channel discrimination. Finally it allows us to get improved bounds on quantum channel capacities.

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The Algebraic Degree of Phase-Type Distributions

Journal of Applied Probability ◽

10.1017/s0021900200006963 ◽

2010 ◽

Vol 47 (03) ◽

pp. 611-629

Author(s):

Mark Fackrell ◽

Qi-Ming He ◽

Peter Taylor ◽

Hanqin Zhang

Keyword(s):

Lower Bound ◽

Upper Bound ◽

Polynomial Algorithm ◽

Algebraic Degree ◽

Nonnegative Matrices ◽

Stieltjes Transform ◽

Special Cases ◽

Phase Type ◽

Phase Type Distributions ◽

The Matrix

This paper is concerned with properties of the algebraic degree of the Laplace-Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator, how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polynomial algorithm, a method for computing the algebraic degree of a PH distribution is developed. The maximum algebraic degree is identified explicitly. Using Perron-Frobenius theory of nonnegative matrices, a lower bound and an upper bound on the minimum algebraic degree are found, subject to some conditions. Explicit results are obtained for special cases.

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"Show Me the Energy Costs": Short and Long-term Energy Cost Disclosure Effects on Willingness-to-pay for Residential Energy Efficiency

The Energy Journal ◽

10.5547/01956574.43.3.jcar ◽

2022 ◽

Vol 43 (3) ◽

Author(s):

James Carroll ◽

Claudia Aravena ◽

Marco Boeri ◽

Eleanor Denny

Keyword(s):

Energy Efficiency ◽

Willingness To Pay ◽

Energy Cost ◽

Energy Costs ◽

Residential Energy ◽

Residential Energy Efficiency ◽

Term Energy ◽

Short And Long Term ◽

Cost Disclosure

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Probabilistic Resumable Quantum Teleportation of a Two-Qubit Entangled State

Entropy ◽

10.3390/e21040352 ◽

2019 ◽

Vol 21 (4) ◽

pp. 352 ◽

Cited By ~ 2

Author(s):

Zhan-Yun Wang ◽

Yi-Tao Gou ◽

Jin-Xing Hou ◽

Li-Ke Cao ◽

Xiao-Hui Wang

Keyword(s):

Quantum Channel ◽

Quantum Teleportation ◽

The State ◽

Entangled States ◽

Entangled State ◽

Quantum Channels ◽

Unknown State ◽

Optimal Probability

We explicitly present a generalized quantum teleportation of a two-qubit entangled state protocol, which uses two pairs of partially entangled particles as quantum channel. We verify that the optimal probability of successful teleportation is determined by the smallest superposition coefficient of these partially entangled particles. However, the two-qubit entangled state to be teleported will be destroyed if teleportation fails. To solve this problem, we show a more sophisticated probabilistic resumable quantum teleportation scheme of a two-qubit entangled state, where the state to be teleported can be recovered by the sender when teleportation fails. Thus the information of the unknown state is retained during the process. Accordingly, we can repeat the teleportion process as many times as one has available quantum channels. Therefore, the quantum channels with weak entanglement can also be used to teleport unknown two-qubit entangled states successfully with a high number of repetitions, and for channels with strong entanglement only a small number of repetitions are required to guarantee successful teleportation.

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The energy cost of fat and protein deposition in the rat

British Journal Of Nutrition ◽

10.1079/bjn19770039 ◽

1977 ◽

Vol 37 (3) ◽

pp. 355-363 ◽

Cited By ~ 246

Author(s):

J. D. Pullar ◽

A. J. F. Webster

Keyword(s):

Regression Analysis ◽

Energy Cost ◽

Metabolizable Energy ◽

Zucker Rats ◽

Energy Costs ◽

Semisynthetic Diet ◽

Direct Calorimetry ◽

Protein Deposition ◽

Body Weights ◽

Gross Energy

1. Measurements were made of energy balance by direct calorimetry, and of nitrogen balance in groups of lean and congenitally obese (‘fatty’) Zucker rats at body-weights of 200 and 350 g given a highly digestible semisynthetic diet at 14.0 or 18.4 g/rat per 24 h.2. Losses of food energy and N in faeces were very small. The fatty rats lost much more N in urine than did lean rats. Despite this the proportion of gross energy that was metabolized was 0.92 for both fatty and lean rats.3. In all trials, fatty rats lost a smaller proportion of metabolizable energy (ME) as heat and deposited less as protein than thin rats but deposited much more as fat.4. The amounts of ME required to deposit 1 kJ of protein and 1 kJ of fat respectively were shown by regression analysis to be 2.25 (±0.16) and 1.36 (±0.06) kJ respectively. These values agree extremely closely with recent, more tentative, estimates based on assumptions as to maintenance requirement which the present experiments were able to circumvent. It may be concluded with confidence that the energy costs of depositing 1 g of protein or fat are almost identical at 53 kJ ME/g.

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Performance characterization of Pauli channels assisted by indefinite causal order and post-measurement

Quantum Information and Computation ◽

10.26421/qic20.15-16-1 ◽

2020 ◽

Vol 20 (15&16) ◽

pp. 1261-1280

Author(s):

Francisco Delgado ◽

Carlos Cardoso-Isidoro

Keyword(s):

Quantum Channel ◽

Communication Channel ◽

Quantum Communication ◽

Quantum Channels ◽

Causal Order ◽

Combined Process ◽

Performance Characterization ◽

Output State ◽

Transmission Of Information

Indefinite causal order has introduced disruptive procedures to improve the fidelity of quantum communication by introducing the superposition of { orders} on a set of quantum channels. It has been applied to several well characterized quantum channels as depolarizing, dephasing and teleportation. This work analyses the behavior of a parametric quantum channel for single qubits expressed in the form of Pauli channels. Combinatorics lets to obtain affordable formulas for the analysis of the output state of the channel when it goes through a certain imperfect quantum communication channel when it is deployed as a redundant application of it under indefinite causal order. In addition, the process exploits post-measurement on the associated control to select certain components of transmission. Then, the fidelity of such outputs is analysed to characterize the generic channel in terms of its parameters. As a result, we get notable enhancement in the transmission of information for well characterized channels due to the combined process: indefinite causal order plus post-measurement.

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Semidefinite Programming-Based Method for Implementing Linear Fitting to Interval-Valued Data

International Journal of Fuzzy System Applications ◽

10.4018/ijfsa.2011070103 ◽

2011 ◽

Vol 1 (3) ◽

pp. 32-46 ◽

Cited By ~ 1

Author(s):

Minghuang Li ◽

Fusheng Yu

Keyword(s):

Lower Bound ◽

Semidefinite Programming ◽

Large Scale ◽

Experimental Studies ◽

Optimal Solution ◽

Data Set ◽

Linear Fitting ◽

Optimal Value ◽

Fitting Model ◽

Interval Valued

Building a linear fitting model for a given interval-valued data set is challenging since the minimization of the residue function leads to a huge combinatorial problem. To overcome such a difficulty, this article proposes a new semidefinite programming-based method for implementing linear fitting to interval-valued data. First, the fitting model is cast to a problem of quadratically constrained quadratic programming (QCQP), and then two formulae are derived to develop the lower bound on the optimal value of the nonconvex QCQP by semidefinite relaxation and Lagrangian relaxation. In many cases, this method can solve the fitting problem by giving the exact optimal solution. Even though the lower bound is not the optimal value, it is still a good approximation of the global optimal solution. Experimental studies on different fitting problems of different scales demonstrate the good performance and stability of our method. Furthermore, the proposed method performs very well in solving relatively large-scale interval-fitting problems.

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