LIMITATION ON THE ACCESSIBLE INFORMATION FOR QUANTUM CHANNELS WITH INEFFICIENT MEASUREMENTS

2005 ◽  
Vol 03 (supp01) ◽  
pp. 87-95
Author(s):  
KURT JACOBS
Keyword(s):  
Quantum System ◽  
Von Neumann Entropy ◽  
Quantum Channels ◽  
Initial State ◽  
Von Neumann ◽  
Classical Information ◽  
Quantum Operations ◽  
Amount Of Information ◽  
Accessible Information

To transmit classical information using a quantum system, the sender prepares the system in one of a set of possible states and sends it to the receiver. The receiver then makes a measurement on the system to obtain information about the senders choice of state. The amount of information which is accessible to the receiver depends upon the encoding and the measurement. Here we derive a bound on this information which generalizes the bound derived by Schumacher, Westmoreland and Wootters [Schumacher, Westmoreland and Wootters, Phys. Rev. Lett. 76, 3452 (1996)] to include inefficient measurements, and thus all quantum operations. This also allows us to obtain a generalization of a bound derived by Hall [Hall, Phys. Rev. A 55, 100 (1997)], and to show that the average reduction in the von Neumann entropy which accompanies a measurement is concave in the initial state, for all quantum operations.

scholarly journals Relating Entropies of Quantum Channels

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1028
Author(s):  
Dariusz Kurzyk ◽  
Łukasz Pawela ◽  
Zbigniew Puchała
Keyword(s):  
Relative Entropy ◽  
Upper Bound ◽  
Quantum Channel ◽  
Von Neumann Entropy ◽  
Quantum Channels ◽  
Von Neumann ◽  
Channel One ◽  
Depolarizing Channel

In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi–Jamiołkowski state. The second one is based on the relative entropy of the output of the extended channel relative to the output of the extended completely depolarizing channel. This entropy then needs to be optimized over all possible input states. Our results first show that the former entropy provides an upper bound on the latter. Next, we show that for unital qubit channels, this bound is saturated. Finally, we conjecture and provide numerical intuitions that the bound can also be saturated for random channels as their dimension tends to infinity.

Entanglement for quantum walks on the line

2011 ◽  
Vol 11 (9&10) ◽  
pp. 855-866
Author(s):  
Yusuke Ide ◽  
Norio Konno ◽  
Takuya Machida
Keyword(s):  
Information Theory ◽  
Shannon Entropy ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Von Neumann Entropy ◽  
Initial State ◽  
Von Neumann ◽  
Time Quantum ◽  
The One ◽  
Path Counting

The discrete-time quantum walk is a quantum counterpart of the random walk. It is expected that the model plays important roles in the quantum field. In the quantum information theory, entanglement is a key resource. We use the von Neumann entropy to measure the entanglement between the coin and the particle's position of the quantum walks. Also we deal with the Shannon entropy which is an important quantity in the information theory. In this paper, we show limits of the von Neumann entropy and the Shannon entropy of the quantum walks on the one dimensional lattice starting from the origin defined by arbitrary coin and initial state. In order to derive these limits, we use the path counting method which is a combinatorial method for computing probability amplitude.

scholarly journals Von Neumann entropy-preserving quantum operations

2011 ◽  
Vol 375 (47) ◽  
pp. 4163-4165 ◽  
Author(s):  
Lin Zhang ◽  
Junde Wu
Keyword(s):  
Von Neumann Entropy ◽  
Von Neumann ◽  
Quantum Operations

scholarly journals THERMODYNAMIC PROCESSES GENERATED BY A CLASS OF COMPLETELY POSITIVE QUANTUM OPERATIONS

2012 ◽  
Vol 26 (12) ◽  
pp. 1241001 ◽  
Author(s):  
SUMIYOSHI ABE ◽  
YUKI AOYAGHI
Keyword(s):  
Temperature Limit ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Positive Operator Valued Measures ◽  
Quantum Operations ◽  
High Temperature Limit ◽  
Point Analysis ◽  
Repeated Applications ◽  
Quantity Of Heat ◽  
Thermodynamic Processes

An attempt toward the operational formulation of quantum thermodynamics is made by employing the recently proposed operations forming positive operator-valued measures for generating thermodynamic processes. The quantity of heat as well as the von Neumann entropy monotonically increases under the operations. The fixed point analysis shows that repeated applications of these operations to a given system transform from its pure ground state at zero temperature to the completely random state in the high temperature limit with intermediate states being generically out of equilibrium. It is shown that the Clausius inequality can be violated along the processes, in general. A bipartite spin-1/2 system is analyzed as an explicit example.

scholarly journals Between entropy and subentropy

2003 ◽  
Vol 3 (1) ◽  
pp. 1-14
Author(s):  
S.R. Nichols ◽  
W.K. Wootters
Keyword(s):  
Quantum State ◽  
Lower Bounds ◽  
Mixed State ◽  
Upper And Lower Bounds ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Accessible Information ◽  
The Given

