We describe an efficient DQC1 (deterministic quantum computation with one quantum qubit) algorithm to quantify the amount of geometric quantum discord present in the output state of a DQC1 computation. DQC1 is a model of computation that utilizes separable states to solve a problem with no known efficient classical algorithm and is known to contain quantum correlations as measured by the discord. For the general case of a $(1+n)$ -qubit DQC1 state we provide an analytical expression for the geometric quantum discord and find that its typical (and maximum) value decreases exponentially with $n$ . This is in contrast to the standard quantum discord whose value for typical DQC1 states is known to be independent of $n$ . We experimentally demonstrate the proposed algorithm on a four-qubit liquid-state nuclear magnetic resonance quantum information processor. In the special case of a two-qubit DQC1 model, we also provide an expression for the quantum discord that only requires the outcome of the DQC1 algorithm.We describe an efficient DQC1 (deterministic quantum computation with one quantum qubit) algorithm to quantify the amount of geometric quantum discord present in the output state of a DQC1 computation. DQC1 is a model of computation that utilizes separable states to solve a problem with no known efficient classical algorithm and is known to contain quantum correlations as measured by the discord. For the general case of a $(1+n)$-qubit DQC1 state we provide an analytical expression for the geometric quantum discord and find that its typical (and maximum) value decreases exponentially with $n$. This is in contrast to the standard quantum discord whose value for typical DQC1 states is known to be independent of $n$. We experimentally demonstrate the proposed algorithm on a four-qubit liquid-state nuclear magnetic resonance quantum information processor. In the special case of a two-qubit DQC1 model, we also provide an expression for the quantum discord that only requires the outcome of the DQC1 algorithm.

arXiv:1202.4475Physical Review AMar 19, 201240 citations

Geometric quantum discord with Bures distance: the qubit case

Dominique Spehner, M Orszag

The minimal Bures distance of a quantum state of a bipartite system AB to the set of classical states for subsystem A defines a geometric measure of quantum discord. When A is a qubit, we show that this geometric quantum discord is given in terms of the eigenvalues of a (2 n B ) × (2 n B ) Hermitian matrix, n B being the Hilbert space dimension of the other subsystem B . As a first application, we calculate the geometric discord for the output state of the DQC1 algorithm. We find that it takes its highest value when the unitary matrix from which the algorithm computes the trace has its eigenvalues uniformly distributed on the unit circle modulo a symmetry with respect to the origin. As a second application, we derive an explicit formula for the geometric discord of a two-qubit state ρ with maximally mixed marginals and compare it with other measures of quantum correlations. We also determine the closest classical states to ρ.The minimal Bures distance of a quantum state of a bipartite system AB to the set of classical states for subsystem A defines a geometric measure of quantum discord. When A is a qubit, we show that this geometric quantum discord is given in terms of the eigenvalues of a (2 n B ) × (2 n B ) Hermitian matrix, n B being the Hilbert space dimension of the other subsystem B . As a first application, we calculate the geometric discord for the output state of the DQC1 algorithm. We find that it takes its highest value when the unitary matrix from which the algorithm computes the trace has its eigenvalues uniformly distributed on the unit circle modulo a symmetry with respect to the origin. As a second application, we derive an explicit formula for the geometric discord of a two-qubit state ρ with maximally mixed marginals and compare it with other measures of quantum correlations. We also determine the closest classical states to ρ.

arXiv:1308.5005Journal of Physics A Mathematical and TheoreticalDec 20, 201353 citations

Experimental investigation of quantum discord in DQC1

Tingwei Li, Yang Wu, Fangzhou Jin +1 more

Quantum discord has been proposed as a resource responsible for the exponential speedup in deterministic quantum computation with one pure qubit (DQC1). Investigation of the quantum discord generated in DQC1 is of significant importance from a fundamental perspective. However, in practical applications of DQC1, qubits generally interact with the environment. Thus, it is also important to investigate the discord when DQC1 is implemented in a noisy environment. We implement DQC1 on an electron spin resonance (ESR) architecture in such an environment and nonzero quantum discord is observed. Furthermore, we find that the values of discord correspond to the values of purity α and quantum Fisher information, which reflect the power of the algorithm. Our results provide further evidence for the role of discord as a resource in DQC1 and are beneficial for understanding the origin of the power of quantum algorithms.Quantum discord has been proposed as a resource responsible for the exponential speedup in deterministic quantum computation with one pure qubit (DQC1). Investigation of the quantum discord generated in DQC1 is of significant importance from a fundamental perspective. However, in practical applications of DQC1, qubits generally interact with the environment. Thus, it is also important to investigate the discord when DQC1 is implemented in a noisy environment. We implement DQC1 on an electron spin resonance (ESR) architecture in such an environment and nonzero quantum discord is observed. Furthermore, we find that the values of discord correspond to the values of purity α and quantum Fisher information, which reflect the power of the algorithm. Our results provide further evidence for the role of discord as a resource in DQC1 and are beneficial for understanding the origin of the power of quantum algorithms.

JUSTCJan 1, 20221 citation

(1+n)

-qubit DQC1 state we provide an analytical expression for the geometric quantum discord and find that its typical (and maximum) value decreases exponentially with

n

. This is in contrast to the standard quantum discord whose value for typical DQC1 states is known to be independent of

n

. We experimentally demonstrate the proposed algorithm on a four-qubit liquid-state nuclear magnetic resonance quantum information processor. In the special case of a two-qubit DQC1 model, we also provide an expression for the quantum discord that only requires the outcome of the DQC1 algorithm.