Optimal two-particle entanglement by universal quantum processes

G Alber; A Delgado; I Jex

doi:10.26421/qic1.3-3

Optimal two-particle entanglement by universal quantum processes

Quantum Information and Computation ◽

10.26421/qic1.3-3 ◽

2001 ◽

Vol 1 (3) ◽

pp. 33-51

Author(s):

G Alber ◽

A Delgado ◽

I Jex

Keyword(s):

Hilbert Spaces ◽

Parameter Family ◽

Entanglement Measure ◽

Input State ◽

Quantum Processes ◽

Single Exception ◽

Universal Quantum

Within the class of all possible universal (covariant) two-particle quantum processes in arbitrary dimensional Hilbert spaces those universal quantum processes are determined whose output states optimize the recently proposed entanglement measure of Vidal and Werner. It is demonstrated that these optimal entanglement processes belong to a one-parameter family of universal entanglement processes whose output states do not contain any separable components. It is shown that these optimal universal entanglement processes generate antisymmetric output states and, with the single exception of qubit systems, they preserve information about the initial input state.

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Privacy in Quantum Estimation

Proceedings ◽

10.3390/proceedings2019012013 ◽

2019 ◽

Vol 12 (1) ◽

pp. 13

Author(s):

Milajiguli Rexiti ◽

Stefano Mancini

Keyword(s):

Mean Square Error ◽

Parameter Family ◽

Input State ◽

Mean Square ◽

The Mean ◽

Fixed Input

We introduce the notion of privacy in quantum estimation by considering an one-parameter family of isometries taking one input into two output systems. It stems on the separate and adversarial control of the two output systems as well as on the local minimization of the mean square error. Applications to two-qubit unitaries (with one qubit in a fixed input state) are presented.

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COMPLEMENTARITY OF ENTANGLEMENT AND INTERFERENCE

International Journal of Modern Physics C ◽

10.1142/s0129183106008716 ◽

2006 ◽

Vol 17 (04) ◽

pp. 493-509 ◽

Cited By ~ 4

Author(s):

A. HOSOYA ◽

A. CARLINI ◽

S. OKANO

Keyword(s):

Quantum Computation ◽

Entanglement Measure ◽

Input State ◽

Quantum Operation ◽

Bipartite Entanglement

A complementarity relation is shown between the visibility of interference and bipartite entanglement in a two qubit interferometric system when the parameters of the quantum operation change for a given input state. The entanglement measure is a decreasing function of the visibility of interference. The implications for quantum computation are briefly discussed.

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Thermodynamic Implementations of Quantum Processes

Communications in Mathematical Physics ◽

10.1007/s00220-021-04107-w ◽

2021 ◽

Author(s):

Philippe Faist ◽

Mario Berta ◽

Fernando G. S. L. Brandao

Keyword(s):

Relative Entropy ◽

Thermal State ◽

Single Letter ◽

Small Scale ◽

Input State ◽

Quantum Channels ◽

Quantum Processes ◽

Cost Rate ◽

Fixed Input

AbstractRecent understanding of the thermodynamics of small-scale systems have enabled the characterization of the thermodynamic requirements of implementing quantum processes for fixed input states. Here, we extend these results to construct optimal universal implementations of a given process, that is, implementations that are accurate for any possible input state even after many independent and identically distributed (i.i.d.) repetitions of the process. We find that the optimal work cost rate of such an implementation is given by the thermodynamic capacity of the process, which is a single-letter and additive quantity defined as the maximal difference in relative entropy to the thermal state between the input and the output of the channel. Beyond being a thermodynamic analogue of the reverse Shannon theorem for quantum channels, our results introduce a new notion of quantum typicality and present a thermodynamic application of convex-split methods.

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Experimental demonstration of entanglement-enabled universal quantum cloning in a circuit

npj Quantum Information ◽

10.1038/s41534-021-00375-5 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Zhen-Biao Yang ◽

Pei-Rong Han ◽

Xin-Jie Huang ◽

Wen Ning ◽

Hekang Li ◽

...

Keyword(s):

Quantum Information Processing ◽

Input State ◽

Experimental Demonstration ◽

Quantum Cloning ◽

Fundamental Interest ◽

Classical Counterpart ◽

Superconducting Circuit ◽

Unknown Quantum State ◽

Universal Quantum ◽

Quantum Behavior

AbstractNo-cloning theorem forbids perfect cloning of an unknown quantum state. A universal quantum cloning machine (UQCM), capable of producing two copies of any input qubit with the optimal fidelity, is of fundamental interest and has applications in quantum information processing. This is enabled by delicately tailored nonclassical correlations between the input qubit and the copying qubits, which distinguish the UQCM from a classical counterpart, but whose experimental demonstrations are still lacking. We here implement the UQCM in a superconducting circuit and investigate these correlations. The measured entanglements well agree with our theoretical prediction that they are independent of the input state and thus constitute a universal quantum behavior of the UQCM that was not previously revealed. Another feature of our experiment is the realization of deterministic and individual cloning, in contrast to previously demonstrated UQCMs, which either were probabilistic or did not constitute true cloning of individual qubits.