The von Neumann entropy and the subentropy of a mixed quantum state are upper and lower bounds, respectively, on the accessible information of any ensemble consistent with the given mixed state. Here we define and investigate a set of quantities intermediate between entropy and subentropy.

scholarly journals Emergent classicality in general multipartite states and channels

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 555
Author(s):  
Xiao-Liang Qi ◽  
Daniel Ranard
Keyword(s):  
Optimization Procedure ◽  
Quantum Channels ◽  
Channel State ◽  
Markov Blanket ◽  
Classical Information ◽  
Accessible Information ◽  
Measured System ◽  
Multipartite States ◽  
Total Environment ◽  
Quantum Measurement Process

In a quantum measurement process, classical information about the measured system spreads throughout the environment. Meanwhile, quantum information about the system becomes inaccessible to local observers. Here we prove a result about quantum channels indicating that an aspect of this phenomenon is completely general. We show that for any evolution of the system and environment, for everywhere in the environment excluding an O(1)-sized region we call the "quantum Markov blanket," any locally accessible information about the system must be approximately classical, i.e. obtainable from some fixed measurement. The result strengthens the earlier result of Brandão et al. (Nat. comm. 6:7908) in which the excluded region was allowed to grow with total environment size. It may also be seen as a new consequence of the principles of no-cloning or monogamy of entanglement. Our proof offers a constructive optimization procedure for determining the "quantum Markov blanket" region, as well as the effective measurement induced by the evolution. Alternatively, under channel-state duality, our result characterizes the marginals of multipartite states.

scholarly journals ENTANGLEMENT OF QUANTUM SPIN SYSTEMS: A VALENCE-BOND APPROACH

2011 ◽  
Vol 25 (12n13) ◽  
pp. 917-928 ◽  
Author(s):  
SYLVAIN CAPPONI ◽  
FABIEN ALET ◽  
MATTHIEU MAMBRINI
Keyword(s):  
Quantum System ◽  
Valence Bond ◽  
Quantum Spin ◽  
Spin Systems ◽  
Von Neumann Entropy ◽  
Quantum Spin Systems ◽  
Von Neumann ◽  
Open Issue

In order to quantify entanglement between two parts of a quantum system, one of the most used estimators is the Von Neumann entropy. Unfortunately, computing this quantity for large interacting quantum spin systems remains an open issue. Faced with this difficulty, other estimators have been proposed to measure entanglement efficiently, mostly by using simulations in the valence-bond basis. We review the different proposals and try to clarify the connections between their geometric definitions and proper observables. We illustrate this analysis with new results of entanglement properties of spin-1 chains.

scholarly journals QUANTUM MEASUREMENT SCHEMES RELATED TO FLAVOR-WEIGHTED ENERGIES

2013 ◽  
Vol 28 (15) ◽  
pp. 1350065 ◽  
Author(s):  
A. E. BERNARDINI
Keyword(s):  
Quantum Mechanics ◽  
Quantum System ◽  
Quantum Measurement ◽  
Single Particle ◽  
Neutrino Energy ◽  
Von Neumann Entropy ◽  
System Framework ◽  
Von Neumann ◽  
Mass Eigenstates ◽  
The Right

The framework of the generalized theory of quantum measurement provides some theoretical tools for computing flavor associated energies correlated to the von-Neumann entropy of a composed system. After defining flavor-averaged and flavor-weighted energies, that are respectively supported by nonselective (selective) quantum measurement schemes, the right correlation between the energies of flavor eigenstates and their measurement probabilities can be obtained. Our results from the composed quantum system framework show that the nonselective measurement scheme for computing flavor-weighted energies is consistent with predictions from single-particle quantum mechanics. As an application of our results, through the expressions for neutrino effective mass values, it is straightforwardly verified that cosmological background neutrino energy densities could be obtained from the coherent superposition of mass eigenstates.

scholarly journals Trade-off relations for operation entropy of complementary quantum channels

2019 ◽  
Vol 17 (05) ◽  
pp. 1950046
Author(s):  
Jakub Czartowski ◽  
Daniel Braun ◽  
Karol Życzkowski
Keyword(s):  
Quantum Channel ◽  
Lower Boundary ◽  
Von Neumann Entropy ◽  
Input State ◽  
Quantum Channels ◽  
Quantum Operation ◽  
Trade Off ◽  
Von Neumann ◽  
State Of The Environment ◽  
Complementary Channel

The entropy of a quantum operation, defined as the von Neumann entropy of the corresponding Choi–Jamiołkowski state, characterizes the coupling of the principal system with the environment. For any quantum channel acting on a state of a given size, one defines the complementary channel, which sends the input state into the state of the environment after the operation. Making use of subadditivity of entropy, we show that for any dimension the sum of both entropies is bounded from below. This result characterizes the trade-off between the information on the initial quantum state accessible to the principal system and the information leaking to the environment. For one qubit maps we describe the interpolating family of depolarizing maps, for which the sum of both entropies gives the lower boundary of the region allowed in the space spanned by both entropies.

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