Creating the Quantum

David Finkelstein

Mohammed J. Mohammed, Mezher B. Saleh, Ismaeel Al-Baidhany

Abstract One of the most important aspects of quantum computation is quantum entanglement, it is an interesting feature of quantum physics, and has many important applications such as quantum teleportation, cryptography, quantum computation, and dense coding. It is an essential task in quantum computing to design circuits that create an entangled system, and many circuits were implied in the quantum computers that generate the desired entangled state of a system. In this paper, we suggest a general method to design different quantum circuits that produce an entangled system for any number of qubits in different manners. Also, we apply the suggested method in order to design different 4-qubits entanglement creating circuits. The results show that it is possible to design different entanglement creating circuits for any number of qubits by following certain method that will be discussed in the paper, and in the case of 4-qubits system we are going to look only at two circuits, the first creates a “GHZ” like state and the second creates a four-basis entanglement state.

Avijit Misra, Uttam Singh, Samyadeb Bhattacharya +1 more

We consider physical situations where the resource theories of coherence and thermodynamics play competing roles. In particular, we study the creation of quantum coherence using unitary operations with limited thermodynamic resources. We find the maximal coherence that can be created under unitary operations starting from a thermal state and find explicitly the unitary transformation that creates the maximal coherence. Since coherence is created by unitary operations starting from a thermal state, it requires some amount of energy. This motivates us to explore the trade-off between the amount of coherence that can be created and the energy cost of the unitary process. We also find the maximal achievable coherence under the constraint on the available energy. Additionally, we compare the maximal coherence and the maximal total correlation that can be created under unitary transformations with the same available energy at our disposal. We find that when maximal coherence is created with limited energy, the total correlation created in the process is upper bounded by the maximal coherence, and vice versa. For two-qubit systems we show that no unitary transformation exists that creates the maximal coherence and maximal total correlation simultaneously with a limited energy cost.

Xueyuan Hu, Heng Fan, D. L. Zhou +1 more

We prove the condition for local trace-preserving channels to create quantum correlation from initially classical states. For two-qubit states, the necessary and sufficient condition for a channel that cannot create quantum correlation in any initially classical state is that it is either a completely decohering channel or a mixing channel. For states in higher dimensions, we show that even a mixing channel can create quantum correlation from a classically correlated state. Our results reveal that mixedness is important for creation of quantum correlation in high-dimension quantum systems.

Alexa Keating