We study the effects of acceleration on fermionic Gaussian states of localized modes of a Dirac field. We consider two wave packets in a Gaussian state and transform these to an accelerated frame of ...reference. In particular, we formulate the action of this transformation as a fermionic quantum channel. Having developed the general framework for fermions, we then investigate the entanglement of the vacuum, as well as the entanglement in Bell states. We find that with increasing acceleration vacuum entanglement increases, while the entanglement of Bell states decreases. Notably, our results have an immediate operational meaning given the localization of the modes.
In this work, we introduce classical holographic codes. These can be understood as concatenated probabilistic codes and can be represented as networks uniformly covering hyperbolic space. In ...particular, classical holographic codes can be interpreted as maps from bulk degrees of freedom to boundary degrees of freedom. Interestingly, they are shown to exhibit features similar to those expected from the AdS/CFT correspondence. Among these are a version of the Ryu-Takayanagi formula and intriguing properties regarding bulk reconstruction and boundary representations of bulk operations. We discuss the relation of our findings with expectations from AdS/CFT and, in particular, with recent results from quantum error correction.
Universality of black hole quantum computing Dvali, Gia; Gomez, Cesar; Lüst, Dieter ...
Fortschritte der Physik,
January 2017, 2017-01-00, 20170101, Letnik:
65, Številka:
1
Journal Article
Recenzirano
Odprti dostop
By analyzing the key properties of black holes from the point of view of quantum information, we derive a model‐independent picture of black hole quantum computing. It has been noticed that this ...picture exhibits striking similarities with quantum critical condensates, allowing the use of a common language to describe quantum computing in both systems. We analyze such quantum computing by allowing coupling to external modes, under the condition that the external influence must be soft‐enough in order not to offset the basic properties of the system. We derive model‐independent bounds on some crucial time‐scales, such as the times of gate operation, decoherence, maximal entanglement and total scrambling. We show that for black hole type quantum computers all these time‐scales are of the order of the black hole half‐life time. Furthermore, we construct explicitly a set of Hamiltonians that generates a universal set of quantum gates for the black hole type computer. We find that the gates work at maximal energy efficiency. Furthermore, we establish a fundamental bound on the complexity of quantum circuits encoded on these systems, and characterize the unitary operations that are implementable. It becomes apparent that the computational power is very limited due to the fact that the black hole life‐time is of the same order of the gate operation time. As a consequence, it is impossible to retrieve its information, within the life‐time of a black hole, by externally coupling to the black hole qubits. However, we show that, in principle, coupling to some of the internal degrees of freedom allows acquiring knowledge about the micro‐state. Still, due to the trivial complexity of operations that can be performed, there is no time advantage over the collection of Hawking radiation and subsequent decoding.
By analyzing the key properties of black holes from the point of view of quantum information a model‐independent picture of black hole quantum computing is derived. It has been noticed that this picture exhibits striking similarities with quantum critical condensates, allowing the use of a common language to describe quantum computing in both systems. The authors analyze such quantum computing by allowing coupling to external modes, under the condition that the external influence must be soft‐enough in order not to offset the basic properties of the system. Model‐independent bounds on some crucial time‐scales are derived, such as the times of gate operation, decoherence, maximal entanglement and total scrambling. For black hole type quantum computers all these time‐scales turn out to be of the order of the black hole half‐life time. Furthermore, a set of Hamiltonians is constructed that generates a universal set of quantum gates for the black hole type computer. These gates work at maximal energy efficiency. Furthermore, a fundamental bound on the complexity of quantum circuits encoded on these systems is established. It becomes apparent that the computational power is very limited due to the fact that the black hole life‐time is of the same order of the gate operation time. As a consequence, it is impossible to retrieve its information, within the life‐time of a black hole, by externally coupling to the black hole qubits. However it is shown, that in principle coupling to some of the internal degrees of freedom allows acquiring knowledge about the micro‐state.
In this work, we introduce classical holographic codes. These can be understood as concatenated probabilistic codes and can be represented as networks uniformly covering hyperbolic space. In ...particular, classical holographic codes can be interpreted as maps from bulk degrees of freedom to boundary degrees of freedom. Interestingly, they are shown to exhibit features similar to those expected from the AdS/CFT correspondence. Among these are a version of the Ryu-Takayanagi formula and intriguing properties regarding bulk reconstruction and boundary representations of bulk operations. We discuss the relation of our findings with expectations from AdS/CFT and, in particular, with recent results from quantum error correction.
We study the entanglement of families of Unruh modes in the Bell states \(|\Phi^\pm\rangle =1/\sqrt{2}(|00\rangle\pm|11\rangle)\) and \(|\Psi^\pm\rangle=1/\sqrt{2}(|01\rangle\pm|10\rangle)\) shared ...by two accelerated observers and find fundamental differences in the robustness of entanglement against acceleration for these states. States \(\Psi^\pm\) are entangled for all finite accelerations, whereas, due to the Unruh effect, states \(\Phi^\pm\) lose their entanglement for finite accelerations. This is true for Bell states of two bosonic modes, as well as for Bell states of a bosonic and a fermionic mode. Furthermore, there are also differences in the degradation of entanglement for Bell states of fermionic modes. We reveal the origin of these distinct characteristics of entanglement degradation and discuss the role that is played by particle statistics. Our studies suggest that the behavior of entanglement in accelerated frames strongly depends on the occupation patterns of the constituent states, whose superposition constitutes the entangled state, where especially states \(\Phi^\pm\) and \(\Psi^\pm\) exhibit distinct characteristics regarding entanglement degradation. Finally, we point out possible implications of hovering over a black hole for these states.
We study the collective dynamics of accelerated atoms interacting with a massless field via an Unruh-deWitt-type interaction. We first derive a general Hamiltonian describing such a system and then, ...employing a Markovian master equation, we study the corresponding collective dynamics. In particular, we observe that the emergence of entanglement between two-level atoms is linked to the building up of coherences between them and to superradiant emission. In addition, we show that the derived Hamiltonian can be experimentally implemented by employing impurities in Bose-Einstein condensates.
We study the effects of acceleration on fermionic Gaussian states of localized modes of a Dirac field. We consider two wave-packets in a Gaussian state and transform these to an accelerated frame of ...reference. In particular, we formulate the action of this transformation as a fermionic quantum channel. Having developed the general framework for fermions, we then investigate the entanglement of the vacuum, as well as the entanglement in Bell states. We find that with increasing acceleration vacuum entanglement increases, while the entanglement of Bell states decreases. Notably, our results have an immediate operational meaning given the localization of the modes.
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