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Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics

Quantum ◽

10.22331/q-2019-12-02-206 ◽

2019 ◽

Vol 3 ◽

pp. 206 ◽

Cited By ~ 8

Author(s):

Ognyan Oreshkov

Keyword(s):

Quantum Mechanics ◽

Hilbert Spaces ◽

Coherent Control ◽

Causal Structure ◽

Physical Realization ◽

Causal Order ◽

Quantum Processes ◽

Standard Quantum ◽

Novel Structure ◽

The Times

It has been shown that it is theoretically possible for there to exist higher-order quantum processes in which the operations performed by separate parties cannot be ascribed a definite causal order. Some of these processes are believed to have a physical realization in standard quantum mechanics via coherent control of the times of the operations. A prominent example is the quantum SWITCH, which was recently demonstrated experimentally. However, the interpretation of such experiments as realizations of a process with indefinite causal structure as opposed to some form of simulation of such a process has remained controversial. Where exactly are the local operations of the parties in such an experiment? On what spaces do they act given that their times are indefinite? Can we probe them directly rather than assume what they ought to be based on heuristic considerations? How can we reconcile the claim that these operations really take place, each once as required, with the fact that the structure of the presumed process implies that they cannot be part of any acyclic circuit? Here, I offer a precise answer to these questions: the input and output systems of the operations in such a process are generally nontrivial subsystems of Hilbert spaces that are tensor products of Hilbert spaces associated with systems at different times---a fact that is directly experimentally verifiable. With respect to these time-delocalized subsystems, the structure of the process is one of a circuit with a causal cycle. This provides a rigorous sense in which processes with indefinite causal structure can be said to exist within the known quantum mechanics. I also identify a whole class of isometric processes, of which the quantum SWITCH is a special case, that admit a physical realization on time-delocalized subsystems. These results unveil a novel structure within quantum mechanics, which may have important implications for physics and information processing.

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Implementation of leakage elimination operators and subspace protection

Scientific Reports ◽

10.1038/s41598-020-75730-1 ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

B. G. Markaida ◽

L.-A. Wu

Keyword(s):

Hilbert Space ◽

Hilbert Spaces ◽

Quantum Computer ◽

Decoupling Control ◽

Dynamical Decoupling ◽

Experimental Implementation ◽

Universal Quantum ◽

Logical Qubits ◽

First Time ◽

Correction Strategies

Abstract Decoherence-induced leakage errors can potentially damage physical or logical qubits embedded in a subspace of the entire Hilbert space by coupling them to other system levels. Here we report the first experimental implementation of Leakage Elimination Operators (LEOs) that aims to reduce this undermining. LEOs are a type of dynamical decoupling control that have been previously introduced to counteract leakage from a chosen subspace into the rest of a Hilbert space, and have been widely explored theoretically. Different from other error correction strategies, LEOs are compatible with any gate sequence in a code space, and thus, compatible with universal quantum computation. Using IBM’s cloud quantum computer (QC), we design three potentially applicable examples of subspaces in two- and three-qubit Hilbert spaces and derive the explicit forms of the corresponding LEOs for these subspaces. For the first time, we experimentally demonstrate that these LEOs significantly suppress leakage. The results also show that the LEO time-scale condition can be satisfied with noise in the IBM’s cloud QC and pave a way for quantum setups to get rid of leakage trouble.

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Classical simulation complexity of extended Clifford circuits

Quantum Information and Computation ◽

10.26421/qic14.7-8-7 ◽

2014 ◽

Vol 14 (7&8) ◽

pp. 633-648

Author(s):

Richard Jozsa ◽

Marrten Van den Nest

Keyword(s):

Quantum Computing ◽

Physical Significance ◽

Quantum Circuits ◽

Quantum Processes ◽

Computing Power ◽

Quantum Operations ◽

Classical Simulation ◽

Universal Quantum ◽

General Product ◽

Computational Basis

Clifford gates are a winsome class of quantum operations combining mathematical elegance with physical significance. The Gottesman-Knill theorem asserts that Clifford computations can be classically efficiently simulated but this is true only in a suitably restricted setting. Here we consider Clifford computations with a variety of additional ingredients: (a) strong vs. weak simulation, (b) inputs being computational basis states vs. general product states, (c) adaptive vs. non-adaptive choices of gates for circuits involving intermediate measurements, (d) single line outputs vs. multi-line outputs. We consider the classical simulation complexity of all combinations of these ingredients and show that many are not classically efficiently simulatable (subject to common complexity assumptions such as P not equal to NP). Our results reveal a surprising proximity of classical to quantum computing power viz. a class of classically simulatable quantum circuits which yields universal quantum computation if extended by a purely classical additional ingredient that does not extend the class of quantum processes occurring.

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