On the capacities of bipartite hamiltonians and unitary gates

Bennett, Charles H.; Harrow, Aram W.; Leung, Debbie; Smolin, John A.

doi:10.1109/tit.2003.814935

Cited by 158 publications

(294 citation statements)

References 38 publications

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“…Thus the asymptotic capacity equals the largest increase in mutual information possible with one use of U if the average entanglement decreases by no more than e. This was proven for e = ∞ by [8].…”

Section: Propositionmentioning

confidence: 83%

“…Alice can also generate entanglement by inputting a superposition of messages (as in [8]), so 1 cobit 1 ebit. The true power of coherent communication comes from performing both tasksclassical communication and entanglement generationsimultaneously.…”

Section: Uses Of Coherent Communicationmentioning

confidence: 99%

“…Achieving C e (U ) ≥ ∆χ e (U ): We base our protocol on the one used in Section 4.3 of [8] to show C ∞ = ∆χ ∞ . For any ensemble E,…”

Section: Propositionmentioning

confidence: 99%

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Coherent Communication of Classical Messages

Harrow

2004

Phys. Rev. Lett.

169

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We define coherent communication in terms of a simple primitive, show it is equivalent to the ability to send a classical message with a unitary or isometric operation, and use it to relate other resources in quantum information theory. Using coherent communication, we are able to generalize super-dense coding to prepare arbitrary quantum states instead of only classical messages. We also derive single-letter formulae for the classical and quantum capacities of a bipartite unitary gate assisted by an arbitrary fixed amount of entanglement per use. Beyond qubits and cbitsThe basic units of communication in quantum information theory are usually taken to be qubits and cbits, meaning one use of a noiseless quantum or classical channel respectively. Qubits and cbits can be converted to each other and to and from other quantum communication resources, but often only irreversibly. For example, one qubit can yield at most one cbit, but to obtain a qubit from cbits requires the additional resource of entanglement. By introducing a new resource, intermediate in power between a qubit and a cbit, we will show that many resource transformations can be modified to be reversible and thus more efficient.If {|x } x=0,1 is a basis for C 2 , then a qubit channel can be described as the isometry |x A → |x B and a cbit can be written as |x A → |x B |x E . Here A is the sender Alice, B is the receiver Bob and E denotes an inaccessible environment, sometimes personified as a malicious Eve. Tracing out Eve yields the traditional definition of a cbit channel with the basis {|x } considered the computational basis.Define a coherent bit (or "cobit") of communication as the ability to perform the map |x A → |x A |x B . Since Alice is free to copy or destroy her channel input, 1 qubit 1 cobit 1 cbit, where X Y means that the resource X can be used to simulate the resource Y . We will also write X Y (c) when X + Z Y + Z for some resource Z used as a catalyst and X Y (a) when the conversion is asymptotic, by which we mean that X ⊗n Y ⊗≈n for n sufficiently large.In Prop. 1, we will see that coherent bits come from any method for sending bits using a coherent procedure (a unitary or isometry on the joint Alice-Bob Hilbert space); hence their name. From their definitions, we see that cobits can be thought of as cbits where Alice controls the environment, making them like classical channels with quantum feedback. Further connections between cobits and cbits will be seen later in this Letter, where we show that irreversible resource transformations are often equivalent to performing "1 cobit 1 cbit," and in [1] where several communication protocols are "made coherent" with the effect of replacing cbits with cobits.In the first half of this paper we will describe how to obtain coherent bits and then how to use them, allowing us to exactly describe the power of cobits in terms of conventional resources. The purpose of this paper is thus not to define a new incomparable quantum resource, but rather to introduce a technique for relating and composin...

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Section: Propositionmentioning

confidence: 83%

Section: Uses Of Coherent Communicationmentioning

confidence: 99%

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Coherent Communication of Classical Messages

Harrow

2004

Phys. Rev. Lett.

169

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“…We start from observing that the unitary evolution with any Hamiltonian H AB can not increase (decrease) the entanglement S(aA) by more than 2 log (d), where d = min (A, B), see [2]. This property can be called small total entangling, as it says that the total increase (decrease) of entanglement throughout the unitary evolution remains bounded as the dimensions of local ancillas a and b go to infinity.…”

Section: Summary Of Resultsmentioning

confidence: 99%

“…Thus for fixed d and H the entangling rate has a constant upper bound independent on how large are dimensions a and b. The authors of [2] also proved that the supremum of Γ(H) over all dimensions of local ancillas a, b coincides with the asymptotic capacity of H to generate entanglement by any protocol in which unitary evolution with H is interspersed with LOCC. It is unknown whether the supremum over a and b can be actually achieved for finite dimensional ancillas.…”

Section: Previous Workmentioning

confidence: 96%

Upper bounds on entangling rates of bipartite Hamiltonians

Bravyi

2007

Phys. Rev. A

117

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We discuss upper bounds on the rate at which unitary evolution governed by a non-local Hamiltonian can generate entanglement in a bipartite system. Given a bipartite Hamiltonian H coupling two finite dimensional particles A and B, the entangling rate is shown to be upper bounded by c log (d) H , where d is the smallest dimension of the interacting particles, H is the operator norm of H, and c is a constant close to 1. Under certain restrictions on the initial state we prove analogous upper bound for the ancilla-assisted entangling rate with a constant c that does not depend upon dimensions of local ancillas. The restriction is that the initial state has at most two distinct Schmidt coefficients (each coefficient may have arbitrarily large multiplicity). Our proof is based on analysis of a mixing rate -a functional measuring how fast entropy can be produced if one mixes a time-independent state with a state evolving unitarily.

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Entanglement and Coherence Created by Photoionization of $$\mathrm {H_2}$$

Nishi

2022

Photoelectron-Ion Correlation in Photoionization of a Hydrogen Molecule and Molecule-Photon Dynamics in a Cavity

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On the capacities of bipartite hamiltonians and unitary gates

Cited by 158 publications

References 38 publications

Coherent Communication of Classical Messages

Coherent Communication of Classical Messages

Upper bounds on entangling rates of bipartite Hamiltonians

Entanglement and Coherence Created by Photoionization of $$\mathrm {H_2}$$

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